Citation: Damgaard, M.R.; Pedersen,
R.; Bak, T. Study of Variational
Inference for Flexible Distributed
Probabilistic Robotics. Robotics 2022,
11, 38. https://doi.org/10.3390/
robotics11020038
Academic Editor: Dario Richiedei
Received: 2 February 2022
Accepted: 21 March 2022
Published: 24 March 2022
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Article
Study of Variational Inference for Flexible Distributed
Probabilistic Robotics
Malte Rørmose Damgaard * , Rasmus Pedersen and Thomas Bak
Department of Electronic Systems, Automation and Control, Aalborg University, 9220 Aalborg, Denmark;
rpe@es.aau.dk (R.P.); tba@es.aau.dk (T.B.)
* Correspondence: mrd@es.aau.dk
Abstract:
By combining stochastic variational inference with message passing algorithms, we show
how to solve the highly complex problem of navigation and avoidance in distributed multi-robot
systems in a computationally tractable manner, allowing online implementation. Subsequently,
the proposed variational method lends itself to more flexible solutions than prior methodologies.
Furthermore, the derived method is verified both through simulations with multiple mobile robots
and a real world experiment with two mobile robots. In both cases, the robots share the operating
space and need to cross each other’s paths multiple times without colliding.
Keywords:
distributed robotics; probabilistic robotics; variational inference; message-passing
algorithm
;
stochastic variational inference
1. Introduction
Uncertainty is an inherent part of robotics that must be dealt with explicitly through
the robust design of sensors, mechanics, and algorithms. Unlike many other engineering
research areas that also have to deal with uncertainties, robotics problems usually also
consist of a heterogeneous set of interconnected sub-problems and have strict real-time
requirements, making it even harder to deal with uncertainty in an appropriate manner [
1
].
A common approach to model uncertainties in robotics is to employ probability
mass functions and/or probability density functions, hereinafter jointly referred to as
probability distributions, over model variables. One can then represent many classical
robotics problems as a joint distribution,
p
(
x, z
)
, over observable variables,
x
, and latent
variables,
z
. Given the knowledge that the observable variables,
x
, can be assigned specific
values
x
, solving the problem then boils down to solving the posterior inference problem
given by the conditional distribution
p
(
z|x = x
)
=
p
(
x = x, z
)
p
(
x = x
)
(1)
=
p
(
x = x, z
)
R
p
(
x = x, z
)
dz
. (2)
Unfortunately, the marginalization by the integral in the denominator of Equation (2)
is, in general, intractable to compute in most realistic problems, and thereby the reason
why one often has to resort to approximate inference [2].
The classical solution to this problem has been to simplify the model of a problem,
p
,
sufficiently to obtain an approximate problem definition,
q ≈ p
, for which one can derive or
use analytical solutions such as the Kalman filter [3], henceforth referred to as the “model
simplification method”. Typically, it is only possible to derive analytical solutions for a
very limited set of probability distributions. Thereby, it may be necessary to apply crude
approximations to obtain a solution, making it a rather inflexible method. However, such
solutions tend to be computationally efficient, which is why they were commonly used
Robotics 2022, 11, 38. https://doi.org/10.3390/robotics11020038 https://www.mdpi.com/journal/robotics
