# Dual Quaternion Control of UAVs with Cable-suspended Load

Yuxia Yuan1 and Markus Ryll2 1Yuxia Yuan is with Autonomous Aerial Systems,
School of Engineering and Design, Technical University of Munich, Lise-
Meitner-Straße 9, 85521 Ottobrunn, Germany
yuxia.yuan<EMAIL_ADDRESS>Ryll is with Munich Institute
of Robotics and Machine Intelligence (MIRMI) and Autonomous Aerial Systems,
School of Engineering and Design, Technical University of Munich, Lise-
Meitner-Straße 9, 85521 Ottobrunn, Germany<EMAIL_ADDRESS>
###### Abstract

Modeling the kinematics and dynamics of robotics systems with suspended loads
using dual quaternions has not been explored so far. This paper introduces a
new innovative control strategy using dual quaternions for UAVs with cable-
suspended loads, focusing on the sling load lifting and tracking problems. By
utilizing the mathematical efficiency and compactness of dual quaternions, a
unified representation of the UAV and its suspended load’s dynamics and
kinematics is achieved, facilitating the realization of load lifting and
trajectory tracking. The simulation results have tested the proposed
strategy’s accuracy, efficiency, and robustness. This study makes a
substantial contribution to present this novel control strategy that harnesses
the benefits of dual quaternions for cargo UAVs. Our work also holds promise
for inspiring future innovations in under-actuated systems control using dual
quaternions.

##  I Introduction

In recent years, interest in using aerial robots, commonly known as unmanned
aerial vehicles (UAVs), across diverse applications has experienced fast
growth. The multifaceted capabilities of UAVs—vertical takeoff and landing,
hovering with directional changes, and lateral and altitude adjustments—have
opened an extensive array of applications, including surveillance,
photography, rescue missions, cargo delivery, and so on [1, 2]. Notably, the
realm of cargo transportation has gained substantial popularity, evidenced by
major online retailers like Amazon, Google, DHL, and Walmart announcing the
incorporation of UAVs into their parcel delivery operations [1]. Utilizing a
cable to connect a UAV and its load is efficient and cost-effective, but it
introduces greater control challenges for UAVs due to the potential swinging
of the cargo, which can impact UAV dynamics [3]. Consequently, a crucial
aspect of UAV transportation control is to limit the swing and oscillations of
the load suspended beneath the UAV. In this paper, we use the term ”cargo UAV”
to denote a UAV with a cable-suspended load beneath it.

Controlling UAVs poses challenges due to the nonlinearity of their dynamics
and the under-actuation. A UAV’s control typically involves managing attitude
and altitude through four thrust inputs. Researchers have made several efforts
in developing control systems, such as proportional-derivative controllers,
linear quadratic regulators (LQR), and nonlinear controllers [4]. Among these,
a geometric controller proposed in [5] stands out. It expressed UAV dynamics
globally on the configuration manifold of the special Euclidean group $SE(3)$.
Compared to other geometric control approaches, it performed well in
controlling an underactuated UAV. The reseachers then further extended their
work on a cargo UAV system, defined on the configuration space $SE(3)\times
S2$ [6]. This geometric controller was then widely applied to cargo UAV
control [3, 7, 8]. For example, the authors proposed a hybrid model in [7] to
lift a cable-suspended load based on this geometric controller. They
decomposed the lifting maneuver into three modes in this study: Setup, Pull,
and Raise to formulate the dynamics of the cargo UAV system separately.

Further explorations into cargo UAV systems include LQR control algorithm [9],
decoupling of cargo UAV dynamics in longitudinal and lateral planes [10], and
a fixed-time control approach to enhance system robustness considering
external disturbances [11]. Additionally, researchers also trained neural
networks for cargo UAV control, as demonstrated in [12], where a convolutional
neural network was used to estimate the position and orientation of the load.

Figure 1: Dual quaternion transformations among three frames. $R_{I}$ is the
inertial frame, $\hat{\mathit{q}}_{v}$ denotes the transformation from $R_{I}$
to $R_{v}$ frame, and $\hat{\mathit{q}}_{l}$ is the transformation from
$R_{I}$ to $R_{l}$. $\hat{\mathit{q}}_{v}^{l}$ indicates the transformation
from $R_{l}$ to $R_{v}$.

This paper introduces a novel control strategy for cable-suspended UAVs using
dual quaternions to enhance the efficiency and compactness of sling load
lifting and trajectory tracking. Dual quaternion transformations between
different frames are shown in Fig. 1, which provides a mathematical framework
that allows us to represent both the dynamics and kinematics of the UAV and
its sling load in a unified representation. Dual quaternions can be seen as an
extension of unit quaternions to represent the position and orientation of a
rigid body [13]. They provide several advantages compared to homogeneous
transformation matrices [14, 5] for the representation of pose transformation,
such as higher computational efficiency, mathematical compactness, lack of
singularities, and optimal rigid transformation blending. These features of
dual quaternions have been used for the description of rigid-body kinematic
models like the pose following control law in [15], and the modeling of
kinematics and dynamics of systems like UAVs [16, 17]. The authors of [16]
provided a trajectory tracking controller based on unit dual quaternions for a
rigid body, where the error dynamics were described by a unit dual quaternion.
[17] adopted a similar approach for quadrotor aerial manipulator control. The
manipulator in their work also modeled an external load for the quadrotor,
despite being connected using rigid links rather than a flexible cable.

To the best of the authors’ knowledge, modeling the dynamics of UAVs with
cable-suspended loads using dual quaternions has not been addressed in the
literature so far. To explore and meet this research gap, this paper provides
a novel control strategy to control cargo UAVs using dual quaternions. The
cargo UAV system can be treated as two subsystems, the UAV and the sling-load,
involving three orientation frames (the inertial frame, the sling-load frame,
and the UAV frame).

The main contributions of this study are twofold: First, we formulate the
dynamic model for under-actuated cargo UAV systems using dual quaternions,
which facilitates the analysis of the translational and rotational dynamics of
a UAV with a sling load. Second, we develop a novel control strategy for UAVs
with cable-suspended load to track a desired trajectory. The development of
this controller is inspired by the unit dual quaternion tracker [16] and
geometric control [6]. Finally, we tested our approach using two sets of
simulations. The first one shows that our developed controller performs well
for load lifting and trajectory tracking maneuvers. The second simulation
evaluates the efficiency and robustness of our control strategy by considering
system uncertainties and external disturbances and comparing it with the
geometric controller. Our work not only addresses the technical challenges
associated with cargo UAV control, but also opens up avenues for further
innovation in the realm of cargo UAV control using dual quaternions.

The rest of this paper is structured as follows. Sec. II outlines the
assumptions for the cargo UAV systems and introduces the mathematical basis of
dual quaternions. The dynamic models of the cargo UAV system considering the
cable state are presented in Sec. III. Then, the control strategies to address
lifting and tracking problems are stated in Sec. IV, along with the
decomposition of the lifting maneuver into three modes. In Sec. V, the system
setup and the simulation results are discussed. Finally, Sec. VI concludes our
work.

##  II Assumptions and Preliminary Knowledge

###  II-A Assumptions and Notations

The cargo UAV studied in our work consists of a UAV and a sling load. It can
be considered as two subsystems and each of them is a rigid body, which
involves three orientation frames, as shown in Fig. 1. The load is physically
attached to the UAV by a cable. Modeling all internal and external forces can
quickly become very complex. For this study, we made the following
simplifications and assumptions:

  1. 1.

We ignore elastic deformations of the rope, the UAV, and the load.

  2. 2.

The load is considered as a point mass.

  3. 3.

The cable is mass-free, and only forces and no torques are transmitted via the
cable.

  4. 4.

The offset between the attached point of the load with the CoM of the UAV is
considered as zero.

  5. 5.

The air drag and other disturbances are ignored.

Before going further, the following notation rules are adopted:

$\begin{array}[]{ll}{}_{v},_{l},_{c}&\text{Subscripts indicate UAVs, loads,
and cables.}\\\ {}^{d}&\text{Superscript $d$ represents the desired
states.}\\\ {}^{b}&\text{Superscripts $b$ indicate the body frame.}\\\
\mathit{q},\hat{\mathit{q}}\in\mathbb{H}&\text{Quaternions and dual
quaternions.}\\\ \mathbf{v}\in\mathbb{R}^{3}&\text{Vectors (vector
quaternions).}\\\ \hat{\mathbf{v}}\in\mathbb{H}&\text{Dual vector
quaternions.}\\\ \mathit{I},\mathit{0}\in\mathbb{H}&\text{Unit quaternion
$[1,0,0,0]$ and zero quaternion.}\\\ \mathbf{0}\in\mathbb{H}&\text{Zero vector
quaternion.}\end{array}$

###  II-B Dual Quaternion

As described in [13], the components of a dual quaternion are both quaternions
belonging to $\mathbb{H}$, which is represented as
$\hat{\mathit{q}}=q_{r}+q_{d}\epsilon,q_{r},q_{d}\in\mathbb{H}$. The involved
operations for dual quaternions are listed below:

  * •

Sum:
$\hat{\mathit{q}}_{1}+\hat{\mathit{q}}_{2}=q_{1r}+q_{2r}+[q_{1d}+q_{2d}]\epsilon$

  * •

Product: $\hat{\mathit{q}}_{1}\otimes\hat{\mathit{q}}_{2}=q_{1r}\otimes
q_{2r}+[q_{1r}\otimes q_{2d}+q_{1d}\otimes q_{2r}]\epsilon$

  * •

Conjugate: $\hat{\mathit{q}}^{*}=q_{r}^{*}+q_{d}^{*}\epsilon$

  * •

Norm for unit dual quaternions: $||\hat{\mathit{q}}||^{2}=1+0\epsilon$

  * •

Inverse for unit dual quaternions:
$\hat{\mathit{q}}^{-1}=\hat{\mathit{q}}^{*}$.

  * •

Natural logarithm mapping:
$\ln\hat{\mathit{q}}=\frac{1}{2}(\overline{\theta}+T\epsilon)$;
$\overline{\theta}$ is the rotation angle vector.

  * •

Adjoint transformation:
$Ad_{\hat{\mathit{q}}}\hat{\mathit{r}}=\hat{\mathit{q}}\otimes\hat{\mathit{r}}\otimes\hat{\mathit{q}}^{*}$

  * •

Dual vector quaternion:
$\hat{\mathbf{v}}=\mathbf{v}_{r}+\mathbf{v}_{d}\epsilon$. $\hat{\mathbf{v}}$
can be treated as
$\hat{\mathit{v}}=[0,\mathbf{v}_{r}]+[0,\mathbf{v}_{d}]\epsilon$.

