  A new belief space planning algorithm, called covariance steering Belief
RoadMap (CS-BRM), is introduced, which is a multi-query algorithm for motion
planning of dynamical systems under simultaneous motion and observation
uncertainties. CS-BRM extends the probabilistic roadmap (PRM) approach to
belief spaces and is based on the recently developed theory of covariance
steering (CS) that enables guaranteed satisfaction of terminal belief
constraints in finite-time. The nodes in the CS-BRM are sampled in belief space
and represent distributions of the system states. A covariance steering
controller steers the system from one BRM node to another, thus acting as an
edge controller of the corresponding belief graph that ensures belief
constraint satisfaction. After the edge controller is computed, a specific edge
cost is assigned to that edge. The CS-BRM algorithm allows the sampling of
non-stationary belief nodes, and thus is able to explore the velocity space and
find efficient motion plans. The performance of CS-BRM is evaluated and
compared to a previous belief space planning method, demonstrating the benefits
of the proposed approach.
