# Online Information-Aware Motion Planning with Inertial Parameter Learning
for Robotic Free-Flyers

Monica Ekal1∗, Keenan Albee2∗, Brian Coltin3, Rodrigo Ventura1, Richard
Linares2, and David W. Miller2 *Both authors contributed equally to this
work.1Institute for Systems and Robotics, Instituto Superior Técnico, {mekal,
<EMAIL_ADDRESS>Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, {albee, linaresr,
<EMAIL_ADDRESS>SGT Inc., NASA Ames Research Center<EMAIL_ADDRESS>
###### Abstract

Space free-flyers like the Astrobee robots currently operating aboard the
International Space Station must operate with inherent system uncertainties.
Parametric uncertainties like mass and moment of inertia are especially
important to quantify in these safety-critical space systems and can change in
scenarios such as on-orbit cargo movement, where unknown grappled payloads
significantly change the system dynamics. Cautiously learning these
uncertainties en route can potentially avoid time- and fuel-consuming pure
system identification maneuvers. Recognizing this, this work proposes RATTLE,
an online information-aware motion planning algorithm that explicitly weights
parametric model-learning coupled with real-time replanning capability that
can take advantage of improved system models. The method consists of a two-
tiered (global and local) planner, a low-level model predictive controller,
and an online parameter estimator that produces estimates of the robot’s
inertial properties for more informed control and replanning on-the-fly; all
levels of the planning and control feature online update-able models.
Simulation results of RATTLE for the Astrobee free-flyer grappling an
uncertain payload are presented alongside results of a hardware demonstration
showcasing the ability to explicitly encourage model parametric learning while
achieving otherwise useful motion.

##  I Introduction

Robotic space systems are gearing up to perform a variety of tasks
autonomously, including in-space assembly and payload transportation [1] [2]
[3] [4] [5]. Precise execution of these tasks means that acceptable
characterization of the dynamical system involved is often necessary. However,
there is frequently underlying uncertainty in these systems; in addition to
any existing model uncertainty, fuel depletion and grasping of payloads can
further modify the inertial characteristics of the system during operation.
Moreover, operation in cluttered, dynamic environments such as the interior of
an orbiting space station calls for re-planning of trajectories in real-time
to account for system and environmental changes, e.g., other free-floating
payloads. Fortunately, some forms of uncertainty like inertial properties are
parametric and can be resolved using knowledge of the system model. One key
example of this is payload manipulation by robotic free-flyers, robots that
propel themselves in microgravity.

Figure 1: The Astrobee robotic free-flyer on an air-bearing grasping a new
payload using its underactuated gripper.

NASA’s Astrobee robot (Fig. 1), recently deployed to the International Space
Station (ISS), is a prime example of a free-flying robotic system [6] [7] [8]
[9]. With proposed uses including automatic cargo repositioning onboard future
microgravity outposts, Astrobee includes a robotic manipulator for grappling
payloads and perching [10]. Astrobee’s proposed functionality is a key example
of the need to account for system model changes and the underlying or
inherited system uncertainty. Operating around moving astronauts and free-
floating cargo, these systems must account for parametric model uncertainty or
face poor trajectory tracking and inefficient execution, as recently shown in
[11].

This places the robotic free-flying motion planning problem in the context of
motion planning under parametric uncertainty. Existing planning under
parametric uncertainty approaches are wide-ranging, but can be broadly placed
into two categories. Some approaches attempt full system identification (sys
ID) before even attempting motion planning [12], [13, 14] followed by planning
with the estimated nominal model; otherwise, robust or chance-constrained
approaches that operate under an assumed uncertainty bound [15] [16] [17] are
applied. Many approaches from robust and adaptive control can be applied to
the uncertain tracking problem, but do not address the higher-level motion
planning. Direct adaptive control [18] and sliding mode control can be
employed to reject disturbances from parametric model uncertainty [19], [20],
[21]. Indirect adaptive control approaches on the other hand, pair an
estimator and a controller, relying on the estimator to provide a better model
for the control method under the condition of a persistently exciting control
signal [22], [23]. Providing robustness against assumed uncertainty bounds
neglects the higher-level motion planning problem, and does not consider
online reduction of uncertainty. For learnable robotic parametric unknowns,
replanning capability is desirable due to an evolving understanding of the
unknown parameters; further, excitation might be desired in order to aid in
this model-learning process.