###  II-C Dual Quaternion Dynamic Model

Using the Newton-Euler approach, the rotational dynamics of a rigid body can
be expressed as

$J\dot{\mathbf{\omega}}^{b}+\mathbf{\omega}^{b}\times(J\mathbf{\omega}^{b})=\mathbf{\tau}$
(1)

where $J\in\mathbb{R}^{3\times 3}$ is the inertia matrix of the body, and
$\mathbf{\tau}\in\mathbb{R}^{3}$ is the sum of the control input torques and
the external torques. Similarly, the translational dynamics relative to its
body frame is given by

$m\ddot{\mathbf{T}}^{b}=\mathbf{F}$ (2)

where $m\in\mathbb{R}$ is the mass and $\mathbf{F}\in\mathbb{R}^{3}$ is the
sum of the control input forces and external forces (e.g., gravity) in the
body frame.

The kinematics of a rigid body in terms of its orientation, position, and
twist is given in [16] by

$\displaystyle\dot{\hat{\mathit{q}}}=\frac{1}{2}\hat{\mathit{q}}\otimes\hat{\mathit{\xi}}^{b}$
(3)
$\displaystyle\hat{\mathit{\xi}}^{b}=\mathbf{\omega}^{b}+[\mathbf{\omega}^{b}\times\mathbf{T}^{b}+\dot{\mathbf{T}}^{b}]\epsilon$
(4)

where $\hat{\mathit{\xi}}^{b}$ is the twist, which is a dual quaternion
combining rotational velocity $\mathbf{\omega}^{b}$ and translational velocity
$\dot{\mathbf{T}}^{b}$. Then the dual quaternion dynamic model of a rigid body
is given by Eq (5). For details, readers can refer to [16].

$x=\left[\begin{array}[]{c}\hat{\mathit{q}}\\\
\hat{\mathit{\xi}}^{b}\end{array}\right],~{}~{}\dot{x}=\left[\begin{array}[]{c}\dot{\hat{\mathit{q}}}\\\
\dot{\hat{\mathit{\xi}}}^{b}\end{array}\right]=\left[\begin{array}[]{c}\frac{1}{2}\hat{\mathit{q}}\otimes\hat{\mathit{\xi}}^{b}\\\
\hat{\mathit{F}}+\hat{\mathit{u}}\end{array}\right]$ (5)

with

$\begin{cases}\hat{\mathit{F}}=a+[a\times\mathbf{T}^{b}+\mathbf{\omega}^{b}\times\dot{\mathbf{T}}^{b}]\epsilon\\\
\hat{\mathit{u}}=J^{-1}\mathbf{\tau}+[J^{-1}\mathbf{\tau}\times\mathbf{T}^{b}+m^{-1}\mathbf{F}]\epsilon\\\
a=-J^{-1}\mathbf{\omega}^{b}\times J\mathbf{\omega}^{b}\end{cases}.$

###  II-D Dual Quaternion Error Dynamics

Given the desired configuration $\hat{\mathit{q}}^{d}$, and the twist
$\hat{\mathit{\xi}}^{d}$, the errors can be found as

$\displaystyle\hat{\mathit{q}}_{e}=\hat{\mathit{q}}^{d*}\otimes\hat{\mathit{q}},$
(6)
$\displaystyle\hat{\mathit{\xi}}^{b}_{e}=\hat{\mathit{\xi}}^{b}-Ad_{\hat{\mathit{q}}_{e}^{*}}\hat{\mathit{\xi}}^{d}$
(7)

where $\hat{\mathit{q}}^{d*}$ is the conjugate of $\hat{\mathit{q}}^{d}$ and
$Ad_{\hat{\mathit{q}}_{e}^{*}}\hat{\mathit{\xi}}^{d}$ is adjoint
transformation. For calculation details, readers are referred to [16].

By taking the derivative of $\hat{\mathit{\xi}}^{b}_{e}$, we get

$\dot{\hat{\mathit{\xi}}}^{b}_{e}=\dot{\hat{\mathit{\xi}}}^{b}-E_{\hat{\mathit{q}}_{e}^{*}}\hat{\mathit{\xi}}^{d}$
(8)

with
$E_{\hat{\mathit{q}}_{e}^{*}}\hat{\mathit{\xi}}^{d}=\dot{\hat{\mathit{q}}}_{e}^{*}\otimes\hat{\mathit{\xi}}^{d}\otimes\hat{\mathit{q}}_{e}+Ad_{\hat{\mathit{q}}_{e}^{*}}\dot{\hat{\mathit{\xi}}}^{d}+\hat{\mathit{q}}_{e}^{*}\otimes\hat{\mathit{\xi}}^{d}\otimes\dot{\hat{\mathit{q}}}_{e}$.

From Eq. (5), we have

$\dot{\hat{\mathit{\xi}}}^{b}_{e}=\hat{\mathit{F}}+\hat{\mathit{u}}-E_{\hat{\mathit{q}}_{e}^{*}}\hat{\mathit{\xi}}^{d}.$
(9)

##  III The Cargo UAV System

The cargo UAV system contains a sling load attached to the CoM of the UAV,
which can be separated into two subsystems, the sling-load and the UAV, to
study its dynamics. In the following, we develop cable state-dependent
scenarios to derive the complete model.

###  III-A Dual Vector Quaternion of the Dynamics of the Sling-load

In our research, the sling load is attached to the UAV by a cable. We treat
the load and the cable as a sling-load subsystem. Though we assume the cable
is rigid, there is no torque transmitted by the cable to the load. The dual
vector quaternion $\hat{\mathbf{q}}$ is adopted to describe the configuration
of the sling load as

$\displaystyle\hat{\mathbf{q}}_{l}=\mathbf{q}_{c}+\mathbf{T}_{l}\epsilon$ (10)
$\displaystyle\hat{\mathbf{\xi}}_{l}=\dot{\hat{\mathbf{q}}}_{l}=\dot{\mathbf{q}}_{c}+\dot{\mathbf{T}}_{l}\epsilon,$
(11)

where $\mathbf{q}_{c}$ is the direction vector from the UAV to the load and
$\mathbf{T}_{l}$ is the position of the load in the initial frame.

###  III-B Dynamic Model with Slack Cable

When the cable is slack, the UAV and the sling load can be considered as two
separate subsystems. The kinematics and dynamics of the UAV can refer to the
rigid body model formulation in Sec. II-C. For the sling load subsystem it is
static on the ground or in free fall. The motion equations of the system are
as follows

$\displaystyle
J_{v}\dot{\mathbf{\omega}}^{b}_{v}+\mathbf{\omega}^{b}_{v}\times(J_{v}\mathbf{\omega}^{b}_{v})=\mathbf{\tau}_{v}$
(12) $\displaystyle m_{v}\ddot{\mathbf{T}}^{b}_{v}=\mathbf{F}_{v}$ (13)
$\displaystyle m_{l}\ddot{\mathbf{T}}_{l}=-m_{l}g\mathbf{e}_{3},$ (14)

Combining the dual quaternion dynamic model presented in Sec. II-C, the
dynamic model in this case is

$\displaystyle\dot{x}=$
$\displaystyle\left[\begin{array}[]{c}\dot{\hat{\mathit{q}}}_{v}\\\
\dot{\hat{\mathit{\xi}}}^{b}_{v}\\\ \dot{\hat{\mathit{q}}}_{l}\\\
\dot{\hat{\mathit{\xi}}}^{b}_{l}\end{array}\right]=\left[\begin{array}[]{c}\frac{1}{2}\hat{\mathit{q}}_{v}\otimes\hat{\mathit{\xi}}^{b}_{v}\\\
\hat{\mathit{F}}_{v}+\hat{\mathit{u}}_{v}\\\ \dot{\mathbf{T}}_{l}\epsilon\\\
-g\mathbf{e}_{3}\epsilon\end{array}\right]$ (23)

###  III-C Dynamic Model with Taut Cable

When the cable is taut, the conﬁguration of the system is deﬁned by the
position and attitude of the load with respect to the inertial frame, and the
UAV attitude. The position and velocity relationships between the UAV and the
load are expressed as

$\displaystyle\mathbf{T}_{v}=\mathbf{T}_{l}+l\mathbf{q}_{c}$ (24)
$\displaystyle\dot{\mathbf{T}}_{v}=\dot{\mathbf{T}}_{l}+l\dot{\mathbf{q}}_{c}$
(25)

where $\mathbf{T}_{v}$ and $\mathbf{T}_{l}$ are the positions of the UAV and
the load, and $l$ is the length of the cable between the UAV and the load.

The motion equations of the sling load are obtained from previous work [6, 8].
The motion equations of the cargo UAV system are

$\displaystyle
J_{v}\dot{\mathbf{\omega}}^{b}_{v}+\mathbf{\omega}^{b}_{v}\times(J_{v}\mathbf{\omega}^{b}_{v})=\mathbf{\tau}_{u}+\mathbf{\tau}_{\text{ext}}$
(26) $\displaystyle
m\ddot{\mathbf{T}}_{l}+m_{v}l(\dot{\mathbf{q}}_{c}\cdot\dot{\mathbf{q}}_{c})\mathbf{q}_{c}=(\mathbf{q}_{c}\cdot\mathbf{F}_{uI})\mathbf{q}_{c}+\mathbf{F}_{\text{ext}}$
(27) $\displaystyle
m_{v}l\ddot{\mathbf{q}}_{c}+m_{v}l(\dot{\mathbf{q}}_{c}\cdot\dot{\mathbf{q}}_{c})\mathbf{q}_{c}=\mathbf{q}_{c}\times\mathbf{q}_{c}\times\mathbf{F}_{uI},$
(28)

with $m=m_{v}+m_{l}$ as the sum of UAV’s mass $m_{v}$ and load’s mass $m_{l}$.
$\mathbf{F}_{uI}=\mathit{q}_{v}\otimes\mathbf{F}_{th}\otimes\mathit{q}_{v}^{*}$
is the expression of thrust vector $\mathbf{F}_{th}$ of the UAV in the initial
frame. The full dynamical model has then obtained according to Sec. II-C

$\displaystyle x=\left[\begin{array}[]{c}\hat{\mathbf{q}}_{l}\\\
\hat{\mathbf{\xi}}_{l}\\\
\hat{\mathit{\xi}}^{b}_{v}\end{array}\right],\dot{x}=\left[\begin{array}[]{c}\dot{\hat{\mathbf{q}}}_{l}\\\
\dot{\hat{\mathbf{\xi}}}_{l}\\\
\dot{\hat{\mathit{\xi}}}^{b}_{v}\end{array}\right]=\left[\begin{array}[]{c}\dot{\mathbf{q}}_{c}+\dot{\mathbf{T}}_{l}\epsilon\\\
\hat{\mathit{\mathbf{F}}}_{l}+\hat{\mathit{\mathbf{u}}}_{l}\\\
\hat{\mathit{F}}_{v}+\hat{\mathit{u}}_{v}\end{array}\right]$ (38)

with

$\displaystyle\hat{\mathit{u}}_{v}=J_{v}^{-1}\mathbf{\tau}_{u}+[J_{v}^{-1}\mathbf{\tau}_{u}\times\mathbf{T}_{v}^{b}+\ddot{\mathbf{T}}_{v}^{b}]\epsilon$
(39)
$\displaystyle\hat{\mathit{F}}_{v}=a_{v}+[a_{v}\times\mathbf{T}_{v}^{b}+\mathbf{\omega}^{b}_{v}\times\dot{\mathbf{T}}_{v}^{b}]\epsilon$
(40) $\displaystyle
a_{v}=J_{v}^{-1}(\mathbf{\tau}_{\text{ext}}-\mathbf{\omega}^{b}_{v}\times
J_{v}\mathbf{\omega}^{b}_{v})$ (41)
$\displaystyle\hat{\mathit{\mathbf{u}}}_{l}=\frac{\mathbf{q}_{c}\times\mathbf{q}_{c}\times\mathbf{F}_{uI}}{m_{v}l}+\frac{(\mathbf{q}_{c}\cdot\mathbf{F}_{uI})\mathbf{q}_{c}}{m}\epsilon$
(42)
$\displaystyle\hat{\mathit{\mathbf{F}}}_{l}=-(\dot{\mathbf{q}}_{c}\cdot\dot{\mathbf{q}}_{c})\mathbf{q}_{c}+[\frac{\mathbf{F}_{\text{ext}}-m_{v}l(\dot{\mathbf{q}}_{c}\cdot\dot{\mathbf{q}}_{c})\mathbf{q}_{c}}{m}]\epsilon.$
(43)

##  IV Control Design for Cargo UAV System

Figure 2: The lifting maneuver of the cargo UAV is separated into three modes:
Setup, Pull, and Raise.

