Bayesian inference for motion control and planning
Technical University Berlin, Technical Report.
Bayesian motion control and planning is based on the idea of fusing motion objectives
(constraints, goals, priors, etc) using probabilistic inference techniques in a way similar
to Bayesian sensor fusing. This approach seems promising for tackling two fundamental
problems in robotic control and planning: (1) Bayesian inference methods are an ideal candidate
for fusing many sources of information or constraints – usually employed in the sensor
processing context. Complex motion is characterised by such a multitude of concurrent constraints
and tasks and the Bayesian approach provides a solution of which classical solutions
(e.g., prioritised inverse kinematics) are a special case. (2) In the future we will require planning
methods that are not based on representing the system state as one high-dimensional
state variable but rather cope with structured state representations (distributed, hierarchical,
hybrid discrete-continuous) that more directly reflect and exploit the natural structure of the
environment. Probabilistic inference offers methods that can in principle handle such representations.
Our approach will, for the first time, allow to transfer these methods to the realm
of motion control and planning.
The first part of this technical report will review standard optimal (motion rate or dynamic)
control from an optimisation perspective and then derive Bayesian versions of the classical
solutions. The new control laws show that motion control can be framed as an inference problem
in an appropriately formulated probabilistic model. In the second part, by extending the
probabilistic models to be Markovian models of the whole trajectory, we show that probabilistic
inference methods (belief propagation) yield solutions to motion planning problems. This
approach computes a posterior distribution over trajectories and control signals conditioned
on goals and constraints.