Relevant approaches explicitly consider the value of parametric information-
awareness in the motion planning. They include a POMDP formulation with
covariance minimization in the cost function [24], which was only demonstrated
for an unconstrained double integrator system with uncertain mass, and recent
work on covariance steering [25] [26], which attempts to answer exactly when
system excitation is most useful for model uncertainty resolution. However,
these approaches have not yet been implemented on hardware, their scalability
has not yet been demonstrated, and they do not address some of the
practicalities of motion planning such as dealing with global long-horizon
planning.

This paper proposes a method called RATTLE (Real-time information-Aware
Targeted Trajectory planning for Learning via Estimation) that combines
parameter information-aware motion planning with real-time model updates.
Building on the the authors’ previous work [27] where the idea of making
trajectory progress while accounting for information gain was explored, RATTLE
proposes a user-adjustable weighting toward gaining information about
parametric uncertainties to aid an online parameter estimator, with the
ultimate goal of incorporating model updates. The approach is real-time
receding-horizon, with the ability to also incorporate replanning. Further,
the user-specified information weighting can be customized for the environment
and dynamics at hand. Compared to traditional up-front sys ID, this approach
only applies as much excitation as desired simultaneously with goal-achieving
motion. The intent is to avoid interrupting the current maneuver and spending
time on full sys ID if a sufficient amount of uncertainty reduction can
instead be performed online, during otherwise useful motion.

RATTLE is especially relevant for free-flyer load transportation scenarios,
where an uncharacterized grappled payload might change the dynamics
dramatically (and parametrically). Space systems requiring careful execution
in cluttered space station interiors will benefit from a learning, replanning
approach that is not overly conservative. To the authors’ knowledge, this is
the first time that a parametric information-aware planning algorithm with
uncertainty reduction by parameter learning has been used for for robotic
free-flyers. Though RATTLE has been employed specifically for this robotic
free-flyer load transportation scenario, the algorithm’s applicability extends
to many systems with parametric model unknowns.

The main contributions of this paper are:

  1. 1.

RATTLE, a novel motion planning method for creating selectively information-
aware plans with online parameter estimation to reduce parametric uncertainty;

  2. 2.

The incorporation of global motion planning into such an approach;

  3. 3.

Validation of the approach via a high-fidelity simulation of the Astrobee
free-flyer transporting payload under ground testing dynamics and proof of
concept results on the Astrobee hardware, demonstrating improved parametric
model learning under information-aware planning.

Section I has introduced planning under parametric uncertainty and
applications to robotic free-flyers in particular; Section II formulates the
parametric information-aware motion planning problem and introduces the free-
flying dynamics; Section III introduces RATTLE, a novel parametric
information-aware motion planning algorithm; Section IV demonstrates RATTLE’s
implementation, shows simulation and hardware results, and explains some of
the method’s key characteristics; Section V discusses the implications of the
approach and what improvements are now being pursued.

##  II Problem Formulation

A robotic system with state $\mathbf{x}\in\mathbb{R}^{n}$, input
$\mathbf{u}\in\mathbb{R}^{m}$, and uncertain parameters
$\boldsymbol{\theta}\in\mathbb{R}^{j}$ is initially positioned at state
$\mathbf{x}_{0}$. A region of the state space that is admissible is specified
as $\mathcal{X}_{free}$, and a constraint on inputs may also be provided as
$\mathcal{U}$. A goal region $\mathcal{X}_{g}$ is also specified. Let the
dynamics and measurement models of the system be represented as

$\displaystyle\dot{\mathbf{x}}=f(\mathbf{x},\mathbf{u},\boldsymbol{\theta})+\mathbf{w}_{x}$
(1)
$\displaystyle\tilde{\mathbf{y}}=h(\mathbf{x},\mathbf{u},\boldsymbol{\theta})+\mathbf{w}_{y},$
(2)

where the vector of the measured quantities is
$\tilde{\mathbf{y}}\in\mathbb{R}^{l}$,
$\mathbf{w_{x}}\sim\mathcal{N}\left(0,\bm{\Sigma}_{Q}\right)$, and
$\mathbf{w_{y}}\sim\mathcal{N}\left(0,\bm{\Sigma}_{R}\right)$ where
$\mathcal{N}$ represents a Gaussian. Only initial estimates of the parameters
are known,
${\boldsymbol{\theta}_{0}}\sim\mathcal{N}(\boldsymbol{\hat{\theta}}_{0},\mathbf{\Sigma}_{\bm{\theta},0})$.