###  IV-A Lifting Modes and Desired Motion States

The lifting maneuver is sketched in Fig. 2, which is broken into three modes:
Setup, Pull, and Raise. In this way, the dynamics of the cargo UAV system in
specific regimes during the maneuver can be characterized separately according
to the state of the cable. During the Setup and Pull modes, the makes
preparations to lift the load, and in the Raise mode, the load is finally
lifted off the ground.

Setup: As shown in Fig. 2, the UAV has to fly to the point above the load from
its initial position. During the process, the cable is slack, so the system
can be considered as two separate subsystems. The dynamics of the UAV and the
load are given in Sec. III-B, while the load remains static.

The UAV is expected to reach the point right above the load with the distance
between them as the cable length. Then, the desired configuration of the UAV
is given by $q_{v}^{d.s}$ and $\mathbf{T}_{v}^{d.s}$ in Table I.

The cargo UAV system turns to Pull mode when the distance between the UAV and
the load is equal to the cable length $l$, which means the cable is fully
extended. It can be expressed as $l=||\mathbf{T}_{v}-\mathbf{T}_{l}||$. To
avoid swinging when lifting the load, we also consider that the UAV should be
in a stable condition, which is measured by the errors
$(q_{ve},\hat{\mathit{\xi}}^{b}_{ve})$ converging to $(I,\hat{\mathbf{0}})$.

Pull: Even though the cable is not slack anymore after Setup mode, the force
on the cable is initially not sufficient to lift the load. Therefore, the load
is still static in dynamic model (38). We assume the cargo UAV turns into
Raise mode until $||\mathbf{T}_{v}-\mathbf{T}_{l}||=l$ and
$m_{v}g\leq||\mathbf{F}_{uI}||$, where $l$ is the cable length.

Raise: The UAV is ready to raise the sling load when
$l=||\mathbf{T}_{v}-\mathbf{T}_{l}||$. During this mode, the load is not
static anymore. The motion equations for the cargo UAV system are as well
coupled as described in Sec. III-C. From pulling until the end of raising, the
load is expected to reach a desired height, which is given by $H$ in Table I.
The corresponding desired states are given by $\mathbf{T}_{l}^{d.r}$ and
$\dot{\mathbf{T}}_{l}^{d.r}$.

###  IV-B Control Law for Slack Cable

When the cable is slack during Setup, the load remains static on the ground.
We just consider the control of the UAV. A control law coming from [15, 16] is
adopted to cancel the non-linearities of the UAV subsystem
$\hat{\mathit{\xi}}^{b}_{v}=\hat{\mathit{F}}_{v}+\hat{\mathit{u}}_{v}$, and
then we get

$\hat{\mathit{u}}_{v}=-2\hat{\mathbf{k}}_{pv}\ln\hat{\mathit{q}}_{ve}-\hat{\mathbf{k}}_{vv}\hat{\mathit{\xi}}^{b}_{ve}-\hat{\mathit{F}}_{v}+E_{\hat{\mathit{q}}_{ve}^{*}}\hat{\mathit{\xi}}_{v}^{d},$
(44)

where $\hat{\mathbf{k}}_{pv}=\mathbf{k}_{pvr}+\mathbf{k}_{pvd}\epsilon$ and
$\hat{\mathbf{k}}_{vv}=\mathbf{k}_{vvr}+\mathbf{k}_{vvd}\epsilon$ are control
gains. Both of them are dual vector quaternions.

Combining Eq. (23) and Eq. (44), we obtain the control commands for the UAV

$\displaystyle\mathbf{\tau}_{u}$
$\displaystyle=\mathbf{\tau}_{v}-\mathbf{\tau}_{\text{ext}}=-J_{v}(\mathbf{k}_{pvr}\overline{\mathbf{\theta}}_{ve}+\mathbf{k}_{vvr}\mathbf{\omega}^{b}_{ve}+a_{v})$
(45) $\displaystyle\mathbf{F}_{u}$
$\displaystyle=\mathbf{F}_{v}-\mathbf{F}_{\text{ext}}=-m_{v}[\mathbf{k}_{pvd}\mathbf{T}^{b}_{ve}+\mathbf{k}_{vvd}(\mathbf{\omega}^{b}_{ve}\times\mathbf{T}^{b}_{ve}$
(46)
$\displaystyle+\dot{\mathbf{T}}^{b}_{ve})+(a_{v}\times\mathbf{T}^{b}_{v}+\mathbf{\omega}^{b}_{v}\times\dot{\mathbf{T}}^{b}_{v})]-m_{v}\overline{g}.$

As the assumptions mentioned in Sec. II-A, we have the external torque
$\mathbf{\tau}_{\text{ext}}=0$, and the external force
$\mathbf{F}_{\text{ext}}=m_{v}\overline{g}$ with
$\overline{g}=\mathit{q}_{v}^{*}\otimes g\mathbf{e}_{3}\otimes\mathit{q}_{v}$
as the representation of the gravity in the body frame.

###  IV-C Control Law for Taut Cable

We aim to track a desired trajectory with the sling load while keeping the
desired yaw angle of the UAV. The position of the sling load is governed by
the control of the UAV and the direction vector of the cable. We define the
desired configuration and twist of the sling load as
$\hat{\mathbf{q}}_{l}^{d}=\mathbf{q}_{c}^{d}+\mathbf{T}_{l}^{d}\epsilon$ and
$\hat{\mathbf{\xi}}_{l}^{d}=\dot{\mathbf{q}}_{c}^{d}+\dot{\mathbf{T}}_{l}^{d}\epsilon$,
where $\mathbf{T}_{l}^{d}$ and $\dot{\mathbf{T}}_{l}^{d}$ are the desired
position and velocity of the load. $\mathbf{q}_{c}^{d}$ is the desired load
attitude. The desired yaw angle of the UAV is set as zero. From the dual
vector quaternion error dynamics of the sling load, we have the tracking
errors as

$\displaystyle\hat{\mathbf{q}}_{le}=\mathbf{q}_{ce}+\mathbf{T}_{le}\epsilon$
(47)
$\displaystyle\hat{\mathbf{\xi}}_{le}=\dot{\mathbf{q}}_{ce}+\dot{\mathbf{T}}_{le}\epsilon.$
(48)

where $\mathbf{T}_{le}$ and $\dot{\mathbf{T}}_{le}$ are the load position and
velocity errors. $\mathbf{q}_{ce}$ and $\dot{\mathbf{q}}_{ce}$ are the errors
of load attitude, which are expressed as

$\displaystyle\mathbf{q}_{ce}=$
$\displaystyle\mathbf{q}_{c}\times(\mathbf{q}_{c}\times\mathbf{q}_{c}^{d})$
(49) $\displaystyle\dot{\mathbf{q}}_{ce}=$
$\displaystyle\dot{\mathbf{q}}_{c}-(\mathbf{q}_{c}^{d}\times\dot{\mathbf{q}}_{c}^{d})\times\mathbf{q}_{c}.$
(50)

From the dynamic model (38), the control force $\mathbf{F}_{uI}$ has coupling
terms between the UAV’s attitude and the load’s position and attitude.
Meanwhile, we can see that the UAV’s attitude is determined by its desired yaw
angle and the load’s position and attitude. Therefore, a controller for the
load’s attitude and position is designed as Eq. (51), and a controller for the
UAV’s attitude is designed considering the dual quaternion error dynamics
described in II-D as Eq. (52).

$\displaystyle\hat{\mathbf{u}}_{l}$
$\displaystyle=-(\hat{\mathit{\mathbf{k}}}_{pl}\hat{\mathbf{q}}_{le}+\hat{\mathit{\mathbf{k}}}_{vl}\hat{\mathbf{\xi}}_{le}+\hat{\mathbf{F}}_{l})$
(51) $\displaystyle\mathbf{\tau}_{u}$
$\displaystyle=-J_{v}(\hat{\mathbf{k}}_{pv}\overline{\mathbf{\theta}}_{ve}+\hat{\mathbf{k}}_{vv}\mathbf{\omega}_{ve}+a_{v})$
(52)

where $\hat{\mathbf{k}}_{pl}=\mathbf{k}_{plr}+\mathbf{k}_{pld}\epsilon$,
$\hat{\mathbf{k}}_{vl}=\mathbf{k}_{vlr}+\mathbf{k}_{vld}\epsilon$,
$\mathbf{k}_{pv}$, and $\mathbf{k}_{vv}$ are control gains.

