Dynamics-compatible potential fields using stochastic perturbations

This paper suggests a method for numerically constructing almost globally converging artificial potential fields for motion planning, in a way that ensures that the resulting gradient field is compatible with the dynamics of the navigating robot. Convergence to an arbitrarily small destination set can be guaranteed, and the size of the destination set can be reduced at the expense of additional off-line computational time. The construction is based on the solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with a related stochastic optimal control problem. This partial differential equation (PDE) is solved numerically by simulating paths of the system with Gaussian random perturbation applied to the input. The resulting control laws are optimal in terms of the magnitude of control actuation. The method is applied to the case of a Dubin´s car navigating amongst obstacles.