The aim is to plan a trajectory minimizing the following cost function while
respecting the input and state constraints, $\mathcal{U}$ and
$\mathcal{X}_{free}$,

$\displaystyle
J(\mathbf{x},\mathbf{u},t)=g(\mathbf{x}(t_{f}),\mathbf{u}(t_{f}))+\int_{t_{0}}^{t_{f}}l(\mathbf{x}(t),\mathbf{u}(t))\
dt.$ (3)

Here, $g(\mathbf{x}(t_{f}),\mathbf{u}(t_{f}))$ is a terminal cost and
$l(\mathbf{x}(t),\mathbf{u}(t))$ is an accumulated cost, computed over the
current nominal system model. Since knowledge of $\boldsymbol{\theta}$ can be
improved through parameter estimation, it is possible to obtain an enhanced
dynamics model that is a closer representation of reality. Details on the
problem setup are also provided in [27]. Even in the deterministic case, the
motion planning problem is known to be at least PSPACE-hard and often requires
approximate solutions [28].

###  II-A Rigid body dynamics

The dynamics model of interest for robotic free-flyers is the rigid body
dynamics with uncertain inertial parameters. The linear and angular dynamics
for a 6 DOF rigid body expressed in a body-fixed frame not coincident with the
center of mass are

$\displaystyle\begin{split}\begin{bmatrix}\mathbf{F}\\\
\boldsymbol{\tau}_{{CM}_{0}}\end{bmatrix}&=\begin{bmatrix}m\mathbf{I}_{3}&-m[\mathbf{c}]_{\times}\\\
-m[\mathbf{c}]_{\times}&\mathbf{I}_{CM}-m[\mathbf{c}]_{\times}[\mathbf{c}]_{\times}\end{bmatrix}\begin{bmatrix}\dot{\mathbf{v}}\\\
\dot{\boldsymbol{\omega}}\end{bmatrix}+\\\
&\begin{bmatrix}m[\mathbf{w}]_{\times}[\mathbf{w}]_{\times}\mathbf{c}\\\
[\mathbf{w}]_{\times}\left(\mathbf{I}_{CM}-m[\mathbf{c}]_{\times}[\mathbf{c}]_{\times}\right)\boldsymbol{\omega}\end{bmatrix}\end{split}$
(4)

where ${\mathbf{v}}$, $\bm{\omega}\in\mathbb{R}^{3}$ denote the linear
velocity and angular velocity of the original center of mass (CM0),
$\mathbf{I}_{CM}$ is the inertia tensor about the center of mass (CM), $m$ is
the system mass, and $\mathbf{c}\in\mathbb{R}^{3}$ is the CM offset from CM0.
$\mathbf{F},\bm{\tau}\in\mathbb{R}^{3}$ are the forces and torques applied
through the $\mathcal{F}_{B}$ body frame, where $\mathcal{F}$ indicates a
frame as in Fig. 2. $[-]_{\times}$ is used to indicate a cross product matrix.
Note that these dynamics are significantly more complex than the Newton-Euler
equations of forces and torques in the center of mass fixed frame. For a 3 DOF
case commonly used in granite table free-flyer testing as in Fig. 1, the
equations can be written as,

$\displaystyle
F_{x}=m\left[\dot{v}_{x}-\dot{\omega}_{z}c_{y}-\omega_{z}^{2}c_{x}\right]$ (5)
$\displaystyle
F_{y}=m\left[\dot{v}_{y}+\dot{\omega}_{z}c_{x}-\omega_{z}^{2}c_{y}\right]$ (6)
$\displaystyle\tau_{z_{0}}=mc_{x}\dot{v}_{y}-mc_{y}\dot{v}_{x}+\left[{I_{zz,CM}}+m\left(c_{y}^{2}+c_{x}^{2}\right)\right]\dot{\omega}_{z}$
(7) which can be conveniently grouped into matrix form,
$\displaystyle\mathbf{F}=\begin{bmatrix}\mathbf{M}\end{bmatrix}\mathbf{\dot{x}}+\begin{bmatrix}\mathbf{C}\end{bmatrix}\mathbf{x}.$
(8)

These dynamics are also described in [29, 30] and are shown for the 3 DOF case
in Fig. 2. The parameter vector of interest is
$\boldsymbol{\theta}=\left\\{m,c_{x},c_{y},I_{zz}\right\\}$.