The desired attitude of the sling load is determined by the tracking errors
and the desired acceleration, which is calculated by

$\displaystyle\mathbf{q}_{c}^{d}=\frac{-\mathbf{k}_{pld}\mathbf{T}_{le}-\mathbf{k}_{vld}\dot{\mathbf{T}}_{le}+\ddot{\mathbf{T}}_{l}^{d}+g\mathbf{e}_{3}}{||-\mathbf{k}_{pld}\mathbf{T}_{le}-\mathbf{k}_{vld}\dot{\mathbf{T}}_{le}+\ddot{\mathbf{T}}_{l}^{d}+g\mathbf{e}_{3}||}$
(53)

Combining Eqs. (38), (51), and (53) we obtain that the desired control force
satisfies

$\displaystyle(\mathbf{q}_{c}\cdot\mathbf{F}_{uI})\mathbf{q}_{c}=-m(\mathbf{k}_{pld}\mathbf{T}_{le}+\mathbf{k}_{vld}\dot{\mathbf{T}}_{le}+\hat{\mathbf{F}}_{l}^{d})$
(54)
$\displaystyle\mathbf{q}_{c}\times\mathbf{q}_{c}\times\mathbf{F}_{uI}=-m_{v}l(\mathbf{k}_{plr}\mathbf{q}_{ce}+\mathbf{k}_{vlr}\dot{\mathbf{q}}_{ce}+\hat{\mathbf{F}}_{l}^{r}),$
(55)

where $\hat{\mathbf{F}}_{l}^{r}$ and $\hat{\mathbf{F}}_{l}^{d}$ indicate the
real part and the dual part of $\hat{\mathbf{F}}_{l}$ respectively. Then, we
obtain the desired $\mathbf{F}_{uI}$

$\displaystyle\mathbf{F}_{uI}=(\mathbf{q}_{c}\cdot\mathbf{F}_{uI})\mathbf{q}_{c}-\mathbf{q}_{c}\times\mathbf{q}_{c}\times\mathbf{F}_{uI}$
(56)
$\displaystyle=-m(\mathbf{k}_{pld}\mathbf{T}_{le}+\mathbf{k}_{vld}\dot{\mathbf{T}}_{le}+\hat{F}_{l})+m_{v}l(\mathbf{k}_{plr}\mathbf{q}_{ce}+\mathbf{k}_{vlr}\dot{\mathbf{q}}_{ce}).$

It is important to note that the desired control force $\mathbf{F}_{u}$ of the
UAV in body frame that is necessary to move the load to the desired reference
is given in Eq. (27) is referenced to the initial frame. $\mathbf{F}_{u}$ is
obtained by quaternion product

$\mathbf{F}_{u}=\mathit{q}_{v}^{*}\otimes\mathbf{F}_{uI}\otimes\mathit{q}_{v}.$
(57)

Considering that the quadrotor is an under-actuated system, the actual force
exerted by the motors is given by

$\mathbf{F}_{th}=[0~{}0~{}||\mathbf{F}_{u}||]^{T}=[0~{}0~{}1]^{T}||\mathbf{F}_{u}||=\mathbf{b}||\mathbf{F}_{u}||$
(58)

For the attitude of the UAV, a quaternion $\mathit{q}_{t}$ exists that rotates
the UAV such that the thrust force vector $\mathbf{F}_{th}$ coincides with the
desired control force $\mathbf{F}_{uI}$ in the inertial frame, and it is
defined as

$\mathit{q}_{t}=\frac{(\mathbf{b}\cdot\mathbf{F}_{uI}+||\mathbf{F}_{uI}||)+\mathbf{b}\times\mathbf{F}_{uc}}{||(\mathbf{b}\cdot\mathbf{F}_{uI}+||\mathbf{F}_{uI}||)+\mathbf{b}\times\mathbf{F}_{uc}||}$
(59)

where $\mathbf{F}_{uc}$ is the current thrust force vector with respect to the
inertial frame. Then if the desired rotation around the $z$ axis is defined
with a quaternion $\mathit{q}_{zd}$, then $\mathit{q}_{t}$ is completed using
a quaternion product [17]

$\mathit{q}_{v}^{d}=\mathit{q}_{zd}\otimes\mathit{q}_{t}$ (60)

Till now, $\mathit{q}_{v}^{d}$ is used as the complete attitude reference to
feedback the rotational control input from Eq. (52) and $\mathbf{F}_{th}$
dictates the thrust driven by the rotors.

TABLE I: Simulation Parameters of the cargo UAV system222Parameters in this paper, such as $J$, $m$, $\mathbf{T}$ ($l$), and $\mathbf{\omega}$, are all using International System of Units ($\mathrm{k}\mathrm{g}\mathrm{*}\mathrm{m}^{2}$, $\mathrm{k}\mathrm{g}$, $\mathrm{m}$, and $\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{/}\mathrm{s}$). The units are omitted therein. UAV |  $m_{v}=0.7$ , $J_{v}=\textit{diag}[0.005,0.007,0.006]$, $\mathbf{d}=[0,l/2,0,0]$ $\mathbf{T}_{v0}=\mathbf{T}_{l0}+\mathbf{d}$, $\dot{\mathbf{T}}_{v0}=\mathbf{0}$, $q_{v0}=I$
---|---
Load |  $m_{l}=0.05$, $l=0.3$, $\mathbf{T}_{l0}=\mathbf{0}$, $\dot{\mathbf{T}}_{l0}=\mathbf{0}$
Controller |  $\hat{\mathbf{k}}_{pv}=[10,10,10]+[1,1,4]\epsilon$,$\hat{\mathbf{k}}_{vv}=[1,1,1]+[1,1,4]\epsilon$, $\hat{\mathbf{k}}_{pl}=[2,2,2]+[1,1,4]\epsilon$, $\hat{\mathbf{k}}_{vl}=[0.5,0.5,0.5]+[1,1,4]\epsilon$
Trajectory |  $q_{v}^{d.s}=I$, $\mathbf{T}_{v}^{d.s}=[0,0,0,l]$, $H=3l$, $\mathbf{T}_{l}^{d.r}=H$, $\dot{\mathbf{T}}_{l}^{d.r}=[0,0,0.5\sin(\frac{\pi}{3}))]$, $t\in[0,6]$, $\mathbf{T}_{l}^{d.t}=[\sin(\frac{\pi}{6}),0.5\sin(\frac{\pi}{6}),\max(0,0.5\sin(\frac{\pi}{3}))]$, $t\in[0,6]$

##  V Simulation

###  V-A Simulation Settings

The performance of the proposed control strategy is tested in a set of
numerical simulations with a time step of $0.01\text{\,}\mathrm{s}$. The
parameters of the cargo UAV system, the control gains, initial values, and
parameters for the desired trajectories are depicted in Table I.

Figure 3: States of the UAV during the lifting and trajectory tracking
process. In these figures, the vertical black dashed lines indicate the time
at which the UAV switches the mode to the next one, colored lines show the
real values and shade areas are the errors with the desired values. The first
figure depicts the position of the UAV and the second one presents the
translational velocity. The two figures in the bottom row show the attitude
and angular velocity of the UAV.

###  V-B Simulation 1: Lifting and Trajectory Tracking

In this simulation, we conduct the tracking of a trajectory including the
take-off maneuver and the tracking of a trajectory with the load. The sling
load lifting maneuver is simulated following the three modes [7] illustrated
in Fig. 2 and explained in Sec. IV-A. After the sling load reaches a desired
height, the reference trajectory is generated and the sling load tracks the
trajectory. The desired trajectory is determined by
$\dot{\mathbf{T}}_{l}^{d.t}$ in Table I.

The simulation results are depicted in Fig. 3, Fig. 4, and Fig. 5. The UAV
takes about $3.9\text{\,}\mathrm{s}$ to finish the setup process. Then, in a
very short time, the UAV completes the Pull mode (about
$0.2\text{\,}\mathrm{s}$) being in a stable state avoiding cable oscillation
[18]. The total time of accomplishing the load lifting maneuver takes
$\approx$$6.9\text{\,}\mathrm{s}$.

Figure 4: States of the load during the lifting and tracking process. The
vertical black dashed lines indicate the time at which the UAV switches the
mode to the next one. The two figures in the first row show the position and
translational velocity of the load. The figures in the bottom row depict the
unit direction vector $\mathbf{q}_{c}$ and its derivative. Figure 5: State
errors of the load during the lifting and tracking process. The vertical black
dashed lines indicate the time at which the mode jumps from one to the next.
The two figures in the first row show the position and translational velocity
errors of the load. The figures in the bottom row depict the errors for the
unit direction vector $q_{c}$ and its derivative.

The results show that the UAV maintains stable status above the load
throughout the Setup and Pull phases. During these phases, the unit direction
vector $\mathbf{q}_{c}$ adapts to the UAV’s position, as depicted in Fig. 4.
Upon entering the Raise mode, the load ascends from the ground and approaches
the desired height. Notably, the errors $\mathbf{q}_{ce}$ and
$\dot{\mathbf{q}}_{ce}$ in this mode remain close to zero, indicating minimal
swing of the sling load, as shown in Fig. 5.

During the tracking maneuver, the position and translational velocity of the
UAV are determined by the position of the sling load and the direction vector
$\mathbf{q}_{c}$, as shown in Fig. 3. The attitude of the UAV is obtained from
Eq. (60). Combining the unit vector $\mathbf{q}_{c}$ and $\mathbf{q}_{c}^{d}$
shown in Fig. 4, we can see that the attitude of the UAV changes when the
sling load tracks the reference trajectory. After the tracking task is
completed, the attitude of the UAV stabilizes horizontally with minimal
tracking errors.

The state errors of the sling load are depicted in Fig. 5. The position errors
in the first figure indicate the sling load is able to track the desired
trajectory with a maximum error around $-0.02\text{\,}\mathrm{m}$. Combining
the translational velocity in the second figure, we can see the developed dual
quaternion controller performs well for the sling load lifting and tracking
tasks. The errors of $\mathbf{q}_{c}$ and $\dot{\mathbf{q}}_{c}$, shown in the
second row, indicate that the proposed control strategy is able to minimize
the swing of the load during the maneuver sufficiently.

###  V-C Simulation 2: System Evaluation

Figure 6: The comparison results of our dq (dual quaternion) controller and
the geo (geometric) controller. The left figure shows the distribution of
tracking errors, and the right one depicts the velocity.  Figure 7: The
L2-norm of tracking errors for the proposed dq (dual quaternion) controller
and the geo (geometric) controller.

The purpose of this set of simulations is to test the robustness of the
proposed controller. To do that we considered both, external disturbances for
control inputs, forces $\mathbf{F}$ and torques $\mathbf{\tau}$, and system
uncertainties. For system uncertainties, we focused on system parameters that
can not be measured precisely including $m_{v}$, $m_{l}$, $l$, and $J_{v}$. In
our simulation, we added white Gaussian noise to these variables with the
signal-to-noise ratio of $35$. For comparison of the performance of our
proposed model, we implemented the geometric controller presented in [6] with
the same settings as the baseline. The simulation was conducted $100$ times
for the two controllers and each time these parameters were initialized
randomly by adding noise to the ideal values. The comparison results are shown
in Fig. 6 and Fig. 7.

The left figure in Fig. 6 presents the average tracking errors for $100$ times
simulations. The right one depicts the corresponding velocity. From the left
figure, we can see the tracking errors of both our controller and the
geometric controller are very small. However, the norm of tracking errors
shown in Fig. 7 indicates that our controller performs better than the
geometric control. This conclusion is also supported by the velocity plots
Fig. 6. The dual quaternion control yields smooth velocity control. The reason
for the fluctuation happening around $7\text{\,}\mathrm{s}$ might be the
sudden changes of velocities on the x-axis and y-axis, and the effects of
control gains. These results demonstrate that the sling is able to track a
desired trajectory with small tracking errors and minimum swing using our
developed controller.

