Control of stochastic unicycle-type robots

This paper addresses the problem of optimal control of a unicycle-type robot perturbed with stochastic noise in an environment with sparsely populated obstacles. The objective is that the robot pose converges to a neighborhood of a desired position and orientation. A feedback control law is constructed such that it is compatible with the differential constraints of the unicycle. The construction is based on numerical solution of the Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) associated with a stochastic optimal control problem. The control law is optimal in terms of control effort and comes with probabilistic guarantees of convergence to the goal set.