Figure 2: The 3 DOF rigid body dynamics model for free-flyers. An original
system CM0 located at $\mathcal{F}_{B}$ is offset by $\mathbf{c}$, with new
system mass $m$ and $\hat{z}$ moment of inertia $I_{zz}$. Note that
$\mathbf{T}_{WB}$ indicates body pose with respect to world frame.

##  III Approach: Information-Aware Planning Algorithm

Figure 3: A sketch of the RATTLE planning framework, demonstrating high-level
(global) long-horizon planning via kino-RRT, and mid-level shorter-horizon
(local) planning incorporating information-aware planning via an adjustable
weighting term, $\gamma$. An online update-able controller, MPC, also benefits
from a more accurate system model. Note that horizon lengths are not
necessarily to scale.

###  III-A RATTLE Overview

RATTLE is an information-aware motion planning method which aims to directly
add informative motion when desired en route, allowing one to improve model
parameter estimates online. Compared to full system identification performed
prior to planning, this approach offers time savings (and potential fuel
savings) by allowing useful model information to be learned en route via an
explicit weighting on information-awareness in the motion planning. Compared
to non-informative planning approaches, RATTLE offers a framework for trading
off standard state and fuel cost minimization with the ability to perform
model-improving actions; this allows the robot to take control of its level of
parametric model knowledge directly via motion planning, rather than ignoring
model improvement altogether.

RATTLE consists of four key ingredients:

  * •

A high-level (global) planner

  * •

A mid-level (local) information-aware planner

  * •

A low-level model predictive controller

  * •

An online parameter estimator

As shown in Fig. 3, a global planner that excels at handling e.g., obstacle
constraints and long time horizons is used to produce a nominal global plan,
using a nominal set of dynamics (Section III-B). Portions of this global plan
are used as waypoints in guiding the local planner, which incorporates an
information awareness metric and operates over a shorter time horizon (Section
III-C). Online, waypoints and information weighting may be updated at each
replan of the local plan. The division into a global and local planner is in
recognition of the fact that the general informative long-horizon trajectory
planning problem is not computationally tractable; the common approach of
using e.g., a sampling-based planner to perform global planning is proposed.
At the lowest level, a model predictive controller runs at the fastest rate
and continually incorporates model updates (Section III-D). A recursive
parameter estimator runs continually, passing off the latest available model
information for each planning/control element to use as desired (Section
III-E). The RATTLE algorithm is outlined in Fig. 4. The subsections that
follow describe each of these components and the estimator in further detail.

###  III-B High-Level (Global) Planner: Kinodynamic RRT

Sampling-based planners (SBPs) operate based on growing a tree or graph of
sample points $\mathbf{x}_{i}$ within a sample space $\mathcal{X}_{free}$ and
have been applied to a large number of robotic motion planning problems [31].
A key advantage of SBPs is that difficult constraints, like collision-
checking, can be explicitly checked during exploration of the state space.
This framework uses kino-RRT, a variant of the popular rapidly exploring
random tree (RRT) algorithm. kino-RRT includes the robot dynamics and is a
good candidate for a long-horizon planner when numerical optimization-based
planning becomes impractical [32]. The reader is referred to Karaman for
implementation specifics [33]. Utilizing the advantage of a direct collision
checking module, one may use ellipsoidal constraints for instance in order to
perform simple collision checking; such constraints are common for space
robotics motion planning scenarios [34]. The result of this initial long-
horizon planning is a path, $\mathcal{P}_{g}$, of
$\mathbf{x}_{0:{N_{g}}}\in\mathcal{X}_{free}$, where each node obeys
$\mathbf{x}_{k+1}=f(\mathbf{x}_{k},\mathbf{u}_{k})$ and any additional
enforced constraints. Dynamics propagation is typically accomplished using a
set of representative motion primitives. The kino-RRT is represented as the
green solid line in Fig. 3, with motion primitive actions connecting adjacent
waypoints. Global planning is nominally performed only once prior to motion,
but online recomputation is enabled by reasonable solve times relative to the
dynamics of interest (e.g., a few seconds for robotic free-flyers).

###  III-C Mid-Level (Local) Planner: Information-Aware Receding Horizon
Trajectory Planner

The mid-level planner performs receding-horizon, information-aware planning.
Starting off with the high-level, global plan $\mathcal{P}_{g}$ given by the
kino-RRT, the planner plans trajectories between selected waypoints using
updated information about the robot’s model $\mathcal{M}$ based on the latest
parameter knowledge $\boldsymbol{\theta}_{k}$. Significantly, this planner has
the ability to optimize a cost function that introduces excitation or richness
in the trajectories, thus facilitating the estimation of dynamic parameters
alongside traditional state error and input use. The result is the ability to
assign system excitation as desired while accomplishing otherwise useful
motion.