##  VI Conclusion

By utilizing the mathematical efficiency and compactness of dual quaternions,
this study introduces a novel control strategy, where the kinematics and
dynamics of the UAV and its sling load are represented by dual quaternions.
This representation significantly improves the control performance of the
cargo UAV system. Two simulations were designed to assess the proposed control
strategy. The lifting and tracking maneuver simulation results show that the
sling load is able to track a desired trajectory with small tracking errors
and swings. The second simulation indicates that the proposed control strategy
is robust to system uncertainties and disturbances. The comparison results
with the geometric controller show that our controller is more stable and
performs better for tracking tasks. In future work, we will consider a
potential offset between the attachment point of the load and the CoM of the
UAV. Then, we will test the proposed controller on real UAVs.

## References

  * [1] G. Macrina, L. D. P. Pugliese, F. Guerriero, and G. Laporte, “Drone-aided routing: A literature review,” _Transportation Research Part C: Emerging Technologies_ , vol. 120, p. 102762, 2020.
  * [2] H. M. Omar, R. Akram, S. M. Mukras, and A. A. Mahvouz, “Recent advances and challenges in controlling quadrotors with suspended loads,” _Alexandria Engineering Journal_ , vol. 63, pp. 253–270, 2023.
  * [3] F. A. Goodarzi, D. Lee, and T. Lee, “Geometric stabilization of a quadrotor uav with a payload connected by flexible cable,” in _2014 American Control Conference_. IEEE, 2014, pp. 4925–4930.
  * [4] S. H. Derrouaoui, Y. Bouzid, M. Guiatni, and I. Dib, “A comprehensive review on reconfigurable drones: Classification, characteristics, design and control technologies,” _Unmanned Systems_ , vol. 10, no. 01, pp. 3–29, 2022.
  * [5] T. Lee, M. Leok, and N. H. McClamroch, “Geometric tracking control of a quadrotor uav on se (3),” in _49th IEEE conference on decision and control (CDC)_. IEEE, 2010, pp. 5420–5425.
  * [6] K. Sreenath, T. Lee, and V. Kumar, “Geometric control and differential flatness of a quadrotor uav with a cable-suspended load,” in _52nd IEEE Conference on Decision and Control_. IEEE, 2013, pp. 2269–2274.
  * [7] P. J. Cruz and R. Fierro, “Cable-suspended load lifting by a quadrotor uav: hybrid model, trajectory generation, and control,” _Autonomous Robots_ , vol. 41, pp. 1629–1643, 2017.
  * [8] P. Lukas, “Safe online trajectory generation methods for quadrotor slung load systems,” Master’s thesis, Technical University of Munich, 2021.
  * [9] Y. Alothman, W. Jasim, and D. Gu, “Quad-rotor lifting-transporting cable-suspended payloads control,” in _2015 21st International Conference on Automation and Computing (ICAC)_. IEEE, 2015, pp. 1–6.
  * [10] M. Belguith, S. Samaali, and S. Bennaceur, “Modeling and control of quadrotor transporting cable-suspended load in the longitudinal & lateral planes,” in _2023 European Control Conference (ECC)_. IEEE, 2023, pp. 1–6.
  * [11] Z. Lv, Y. Wu, X.-M. Sun, and Q.-G. Wang, “Fixed-time control for a quadrotor with a cable-suspended load,” _IEEE Transactions on Intelligent Transportation Systems_ , vol. 23, no. 11, pp. 21 932–21 943, 2022.
  * [12] M. Lopez and J. Martinez-Carranza, “A cnn-based approach for cable-suspended load lifting with an autonomous mav,” _Journal of Intelligent & Robotic Systems_, vol. 105, no. 2, p. 32, 2022.
  * [13] N. Dantam, “Quaternion computation,” _Georgia Institute of Technology, Atlanta, Tech. Rep_ , 2014.
  * [14] F. Bullo and R. M. Murray, “Proportional derivative (pd) control on the euclidean group,” 1995.
  * [15] J. Arrizabalaga and M. Ryll, “Pose-following with dual quaternions,” _arXiv preprint arXiv:2308.09507_ , 2023.
  * [16] X. Wang and C. Yu, “Unit dual quaternion-based feedback linearization tracking problem for attitude and position dynamics,” _Systems & Control Letters_, vol. 62, no. 3, pp. 225–233, 2013.
  * [17] H. Abaunza, P. Castillo, A. Victorino, and R. Lozano, “Dual quaternion modeling and control of a quad-rotor aerial manipulator,” _Journal of Intelligent & Robotic Systems_, vol. 88, pp. 267–283, 2017.
  * [18] M. Bisgaard, J. D. Bendtsen, and A. la Cour-Harbo, “Modeling of generic slung load system,” _Journal of guidance, control, and dynamics_ , vol. 32, no. 2, pp. 573–585, 2009.


[.5em]0em1em

Human-AI Interactions Through A Gricean Lens Laura Panfili, Steve Duman,
Andrew Nave, Katherine Phelps Ridgeway, Nathan Eversole & Ruhi
Sarikaya***Authors: Laura Panfili, Amazon (lpanfili@amazon.com), Steve Duman,
Amazon (dumastev@amazon.com), Andrew Nave, Amazon (andrnave@amazon.com),
Katherine Phelps Ridgeway (k1000ridgeway@gmail.com), Nathan Eversole, Amazon
<EMAIL_ADDRESS>& Ruhi Sarikaya, Amazon<EMAIL_ADDRESS>.

###### Abstract

Grice’s Cooperative Principle (1975), which describes the implicit maxims that
guide effective conversation, has long been applied to conversations between
humans. However, as humans begin to interact with non-human dialogue systems
more frequently and in a broader scope, an important question emerges: what
principles govern those interactions? In the present study, this question is
addressed, as human-AI interactions are categorized using Grice’s four maxims.
In doing so, it demonstrates the advantages and shortcomings of such an
approach, ultimately demonstrating that humans do, indeed, apply these maxims
to interactions with AI, even making explicit references to the AI’s
performance through a Gricean lens. Twenty-three participants interacted with
an American English-speaking Alexa and rated and discussed their experience
with an in-lab researcher. Researchers then reviewed each exchange,
identifying those that might relate to Grice’s maxims: Quantity, Quality,
Manner, and Relevance. Many instances of explicit user frustration stemmed
from violations of Grice’s maxims. Quantity violations were noted for too
little but not too much information, while Quality violations were rare,
indicating high trust in Alexa’s responses. Manner violations focused on speed
and humanness. Relevance violations were the most frequent of all violations,
and they appear to be the most frustrating. While the maxims help describe
many of the issues participants encountered with Alexa’s responses, other
issues do not fit neatly into Grice’s framework. For example, participants
were particularly averse to Alexa initiating exchanges or making unsolicited
suggestions. To address this gap, we propose the addition of human Priority to
describe human-AI interaction. Humans and AIs are not (yet?) conversational
equals, and human initiative takes priority. Moreover, we find that Relevance
is of particular importance in human-AI interactions and suggest that the
application of Grice’s Cooperative Principles to human-AI interactions is
beneficial both from an AI development perspective as well as a tool for
describing an emerging form of interaction.

Keywords. discourse; pragmatics; Cooperative Principle; artificial
intelligence; Alexa; voice assistant

## 1\. Introduction

Grice’s (1975) Cooperative Principle provides a universal framework of how
humans negotiate the intricate practice of conversation. Grice developed this
approach to describe successful and unsuccessful human-human interactions.
However, in recent years, humans are increasingly engaged in language-based
interaction with a new type of interlocutor: voice-based Artificial
Intelligence (AI). From phones to at-home speakers to in-car devices, AIs — as
manifest in voice assistants like Alexa, Google Assistant, Siri, and Cortana —
are pervasive in a myriad of contexts. The ubiquity of these devices, coupled
with steady improvement of the models that drive them, lead to two challenges.
First, developers of AI technology need mechanisms to evaluate the success or
failure of exchanges with AI. Second, researchers require a method by which to
describe the principles that guide this new, pervasive form of language-based
exchanges.

The study we report here takes the novel step of applying Grice’s framework,
one meant to describe human conversation, to exchanges that challenge the
notion of what constitutes a ‘conversation.’ We rely largely on qualitative
observations of in-lab, naturalistic exchanges between participants and an
Alexa device. Participants rated Alexa’s responses and were prompted by an in-
lab researcher to describe the reasoning behind their ratings. The researchers
then reviewed all exchanges, identifying over 700 as potential violations of
Grice’s maxims. In the results reported here, we show the exchanges, ratings,
and explanations from this study. These observations provide strong
preliminary evidence that users do, indeed, apply Gricean maxims to human-AI
interactions.

Based on our findings, we argue that Grice’s Cooperative Principle —
specifically the maxims of Quantity, Quality, Relevance, and Manner — is a
useful framework to describe human-AI interactions, though there are a few
important differences from what we expect with human-human interactions. With
regard to Quantity, participants specifically cite responses that are too
short as reasons for providing low ratings of Alexa’s responses, but they do
not explicitly mention lengthy responses. Quality violations are rare in the
dataset, with very few explicit references by participants as to the quality
of Alexa’s responses. Manner violations are observed with regard to the rate
of Alexa’s speech and the ‘humanness’ of responses. Violations of Relevance
are the most prevalent violations in the dataset, and they are most frequently
associated with lower ratings.

In addition, we also identify another important difference between human-human
interactions and those displayed in human-AI interactions: the inherent power
difference between humans and AIs leads to different expectations in terms of
turn initiations and interruptions. To account for the discrepancies, we
propose a new maxim, Priority, which suggests that humans take priority in
human-AI interactions.

To explore these observations, we first examine previous literature regarding
Grice’s Cooperative Principle, criticisms regarding its universality, and
applications regarding differing discourse contexts. Next, we present the
study of twenty-three participants interacting with Alexa in a lab setting,
focusing primarily on the qualitative observations of the participants.
Lastly, we discuss our findings and their implications regarding AI
evaluation, the limitations of Grice’s framework, and future directions.

## 2\. Background

Understanding user perceptions of AI systems is notoriously difficult, but it
is an important endeavor. Evaluating the performance of AI systems allows us
to identify problem areas as the technology develops. Specifically, how do
human users assess the success or failure of their exchanges with an AI
dialogue system? While several approaches have been suggested for doing so
(see, e.g., Deriu et al. 2019; Schmitt & Ultes 2015), previous attempts are
limited in their scope, examining voice user interfaces that are primarily
transactional or limited to a particular domain, like setting up travel plans.
These limitations become apparent when examining AI voice assistants like
Siri, Google Assistant, and Alexa, which now feature numerous functions
(including naturalistic conversation, in some cases) and can be used in a
variety of contexts. Moreover, the machine learning models that drive the
Natural Language Understanding of these systems are steadily improving,
allowing users to employ more complex linguistic constructions. As a
consequence, it is important to have a well-established, human-based approach
with which to understand how humans interpret their own interactions with AI
systems.

In addition, as humans interact with AIs more frequently and more naturally,
there is increasing evidence that users anthropomorphize AIs, talking and
perhaps even treating them as human-like entities. Purington et al. (2017)
demonstrate that Alexa users frequently personify the device in reviews posted
to Amazon.com (e.g., using female pronouns ‘she’ and ‘her’ to describe Alexa),
and, interestingly, this personification is correlated with higher star
ratings. Given the increasingly complex interactions along with the natural
tendency (and even encouragement) to personify AIs, it makes sense to apply
frameworks traditionally used for human-human interactions in order to
understand people’s perceptions of human-AI interactions. To that end, in this
paper we explore the utility of using Grice’s Cooperative Principle — a
framework traditionally used to describe interactions between humans — as a
framework with which to understand user perceptions of interactions between
humans and AIs.

