Bayesian inference for motion control and planning

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.