####  III-C1 Calculation of Fisher Information

Fisher information is employed as an information-theoretic metric in the cost.
The Fisher Information Matrix (FIM) [35] is a measure of the amount of
information given by an observation $\tilde{y}$ about a parameter of interest,
$\theta$. Assuming that there is no process noise in the parameter model,
i.e., $\boldsymbol{\theta}_{k+1}=\boldsymbol{\theta}_{k}$, and due to the
Gaussian nature of the measurement noise and linear measurement model, over
time $t_{0}..,t_{N}$, the FIM is

$\mathbf{F}=\sum_{k=0}^{N}\mathbf{H}(t_{k})^{T}\mathbf{\Sigma}^{-1}\mathbf{H}(t_{k})$
(9) $\begin{gathered}\mathbf{H}(t_{k})=\frac{\partial
h(\mathbf{x}(t_{k}),\mathbf{u}(t_{k}),\boldsymbol{\theta})}{\partial\boldsymbol{\theta}}+\\\
\frac{\partial
h(\mathbf{x}(t_{k}),\mathbf{u}(t_{k}),\boldsymbol{\theta})}{\partial\mathbf{x}}\cdot\frac{\partial\mathbf{x}(\mathbf{x}(t_{k}),\mathbf{u}(t_{k}),\boldsymbol{\theta})}{\partial\boldsymbol{\theta}}.\end{gathered}$
(10)

More details on calculation of the FIM can be found in [36], [37] and the
authors’ previous work [27]. A cost function is constructed to minimize the
trace of the inverse of the FIM, also known as the A-optimality criterion.
This is equivalent to minimizing the axis lengths of the uncertainty ellipsoid
over the parameters.

As is common in trajectory optimization problems, dynamics equation (3) is
discretized. The optimization problem solved by the mid-level planner over the
horizon is then

$\begin{aligned}
&\underset{\mathbf{u}}{\text{minimize}}&&J=\sum_{k=0}^{N-1}{\mathbf{x}^{T}_{t+k}\mathbf{Q}\mathbf{x}_{t+k}+\mathbf{u}^{T}_{t+k}\mathbf{R}\mathbf{u}_{t+k}}+\gamma
tr\left(\mathbf{F}^{-1}\right)\\\ &\text{subject
to}&&\mathbf{x}_{t+k+1}=f(\mathbf{x}_{t+k},\mathbf{u}_{t+k}),k=0,..,N-1\\\
&&&\mathbf{x}_{t+k}\in\mathcal{X}_{free},k=0,..,N,\\\
&&&\mathbf{u}_{t+k}\in\mathcal{U},k=0,..,N-1,\\\ \end{aligned}$

(11)

where $N$ is the length of the horizon and $\mathbf{Q}\succ 0$ and
$\mathbf{R}\succ 0$ are positive definite weighting matrices. The extent of
information-richness in the trajectory can be adjusted with the relative
weighting term $\gamma$. Mid-level planning occurs on timescales of
approximately every few seconds, providing local plans of sufficient length to
allow for system excitation without excessive recomputation “chattering”.

###  III-D Low-Level Controller: Nonlinear Model Predictive Controller

Model predictive control (MPC) is a control scheme that casts an optimal
control problem as a mathematical optimization problem that is solved
repeatedly online. Using discrete inputs as decision variables, inputs are
found to minimize a cost function while satisfying constraints including the
system dynamics, based on model $\mathcal{M}$. At its core MPC relies on a
mathematical optimization solver to provide inputs over the designated time
horizon, only the first of which is executed before recomputation is performed
online. In the RATTLE framework, nonlinear MPC (NMPC) solves the optimization
problem given in equation (11) with $\gamma=0$ over a shorter horizon,
allowing for faster control free of information metrics. NMPC was selected as
the controller mainly for its ability to update model parameters on-the-fly
and to incorporate input and state constraints while determining control
inputs [38]. Low-level NMPC operates on timescales of approximately a few tens
or hundreds of milliseconds, depending on the system of interest.

###  III-E Online Parameter Estimation: Extended Kalman Filter

An extended Kalman filter (EKF) is used for parameter estimation in this
framework. The EKF is a non-linear extension of the Kalman filter, obtained by
first-order Taylor linearization of the error dynamics about the current
estimate. Employing a filtering approach for parameter estimation in the
RATTLE framework allows the estimation and thus the model updating to be
performed sequentially and in real-time.