Grice’s Cooperative Principle is a descriptive framework to explain the
presumably universal guidelines for effective conversations. The principle is
composed of four maxims: Quantity, Quality, Manner, and Relevance. These
maxims are intended to describe the implicit conversational rules that allow
humans to mutually understand one another. These maxims are briefly described
as follows:

[1em]2em

Quantity: Make your contribution as informative as is required for the current
purposes of the exchange. Do not make your contribution more informative than
required.

Quality: Try to make your contribution one that is true, specifically: Do not
say what you believe to be false; Do not say that for which you lack adequate
evidence

Manner: Be perspicuous, and specifically: Avoid obscurity; Avoid ambiguity; Be
brief; Be orderly

Relevance: Make your contributions relevant

In order for human conversation to be effective, humans need to follow Grice’s
maxims. Violating the maxims leads to ineffective (or, in the case of
flouting, often comical) communicative events.

Since Grice’s seminal work, many researchers have argued that the Cooperative
Principle is not necessarily universal, as contextual factors can influence
the extent to which interlocutors follow the maxims (Habermas 1984; Harris
1995; Thornborrow 2014). As Harris (1995) argues, “Grice has often been
criticised for constructing a theory of universal pragmatics which cannot
handle unequal encounters which are clearly not cooperative and where the
goals of participants conflict in quite obvious ways.” Such situations include
‘institutional discourse,’ or discourse that takes place in institutions like
classrooms or courtrooms. In a courtroom setting, for example, a witness on
the stand does not have the access to the same speech acts as the lawyer or
judge (Habermas 1984).

Kitis (1999) addresses the universality of Grice’s Cooperative Principle by
suggesting that, in fact, Relevance serves as a ‘supermaxim’ that structures
surrounding communication and exerts control of the pragmatic definition of
truth. Relevance, Kitis argues, thus constrains the application of the other
three maxims. This accounts for power dynamics in human-human interactions in
that the interlocutors respond according to the ‘relevance’ of the social and
linguistic context. This line of thinking suggests that one maxim can
influence or filter the others. Like in human-human conversation, the context
of human-AI interactions can vary wildly (e.g., in the kitchen, in the car,
etc.). While the notion of ‘institutional discourse’ covers many of the
contextual variations in Relevance, it does not necessarily capture the power
differences at play between human and AI. This point will be taken up in the
Discussion below.

In short, despite limitations in Grice’s Cooperative Principle for describing
human conversation, it is a well-established and useful starting point when
endeavoring to explore human perceptions of human-AI interactions. Moreover,
applying this framework could help us improve the development process of AIs,
help us better categorize and understand human-AI exchanges, and perhaps even
contribute our understanding of Grice’s maxims.

To these ends, this paper describes an in-lab experiment in which we examine
human-AI exchanges through a Gricean lens. As this is a novel approach to such
interactions, our methodology is primarily qualitative, where we analyze
human-AI exchanges through three means: (1) the researchers’ assessments of
human-AI interactions as violations of Gricean’s maxims, (2) participants’
assessments of exchanges on a 1-5 scale, and (3) participants’ explicit
references to exchanges that the researchers regard as applicable to Grice’s
maxims. This methodology allows us to determine the extent to which applying
Grice’s Cooperative Principle to human-AI interactions is useful as well as
the extent to which participants consciously (and perhaps unconsciously) do so
as well. More specifically, it allows us to address the following research
questions:

[1em]2em

RQ1: Are unsatisfactory interactions between humans and AIs explained as
violations of Grice’s maxims?
RQ2: Which, if any, unsatisfactory interactions are not explained as
violations of Grice’s maxims?
RQ3: Are there fundamental differences between what researchers perceive to be
violations of Grice’s maxims compared to participant assessments?

In order to answer these research questions, we invited twenty-three
participants to a lab where they interacted with an Alexa device. Alexa was
chosen first and foremost because this study was conducted by researchers at
Amazon, Inc. to help facilitate the development of Alexa. Additionally, Alexa
is a widely used voice assistant with a wide range of capabilities. The
details of the methodology are reported below.

## 3\. Methods

Amazon researchers worked with User Research International to recruit twenty-
three participants for this study. Participants were self-reported to have an
Alexa-enabled device at home and to interact with it at least a few times each
week. All participants reported that they had never professionally worked on a
voice assistant and did not have any immediate family members who did, nor
were any employed by Amazon. Participants were all residents of the greater
Seattle area and able to speak and read English, though not necessarily
natively. They received a $100 Amazon.com gift card in exchange for
participating in this experiment. Figure 1 shows participant demographics.

Figure 1: Age, gender, and ethnicity of participants

The study was conducted by Amazon researchers in a usability lab on Amazon’s
campus in Seattle, Washington in the fall of 2019. This lab was set up with a
third generation Echo Dot set to American English and connected to various
Alexa-enabled smart home devices. An in-lab researcher joined each participant
in order to troubleshoot technical issues, facilitate ratings, and encourage
discussion of their reasoning behind ratings.

Participants were instructed to interact with Alexa based on a series of
prompts; they were encouraged to explore anything that piqued their interest
and were free to move on to the next prompt at any point. The prompts were
designed to cover some of the most frequent types of Alexa exchanges, such as
music and smart home requests. They were intended to cause both successful and
unsuccessful interactions and to allow participants to phrase their requests
naturally. Prompts were displayed on a monitor and participants controlled the
pace with a keyboard. Audio of each session was recorded for later analysis.
Prompts were presented in a random order, with not all participants completing
all prompts, depending on their pace.

Participants were asked to rate each of Alexa’s responses an a scale from one
to five, where one is the worst score and five is the best. The points on the
scale were not further specified, allowing for the participants to apply the
scale as they felt was intuitive. Scores were input using number keys on a
modified keyboard and recorded using Psychopy software (Peirce et al. 2019).
In order to preserve the naturalness of the experiment, participants were only
lightly encouraged and reminded to rate their exchanges, resulting in some
unrated turns. Additionally, the in-lab researcher frequently asked
participants to talk through their thought process behind a rating. At the end
of the experiment, participants verbally completed an exit survey that
included a broad discussion of their application of the rating scale.

The resulting data set consists of 23 hours of audio, including exchanges with
Alexa and discussions with the in-lab researcher. We captured 2,279
participant-Alexa exchanges, 1,913 of which were rated on the 1-5 scale. All
exchanges were evaluated by researchers for potential violations of one or
more maxim on Alexa’s part; we also identified implicit and explicit
references to Grice’s maxims in participant conversations with the
researchers. Table 1 shows the frequency of maxim violations and Figure 2
shows the distribution of ratings by maxim violation.

Maxim | n
---|---
Quantity | 135
Quality | 7
Manner | 109
Relevance | 471
Table 1: Maxim violation counts  Figure 2: Distribution of ratings of maxim
violations

As the table demonstrates, approximately 40% of the participant-Alexa
exchanges were identified the researchers as potential Gricean violations. The
most frequently violated maxim was Relevance, where 428 exchanges were tagged
as potential violations. Interestingly, as Figure 2 demonstrates, violations
of Grice’s maxims are associated with both negative and positively-rated
turns. In other words, a researcher-identified maxim violation is not
necessarily a poorly rated exchange by the participants. In fact, many
researcher-identified violations are rated 5 by participants. However, this
seems to be less the case for Relevance, where the distribution of ratings
includes much lower numbers. The following section explores the findings for
each maxim, focusing primarily on participants references to Grice’s maxims in
their evaluations.

## 4\. Results

This section consists of a primarily qualitative analysis of the participant-
Alexa exchanges recorded in the study. The subsections discuss exchanges that
the researchers identified as possible violations of Grice’s four maxims:
Quantity, Quality, Manner, and Relevance. In addition to the participant
ratings for each exchange, we concentrate primarily on explanations that
either implicitly or explicitly reference the maxim.

### 4.1. Quantity

We identified 135 exchanges where Alexa may have violated the Quantity maxim,
with an average rating of 4.15 (SD = 1.22). We saw several trends in how
participants invoked Quantity in their conversations with the in-lab
researcher. First, some participants noted and appreciated when Alexa’s
response hit the Quantity sweet spot (such examples are not included as
violations, but rather demonstrate participants explicitly referring to
Gricean maxims), as seen in Example 4.1.

. User: Alexa, what’s happening with the Thomas Cook collapse over in Europe?
Alexa: Here’s what I found about Thomas Cook from Reuters. The collapse of
British travel operator Thomas Cook has left hundreds of thousands
holidaymakers abroad and forced governments and insurers to coordinate a huge
operation to get them home. The company ran hotels, resorts and airlines
ferrying 19 million people a year to 16 different countries. [rating: 5]
User: The thing I liked about that is it wasn’t too long. So I got a good
amount of info […] It was short and sweet.

When Alexa’s response did not hit the sweet spot and instead provided too
little information, this quantity violation was sometimes cause for a lower
rating. In Example 4.1, Alexa seemed about to provide a list, but only
included one item.

. User: Alexa, tell me about different kinds of bananas.
Alexa: Some examples of bananas are red bananas. [rating: 2]
User: There should’ve been more. I’m giving that a two. I wanted more, like …
yellow and plantains or whatever, I wanted three or four.

However, when Alexa provided what would likely be too much information in a
conversation between humans, this generally went unnoticed by participants. In
Example 4.1, Alexa read the entire first paragraph of the Wikipedia article on
Astronomy. Though the device does ask if the user would like to hear more,
it’s only offered after reading that full first paragraph. Another potential
quantity violation comes in the form of too much detail: in Example 4.1, Alexa
provides distances down to the tenth of a mile for locations on another
continent, and the participant did not comment on this.

. User: Alexa, tell me about astronomy.
Alexa: Here’s the Wikipedia article on Astronomy. Astronomy is a natural
science that studies celestial objects and phenomena. It applies mathematics,
physics, and chemistry in an effort to explain the origin of those objects and
phenomena and their evolution. Objects of interest include […] Would you like
me to continue? [rating: 5]

. User: Alexa, tell me about good restaurants in Paris, France.
Alexa: Here are a few top rated restaurants in Paris, France: one, Chez le
Libanais, 4,997.6 miles away on et 36 rue Saint-André-des-Arts, two, La
Jacobine, 4,997.5 miles away on 59-61 rue Saint-André des Arts […] [rating: 4]

These examples demonstrate that some users seem to have very different
expectations of Alexa compared to humans in terms of an adherence to the maxim
of Quantity. Specifically, these users seem to find responses that we, as
researchers, interpret as too much information — such as an entire paragraph
from Wikipedia or distances in thousands of miles to the decimal point — as
perfectly acceptable. This suggests that some users are sensitive to too
little quantity, but they are less sensitive to greater quantity, in contrast
to what we may expect with human-human interactions. This marks a first
potential difference in the application of Grice’s framework to human-AI
interactions.

These examples may be a reflection of users viewing the AI as a window to the
Internet. Many participants demonstrated a belief that Alexa is conducting
Internet searches to answer their questions, and that the device can access
whatever information an Internet search could access. If Alexa is capable of
accessing all the information that’s out there, responses should provide more
detail than a human can; on the other hand, this expectation sets users up for
disappointment and frustration when Alexa fails to provide sufficient
information.

### 4.2. Quality

Just seven exchanges included Alexa violations of the Quality maxim, with an
average rating of 4.71 (SD = 0.49). Participants demonstrated overwhelming
trust in Alexa’s responses, as indicated by high ratings and commentary to
that effect along with the relative lack of explicit references to Quality. In
Example 4.2, the participant was asked to request the weather in Mordor, a
fictional location from The Lord of the Rings, but this participant did not
know that Mordor does not exist. Due to a speech recognition error, Alexa
reported the weather for Vidor, Texas instead. The participant then assumed
that Alexa was correctly reporting the weather in Mordor, Texas:

. User: Alexa, what’s the weather like in Mordor?
Alexa: In Vidor, Texas, it’s 90 degrees Fahrenheit with mostly cloudy skies.
Today, you can look for partly sunny weather, with a high of 90 degrees and a
low of 77 degrees. [rating: 5]
User: Is that in Texas? I’m gonna say she’s right.

In another example 4.2, Alexa gave factually incorrect information, which did
not seem to bother the participant:

. User: Alexa, what’s the highest point in the Seattle area?
Alexa: The highest point in Seattle is Mount Rainier. [rating: 5]

Mount Rainier is about a three-hour drive from Seattle, not in Seattle (a fact
we can assume any Seattle area resident knows). Nonetheless, the participant
rated this response a five. This is perhaps complicated by the fact that the
original request was, in fact, about the Seattle area, but this factually
incorrect answer did not seem to cause any broad mistrust in Alexa’s
responses.

One of the more striking examples of trust in Alexa comes from a participant
who, after several failed attempts to find out who holds the home run record
for the Seattle Mariners, concluded that that information doesn’t exist; she
has so much faith in Alexa’s ability to find information that she interpreted
Alexa’s repeated failures as an exhaustive search.

. User: Who hit the most home runs for the Seattle Mariners?
Alexa: The Houston Astros at Seattle Mariners game hasn’t started yet. First
pitch will be tomorrow evening at 7:10pm. [rating: 1]
User: Which player on the Seattle Mariners has hit the most home runs?
Alexa: Hmm, I’m not sure. [rating: 3]
User: Who has the home run record for Seattle Mariners?
Alexa: This might answer your question: Yesterday, the Mariners did not hit a
home run during their 2-1 loss to the Orioles. This season, the Mariners are
ranked 5th in the American League with 238 home runs. This season, the
Mariners are 66 and 90 and ranked 5th in the AL West. Did that answer your
question? [rating: 4]
User: […] The second time around she attempted to answer it, and then was like
’wait, is that really what you were asking for?’ and asking that was sort of
like, I’m now understanding that maybe that stat’s not out there in the
universe. [rating: 4]

Alexa occasionally cites sources, and we saw just one instance of a
participant questioning Quality in the form of doubting a source. This
participant rated the exchange a five but expressed some disappointment with
the source of the information. (This participant explicitly refused to rate
any response below a three.)

. User: Alexa, how many spots does a giraffe have?
Alexa: According to another Amazon customer: no individual giraffe has the
same pattern so there is not a way to tell how many spots a giraffe has. Did
that answer your question? [rating: 5]
User: No, who is this other Amazon customer?

In sum, participants in the study demonstrated a very strong trust in Quality
from Alexa, accepting most of the information that was provided, even in cases
where Alexa provided factually incorrect information or did not provide
information that definitely exists. This could suggest that, because Alexa is
an AI entity, humans interlocutors have even higher expectations of Quality
than they do for humans. Like Quantity, this evaluation of Quality may be
impacted by the perception of Alexa as a window to the Internet. We saw
participants generally trust the information that Alexa provides, as they
likely would trust the results of an Internet search (whether or not they
should trust an Internet search is another topic, of course). Judgement of
Quality seems to parallel an Internet search: It is hard to believe that an
Internet search would fail to find information that does exist, and the
trustworthiness of sources can be questioned. Users seem to pin these failures
not on Alexa but rather on the Internet search that they believe the device
conducts.

### 4.3. Manner

109 exchanges were tagged as including potential Manner violations on Alexa’s
part, with an average rating of 3.56 (SD = 1.59). Several participants noted
that Alexa spoke too quickly, posing comprehension problems. Though not
mentioned by participants, unnatural prosody may have compounded the
difficulties posed by speed. Examples 4.3 and 4.3 show two participant
reactions to fast Alexa responses.

. User: Do you have any financial skills?
Alexa: Here are three popular Business & Finance skills. First is Make Me
Smart. Say ‘Alexa, Make Me Smart’ to learn something surprising and timely
about the economy, pop culture, and tech from Marketplace’s Kai Ryssdal and
Molly Wood. Would you like to give that one a try? [rating: 3]
User: No.
Alexa: Okay, next is […] Would you like to give that one a try? [rating: 3]
User: No.
Alexa: Okay, next is […] Would you like to give it a try? [rating: 3]
User: No.
Alexa: Okay. Do you want to hear more? [rating: 5]
User: No.
Alexa: Alright. [rating: 5]s
User: It’s just so fast, it’s like, oh gosh! […] a lot, and a little quick.
Not that I think there’s a way to change the speed of the speech, but it
seemed really fast.

. User: Alexa, adjust the thermostat to sixty five degrees.
Alexa: Auto’s keeping the temperature between 32 and 122.
User: Alexa, can you adjust the thermostat to sixty five degrees.
Alexa: Auto’s keeping the temperature between 32 and 122. [rating: 3]
User: I don’t really know what Alexa was saying. Alexa was reading it kinda
fast. Not even the second time, I didn’t catch what Alexa was saying.

Just one participant commented on obscurity of language, suggesting that the
word ‘intermittent’ was likely not accessible to all audiences.

. User: Alexa, what’s the weather like today?
Alexa: Currently, in Seattle, it’s 65 degrees Fahrenheit with partly sunny
skies. Today, you can expect intermittent clouds with a high of 67 degrees and
a low of 59 degrees. [rating: 4]
User: It was good. I don’t know if people would understand what the word
‘intermittent’ means, that’s all.

Alexa regularly provided rather clunky responses — at least from the human-
human conversation perspective — that went unmentioned by participants. In
Example 4.3, Alexa provides a lot of information in response to a request for
music. This would likely feel unnatural in a conversation between friends, but
Alexa’s status as a non-human interlocutor may impact evaluation.

. User: Alexa, play some country music.
Alexa: Okay. The station: Top Country, free on Amazon Music. [rating: 5]

On the whole, violations of Manner are relatively infrequent in the dataset,
and those that are present—references to speaking speed or vocabulary—are what
we might expect from human-human interactions. However, one difference from
our expectations did appear in the dataset. Despite many participants
overlooking unnatural phrasing, we saw a few hints that humanness may be an
important aspect of Manner when interacting with Alexa. For example, one
participant noted, “The ones that I gave a […] three were the ones that were
more … how do I say, it was like mechanical or rote.” Evaluation of humanness
likely varies from person to person, depending on what expectations users have
of their AI’s capabilities and roles. Regardless, this would be an important
difference from expectations of human-human interactions, where AIs are judged
in terms of how ‘human’ their responses are.

### 4.4. Relevance

Finally, we identified 471 exchanges where Alexa may have violated the
Relevance maxim, with an average rating of 2.86 (SD = 1.58), making Relevance
the most frequently-violated maxim and that with the lowest average rating
compared to the other maxims (a pair of Welch two-sample t-tests demonstrates
that its mean is significantly lower than that of Quantity (Mean = 4.15, SD =
1.23, t = 9.7, df = 259, p $<$ .001) and Manner (Mean = 3.56, SD = 1.59, t =
3.9, df = 140, p $<$ .001))111There are too few observations from the Manner
maxim to run a valid statistical comparison with Relevance..

Two broad types of Relevance violations emerged in our data set. The first is
irrelevant arguments, where a key argument, such as a name or a place, is
different in the user’s request and Alexa’s response. In Example 4.4, the
participant asks about information for one location, and Alexa responds with
that information for a different location.

. User: Alexa, what language do they speak in Monte Carlo, Monaco?
Alexa: This might answer your question: Nossa Senhora do Monte is in Portugal,
where the official languages are Portuguese and Mirandese. [rating: 2]

The second type of Relevance violation we found is irrelevant content, where
the goal, rather than the arguments, is irrelevant. Example 4.4 shows an
instance of the participant asking for a smart home device name and getting
different information about that device.

. User: Alexa, what did I name my thermostat?
Alexa: The thermostat temperature is 68 degrees. [rating: 3]
User: I’m gonna give it a three because that isn’t really what I asked for.

When participants were asked to describe reasons that they would provide a
particular rating, they cited Relevance much more frequently than any of the
other three maxims. Participants described low ratings as including Relevance
violations, noting that “One was where she told me something that I didn’t
even want to know and it went in the wrong direction” and “A two would
probably be asking what’s the weather in Seattle and it giving me Portland.”

These findings show that violations of Relevance are the most frequent and
salient Gricean violations in interactions with Alexa. Relevance, which has
previously been proposed as a supermaxim (Kitis 1999), seems to have a
different status from other maxims in human-AI interactions, with more
violations and a lower average rating. The higher occurrence of Relevance
violations likely speaks more to Alexa’s responses than to how humans apply
Grice’s maxims: Relevance violations can be the result of a failure at
effectively any step of the complex pipeline powering voice AIs, such as
speech recognition errors or natural language understanding errors. However,
the lower ratings indicate that human interlocutors find these violations
particularly grating. Some of this may stem from the largely transactional
nature of human-AI interactions, as Relevance violations impede the basic
expected function of the device.

## 5\. Discussion

Overall, the above findings indicate that Grice’s Cooperative Principle is a
useful framework with which to describe interlocutor assessments of human-AI
interactions. Specifically, we can make the following high-level observations
for each maxim:

With regard to Quantity, participants explicitly disapprove of exchanges where
Alexa provided less information than they expected. Interestingly, however, in
contrast to what the researchers would likely expect from an equivalent human-
human interaction, participants do not explicitly disapprove of several
exchanges where Alexa provided arguably too much information.

For Quality, participants in the study demonstrate a significant amount of
trust in Alexa’s responses. In fact, one participant was so trusting that
Alexa’s inability to provide a statistic led her to believe that the statistic
did not exist. This extreme trust in Alexa’s responses is likely driven both
by the assumption that Alexa is following the maxim as well as lay-person
assumptions about AI being ‘all-knowing.’ This is a particularly interesting
finding that warrants extensive research, for, as AI becomes more prolific,
people will likely more and more frequently use AI as a knowledge resource.
Since no system (or person) will ever be 100% accurate, it is important that
participants have a measured sense of Quality in their interactions with AIs.