1:procedure
RATTLE($\mathbf{x}_{0},\mathcal{X}_{g},\boldsymbol{\theta}_{0},\mathbf{Q},\mathbf{R},\mathcal{M}$)

2: InitParamEst($\boldsymbol{\theta}_{0}$)

3: $\mathcal{P}_{g}\leftarrow$
GlobalPlan($\mathbf{x}_{0},\mathcal{X}_{g},\mathcal{M}$)

4: $k=0$

5: while $\mathbf{x}_{k}\not\in\mathcal{X}_{g}$ do

6: if $\mathcal{P}_{g}\texttt{ replan requested}$ then

7: $\mathcal{P}_{g}\leftarrow$
GlobalPlan($\mathbf{x}_{k},\boldsymbol{\theta}_{k},\mathcal{X}_{g},\mathcal{M}$)

8: $\gamma\leftarrow\texttt{GetInfoWeight}(k)$

9:
$\mathcal{P}_{l},N_{l}\leftarrow\texttt{LocalInfoPlan}(\mathbf{x}_{k},\boldsymbol{\theta}_{k},\mathcal{P}_{g},\mathcal{M},\gamma)$

10: while $k<N_{l}$ do

11:
$\mathbf{u}_{k}\leftarrow\texttt{NmpcControl}(\mathbf{x}_{k},\boldsymbol{\theta}_{k},\mathcal{P}_{l},\mathcal{M})$

12: $\mathbf{x}_{k+1}=f(\mathbf{x}_{k},\mathbf{u}_{k})$ $\triangleright$
system dynamics

13:
$\boldsymbol{\theta}_{k+1}\leftarrow\texttt{ParamEst}(\boldsymbol{\theta}_{k},\mathbf{\tilde{y}}_{k},\mathbf{u}_{k})$

14: $k=k+1$

15:

16:procedure
LocalInfoPlan($\mathbf{x}_{k},\boldsymbol{\theta}_{k},\mathcal{P}_{g},\mathcal{M},\gamma$)

17:
$\mathcal{M}\leftarrow\texttt{UpdateModel}(\boldsymbol{\theta}_{k},\mathcal{M})$

18: UpdateCost$(k)$

19: $\mathbf{x}_{N},N_{l}\leftarrow\texttt{UpdateWaypoint}(k,\mathcal{P}_{g})$

20:
$\mathcal{P}_{l}\leftarrow\texttt{RunTrajOpt}(\mathbf{x}_{k},\mathbf{x}_{N},\texttt{CalcFisher}(),\mathcal{M})$

21: return $\mathcal{P}_{l},N_{l}$

Figure 4: The algorithmic overview of the RATTLE framework. Note that
$\mathcal{M}$ indicates a system model, consiting of $f(-)$ and $h(-)$ as in
equation 2 with accompanying constraints $\mathcal{X}_{free}$ and
$\mathcal{U}$. $N_{l}$ indicates a local plan horizon length index, and
$\mathcal{P}_{[-]}$ indicates a plan, i.e., a set of $\mathbf{x}_{k:k+N}$ and
$\mathbf{u}_{k:k+N}$ over a time horizon.

##  IV Results

RATTLE was validated in a high-fidelity simulator of the free-flyer dynamics
of NASA’s Astrobee robot; a proof of concept demonstration of the information-
aware planning and parameter estimator was also carried out on Astrobee
hardware at the NASA Ames granite table facility111A granite table is a near-
frictionless surface used for simulating the microgravity free-flyer dynamics.
They also require impeccable cleaning for successful tests, which the authors
were able to partake in firsthand..

The Astrobee free-flyer is a cube-shaped robot, measuring 32 cm per side [8].
Its holonomic propulsion system draws in air through two central impellers,
which is expelled precisely through 12 exhaust nozzles for thrust [7]. The
Astrobee Robot Software uses ROS as middleware for communication, with about
46 nodelets grouped into approximately 14 processes running on two ARM
processors [6] [39]. The Astrobee Robot Software consists of a simulator,
which enables testing of developed algorithms before implementation on
hardware. The simulator is essentially a set of plug-ins for the Gazebo robot
simulator, which offer the same ROS interfaces as the hardware. The
ROS/Gazebo-based simulation environment includes extensive modeling of
Astrobee including its impeller propulsion system, onboard visual navigation,
environmental disturbances, and many more true-to-life models [6].

A few key properties of the motion planning method were demonstrated.
Primarily, the ability of the method to selectively add parameter information
gathering was shown by setting informative values of $\gamma$. The convergence
of system parameter estimates was then compared to tests in which no
information weighting was provided. This illustrated the improved quality of
parameter estimates with on-the-fly parameter learning, thus offering the
ability to make goal-achieving plans that also accomplish parameter learning,
as opposed to conventional system identification. The full RATTLE pipeline was
demonstrated in simulation to show the selective addition of informativeness
to goal-achieving plans. Hardware results were also obtained specifically for
the mid-level planner, showing targeted parameter learning for a regulation
task. Ground truth parameter values used for both experiments are shown in
Table I.

Figure 5: Examples of the global planner under different obstacle constraints.
Here, global plans are shown in green with obstacles shown in red.

###  IV-A Simulation Demonstration: RATTLE in the Astrobee High-Fidelity 3 DOF
Simulation

Figure 6: Parameter estimates while tracking without information-aware
planning (blue), and with information-awareness (red) for the robot-grasping-
payload system in simulation. Four parameters of interest are shown for each
case, and ground truth values are shown in black. Three runs of each case are
illustrated with 1-sigma confidence shown as a highlight.

The RATTLE framework was implemented in the high-fidelity Astrobee
simulation222https://github.com/nasa/astrobee to demonstrate its capabilities
for a 3 DOF cargo re-positioning scenario, matching the environment and
dynamics used for hardware testing. After Astrobee rigidly grapples a payload
as in Fig. 1 or Fig. 8, the ground truth parameters
$\boldsymbol{\theta}=\left\\{m,c_{x},c_{y},I_{zz}\right\\}$ change and
parametric uncertainty enters the problem. Equipped with the payload, Astrobee
was tasked with moving within a tolerance of a goal region $\mathcal{X}_{g}$.
Note that Astrobee has severe input limits of $u_{max}\leq 0.4\ [N]$, meaning
that system inertial parameters are particularly important to know before
safety critical maneuvering is needed.

A kinodynamic RRT for the translational states was used as a global planner.
Some examples of the planner’s flexibility are shown in Fig. 5, which also
shows an example of the granite table simulation environment. Any real-time
global planning method could be used, but kinodynamic RRT was selected because
it uses dynamics model knowledge in its planning but with real-time
computation capabilities. An $n=50$ Monte Carlo set of test runs was performed
on the randomly reordered obstacle world of the bottom left of Fig. 5 to
demonstrate real-time properties. Running on a quad-core Intel i7-4700MQ
machine alongside the full Astrobee autonomy stack, a C++ implementation of
the global planner computed plans in $3.59\pm 3.63\ [s]$ for $\sim 2\ [m]$
global plans with obstacle density of $\sim 30\%$. This was a particularly
challenging scenario—in practice for tests as in Fig. 8 runtimes were usually
below $0.5\ $ [s].

The ACADO toolkit [40] was used to implement the nonlinear programming-based
information-aware local planner running with a replan period of $12\ $[s] and
the low-level model predictive controller running at $10\ $[Hz]. The
information-aware mid-level planning scheme of Section III-C was used, with an
exponentially decaying weighting on $\mathbf{\gamma}$ with time constant
$\tau$ of $\frac{1}{10}$ the global plan horizon. The number of local replans
used was 11. A sample run of RATTLE can be seen in Fig. 7, where the global
plan is tracked by local plans containing desired levels of information-
awareness. As this weighting decreases and estimation accuracy improves, the
controller and planner models resemble the system behaviour to a greater
degree of accuracy. The parameter estimator used poses and twists from
Astrobee’s localization algorithm, along with the applied forces and torques
as inputs. Estimated parameters were incorporated into the system model of the
local planner and controller at a period of $16\ $[s]. This avoided updates
using transient estimates and controller instabilities due to a rapidly
changing system model. The parameter estimation comparison is shown explicitly
in Fig. 6, where non-informative plans for three representative runs are shown
at left (blue) compared to information-aware plans at right (red). $\hat{m}$
and $\hat{I}_{zz}$ in particular show improvement in information-aware plans,
while poor observability rendered accurate center of mass estimates difficult
to obtain for both cases.