In terms of Manner, participants make explicit reference to the speed at which
Alexa speaks (likely a way of talking about prosody as well), and one even
mentioned obscurity as a potential problem. User perceptions of Alexa’s
humanness may play a role in their perception of Manner. Interestingly —
perhaps related to Quantity — the amount that Alexa reports when performing an
action like playing a song was not explicitly referenced as problematic.

In this study, Relevance is far and away the most commonly violated maxim as
well as the mostly lowly rated on average. It is also the most explicitly
mentioned by participants in the study. Participants cited relevance (worded
as “the wrong direction,” not “what I asked for,” etc.) as a primary reason
for providing a low rating in exchanges with Alexa. Relevance violations can
be particularly detrimental to more transactional exchanges, which are common
for human-AI interactions.

### 5.1. The Priority Maxim

In addition to the observations of the above maxims, we also observed an
interesting element of human-AI interactions that is not clearly captured by
Grice’s Cooperative Principle. This can be seen in the following exchange:

. User: Alexa, set a timer for—
Alexa: [interrupting] Timer for how long? [rating: 4]
User: Ugh, that’s so annoying.

In broad terms, participants did not have a problem interrupting or speaking
over Alexa. However, participants were particularly averse to Alexa
interrupting them, as in the above exchange. In other words, many participants
demonstrated a strong assumption the human interlocutor begins every exchange,
or has the floor, in any given human-AI interaction. This observation was
supported by similar situations, such as when Alexa makes a suggestion
seemingly unrelated to the previous exchange. This can be seen here:

. User: Alexa, what’s the weather today?
Alexa: In Seattle, it’s 64 degrees Fahrenheit with mostly cloudy skies. Today,
you can look for cloudy skies, with a high of 66 degrees and a low of 52
degrees. By the way, there are more things to try. Just say ‘what are your top
skills?’ [rating: 5]
User: I don’t know, I don’t always love the extra tips, but that’s me being
cranky.

Here, the participant explicitly mentions her frustration at Alexa offering a
seemingly unrelated request. In other words, the participant is demonstrating
a dispreference for Alexa initiating a turn (though it should be noted that
not all participants share this dispreference for suggestions).

These observations suggest that humans inherently take priority over AI in
human-AI interactions. In this way, it is reminiscent of Harris’ (1995) notion
of a “unequal encounters.” However, previous researchers have examined the
extent to which context influences the speech acts available or unavailable to
two human interlocutors. In the case of human-AI interactions, the inequity of
the encounter is inherent to the AI and does not vary by context. In other
words, there is an apparent power difference at play between the
interlocutors, but it is intrinsic to the AI, rather than the context.

For this reason, coupled with the observations from this study, we hypothesize
that another maxim — a Priority maxim — is at play in human-AI interactions.
The Priority maxim can be summarized as follows: Humans take conversational
priority over AI. This priority is driven by the inherent power imbalance
between humans and AI.

Verification of the Priority maxim would have significant implications. First,
it would demonstrate the extent to which human interlocutors accommodate
conversational exchanges, even when the exchange itself challenges the
prototypical notion of a ‘conversation.’ Second, the Priority maxim could have
important implications in terms of variation across interlocutors. For
example, it may be the case that younger, more experienced AI users adhere the
Priority maxim much more strongly than older, less experienced AI users.
Furthermore, the Priority maxim may be implicitly acquired much like Grice’s
four maxims, and the conditions under which the maxim are acquired would be
important for future work. Lastly, the Priority maxim can be important guiding
principle in the design of AI. The Priority maxim suggests that power dynamics
are at play in human-AI interactions at a turn-taking level, where humans are
assumed to take priority in initiating turns. Developing proper turn-taking
strategies is notoriously difficult in AI design (Portela & Granell-Canut
2017; Liao et al. 2016; Chaves & Gerosa 2018). Taking the Priority maxim into
account could help resolve some of these issues, where designers can take
human expectations of their priority into account.

### 5.2. Limitations

Of course, there are limitations in the application of a framework meant to
describe human conversation to a novel form of interaction. First, it is not
entirely clear whether people perceive AI to be human-like enough to apply
conversational rules at all. Second, given that exchanges with AI are
currently largely transactional (e.g., the human has a desired goal, and the
AI is expected to fulfill this desired goal), one could argue that an exchange
between a human and AI is not necessarily a conversation. These issues can be
summarized into two broad categories: human perception of AI entity and human
perception of the human-AI exchange.

With regard to human perception of AI, it is clear that AI has no free will to
actually follow a maxim. Nevertheless, several participants in the study
reported here personified the device, even applying verbs of volition to
describe the AI’s performance. For example, participants described Alexa’s
failure to perform a particular action with language like “She tried” and “She
did the very best that she could.” Such descriptions indicate that
participants — whether driven by the wake word, the marketing of the product,
or the fact that voice assistants are specifically designed to be human-like
and conversational — speak about AI as a volitional entity. It is thus a
natural step for them to also apply Grice’s maxims to such an entity.

With regard to human perception of the human-AI exchange, several participants
in the study also explicitly mentioned that they believe human-AI interactions
to be cooperative: they were both willing and eager to cooperate with the AI,
placing blame on themselves for unsuccessful exchanges or considering the
exchange to be game-like. One participant blamed himself for an unsatisfactory
Alexa response, saying, “I should’ve been more specific with my question.
That’s on me.” Another participant, after several attempts to rephrase a
question, expressed enjoyment rather than frustration, saying, “It’s actually
part of the fun, I figure out oh, she needs me to speak like this.” In this
way, participants demonstrated the they consider the exchange to be
cooperative, not simply one-sided in favor of the human. Given that the
exchange is language-based, it is therefore natural that they would also
assume the conversation to be guided by Grice’s maxims.

Lastly, for both perception of AI and the exchange, it should also be noted
that machine learning technology is rapidly evolving, making voice assistants
more human-like and conversational. In this way, we can expect human
perception of the AI’s conversational role to evolve alongside technological
advances.

## 6\. Conclusion

This study has demonstrated that Grice’s Cooperative Principle is a useful
framework for understanding human assessments of their interaction with AIs.
Based on the in-lab observations of twenty-three participants interacting with
an Alexa device, we report on over 700 exchanges that we identified as
potential maxim violations by the AI. Exploring participant commentary
referencing the potential maxim violations shows that, in broad terms,
participants do seem to be guided by these maxims in their evaluation of
interactions with AI; they judge interactions similarly to human-human
interactions, but with some small differences.

Specifically, the computer component of entities like Alexa seems to play an
important role in terms of user perceptions of AI. With Quantity, users do not
seem to be bothered by what is arguably ‘too much’ information, and this
expectation is likely driven by user expectations of a machine. In a similar
vein, for Quality, users are extremely trustful of Alexa’s responses. This
seems to be driven by assumptions that a computer query will deliver accurate
results. Of course, this may or may not be correct assumption, and it is an
important phenomenon that requires further research.

In addition, this study shows that Relevance is the most salient maxim
violation for the in-lab participants, occurring most frequently and rated
lower on average than the other maxim violations. In other words, users seem
to be more keyed in to violations of Relevance than any of the other maxims.
This observation is particularly useful for the development of future AIs,
where relevant exchanges seem to be key to user perceptions.

We also observe that there is an inherent power difference between humans and
AI, where humans take priority in all exchanges, as evident in turn-initiating
sequences and interruptions. To accommodate these observations, we posit a
Priority maxim that guides human-AI interactions. Of course, further research
needs to be done to validate the Priority maxim, as well as the extent to
which Grice’s Cooperative Principle helps explain user perceptions of human-AI
interactions.

This work is critical for multiple reasons. First, from an AI development
perspective, in order to improve AI systems like Alexa, it is important to
know how users assess exchanges and what framework they are using to make
those judgments. Second, while human-AI interactions may stretch the boundary
of the prototypical ‘conversation,’ it is clear that human-AI interactions are
becoming more and more prolific. There are multiple voice assistants
available, and the contexts in which they are available is ever-increasing.
This all means that the volume and variety of language-based interactions in
which humans are engaging with AI is steadily increasing, and, in our opinion,
this novel use of language warrants further research.

## References

  * Chaves & Gerosa (2018) Chaves, A.P. & M.A. Gerosa. 2018.  Single or multiple conversational agents? An interactional coherence comparison.  In _Proceedings of the 2018 CHI conference on human factors in computing systems_ , 1–13.
  * Deriu et al. (2019) Deriu, J., A. Rodrigo, A. Otegi, G. Echegoyeen, S. Rosset, E. Agirre & M. Cieliebak. 2019.  Survey on evaluation methods for dialogue systems.  arXiv preprint arXiv:1905.04071.
  * Grice (1975) Grice, H.P. 1975.  Logic and conversation.  In _Speech acts_ , Brill.
  * Habermas (1984) Habermas, J. 1984.  _The theory of communicative action_.  Beacon Press.
  * Harris (1995) Harris, S. 1995.  Pragmatics and power.  _Journal of Pragmatics_ 23(2). 117–135.
  * Kitis (1999) Kitis, E. 1999.  On relevance again: From philosophy of language across ‘pragmatics and power’ to global relevance.  _Journal of Pragmatics_ 31(5). 643–667.
  * Liao et al. (2016) Liao, Q.V., M. Davis, W. Geyer, M. Muller & N.S. Shami. 2016.  What can you do? Studying social-agent orientation and agent proactive interactions with an agent for employees.  In _Proceedings of the 2016 acm conference on designing interactive systems_ , 264–275.
  * Peirce et al. (2019) Peirce, J.W., J.R. Gray, S. Simpson, M.R. MacAskill, R. Hochenberger, H. Sogo, E. Kastman & J. Lindelov. 2019.  Psychopy2: Experiments in behavior made easy.  _Behavior Research Methods_ .
  * Portela & Granell-Canut (2017) Portela, M. & C. Granell-Canut. 2017.  A new friend in our smartphone? Observing interactions with chatbots in the search of emotional engagement.  In _Proceedings of the xviii international conference on human computer interaction_ , 1–7.
  * Purington et al. (2017) Purington, A., J.G. Taft, S. Sannon, N.N. Gazarova & S.H. Taylor. 2017.  “Alexa is my new BFF” social roles, user satisfaction, and personification of the Amazon Echo.  In _Proceedings of the 2017 CHI conference extended abstracts on human factors in computing systems_ , 2853–2859.
  * Schmitt & Ultes (2015) Schmitt, A. & S. Ultes. 2015.  Interaction quality: assessing the quality of ongoing spoken dialog interaction by experts—and how it relates to user satisfaction.  _Speech Communication_ 74\. 12–36.
  * Thornborrow (2014) Thornborrow, J. 2014.  _Power talk: Language and interaction in institutional discourse_.  Routledge.