Figure 7: An example of a robot-grasping-payload information-aware trajectory using RATTLE, in simulation. The yellow dot denotes the start point. Note the reduction of excitation in local plans towards the end of the trajectory. |  Astrobee+ Arm+Carriage |  Payload+ Carriage |  Combined System ($I_{zz}$ about CM)
---|---|---|---
Sim |  |  |
$m\ $[kg] | 19.568 | 11.8 | 31.368
$I_{zz}\ $[kg-m2] | 0.282 | 0.015 | 0.980
$c_{x}\ $[m] | 0.0 | 0.0 | 0.0
$c_{y}\ $[m] | 0.0 | -.305 | -0.115
Hardware |  |  |
$m\ $[kg] | $19.0$ | 11.8 | 30.8
$I_{zz}\ $[kg-m2] | $0.25$ | 0.015 | 0.94
$c_{x}\ $[m] | $0.0$ | $0.0$ | 0.0
$c_{y}\ $[m] | 0.0 | -.305 | -0.12
Table I: Simulation and hardware ground truth values. Note that hardware
values are approximations, accounting for gas level, arm extension, and number
of batteries used. Figure 8: Top-down view of the test setup used for Fig. 6,
representing a room with a narrow opening and cluttered obstacles inside
(inflated for Astrobee radius). Here, the global plan can be seen in green
with a local plan (with some information weighting) in red.

###  IV-B Hardware Demonstration: Information-Aware Motion Planning Proof of
Concept on 3 DOF Astrobee Testbed

A series of hardware tests were conducted on the Astrobee free-flyer granite
table facility, using a “without payload” and “with payload” configuration,
shown in Fig. 1, using nominal and information-aware versions of the mid-level
planner. Experiments included a three-waypoint maneuver; variance of estimates
of the targeted parameters was compared post-maneuver between nominal and
information-aware planning, with results indicated in Table II. The mid-level
planner ran onboard Astrobee, providing real-time updates at 3 Hz. $I_{zz}$ in
particular saw a large reduction in variance when information-aware planning
was used, as rotational excitation was not as frequently used in nominal
planning. This indicates the dramatic affect of intentional excitation in
parameter information-awareness for parameters which are not otherwise
excited; notably, mass saw little variation between nominal and information-
aware planning since nominal plans already include translational excitation.

| Without Payload | With Payload
---|---|---
$I_{zz}$ Covariance $[$% Change$]$ | -25.01% | -38.05%
$m$ Covariance $[$% Change$]$ | 2.47% | -3.71%
Table II: Parameter estimate variance reduction of information-aware plans
relative to non-informative plans for hardware testing. Decreases indicate
greater precision of estimated model parameters. Both “without payload” and
“with payload” cases are shown (average of three runs at the final timestep of
motion).

##  V Conclusion

This paper introduced RATTLE (Real-time information-Aware Targeted Trajectory
planning for Learning via Estimation) for robotic systems operating under
parametric uncertainty. Particularly relevant for free-flyer cargo
transportation scenarios, this method encourages model-learning through
information-awareness in motion planning while fulfilling the primary control
objectives. A sampling-based global planner (kinodynamic RRT) and a receding
horizon planner that maximizes information content of a local trajectory
constitute the planning module. Non-linear model predictive control (NMPC) is
used for trajectory tracking. An online filtering estimator, EKF in this case,
provides real-time model updates for all planning and control elements,
providing an improved system model for future use. The ability of this
framework to plan for information gain and the resulting improvement in
estimate accuracy was validated with results from high-fidelity 3 DOF
simulation of the Astrobee free-flyer, as well as granite table hardware
testing using Astrobee; video results are
available333https://youtu.be/Kim32sjs2VM. Future work aims to expand
robustness guarantees to the approach, refine methods of updating the global
plan, discuss RATTLE tuning in further detail, and explore the application of
the approach to 6 DOF Astrobee cargo transportation on the International Space
Station.

## Acknowledgments

Funding for this work was provided by the NASA Space Technology Mission
Directorate through a NASA Space Technology Research Fellowship under grant
80NSSC17K0077. This work was also supported by the LARSyS - FCT Plurianual
funding 2020-2023, P2020 INFANTE project 10/SI/2016, and an MIT Seed Project
under the MIT Portugal Program. The authors gratefully acknowledge the support
that enabled this research. The authors would like to thank Marina Moreira,
Ruben Garcia Ruiz, and the Astrobee team at NASA Ames for their help in
setting up the hardware for experiments. Thank you to Alex Cabrales and Oliver
Jia-Richards for insightful conversations.

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