Stochastic receding horizon control for robots with probabilistic state constraints

Abstract

This paper presents a receding horizon control design for a robot subject to stochastic uncertainty, moving in a constrained environment. Instead of minimizing the expectation of a cost functional while ensuring satisfaction of probabilistic state constraints, we propose a two-stage solution where the path that minimizes the cost functional is planned deterministically, and a local stochastic optimal controller with exit constraints ensures satisfaction of probabilistic state constraints while following the planned path. This control design strategy ensures boundedness of errors around the reference path and collision-free convergence to the goal with probability one under the assumption of unbounded inputs. We show that explicit expressions for the control law are possible for certain cases. We provide simulation results for a point robot moving in a constrained two-dimensional environment under Brownian noise. The method can be extended to systems with bounded inputs, if a small nonzero probability of failure can be accepted.

Stochastic receding horizon control: application to an octopedal robot

“…On the other hand, there has been recent efforts on directly considering stochastic uncertainty during control design. 3,4,11,12 For stochastic Dubin's car type vehicles, there are minimum-expected-time controllers 11 computed using the Hamilton-Jacobi-Bellman (hjb) partial differential equation (pde), however obstacle avoidance is not addressed. A stochastic target tracking problem has also been considered for Dubin-type vehicles.…”

“…Our receding horizon-based framework can provide sub-optimal solutions 3,4 even in case of large non-convex workspaces by using appropriate planning method. The theoretical foundations of stochastic optimal control with exit constraints 15 was used in a recursive fashion 3,4 to achieve probabilistic guarantees of reaching each intermediate goal sets.…”

“…Our receding horizon-based framework can provide sub-optimal solutions 3,4 even in case of large non-convex workspaces by using appropriate planning method. The theoretical foundations of stochastic optimal control with exit constraints 15 was used in a recursive fashion 3,4 to achieve probabilistic guarantees of reaching each intermediate goal sets. While the aforementioned work 3,4 applies stochastic receding horizon control to holonomic systems and tests it in simulation, in this paper, we demonstrate through experimentation, the application of the same method to nonholonomic stochastic Dubin's car type vehicles and achieve convergence to a goal while avoiding workspace boundary.…”

“…1(a), it is also desirable to have controllers that are input-optimal and computationally efficient, because of severe limitations in terms of payload and available energy storage capacity. Our goal in this work is to demonstrate application of input-optimal stochastic receding horizon controllers 3,4 for autonomous navigation of these miniature robots.…”

“…The theoretical foundations of stochastic optimal control with exit constraints 15 was used in a recursive fashion 3,4 to achieve probabilistic guarantees of reaching each intermediate goal sets. While the aforementioned work 3,4 applies stochastic receding horizon control to holonomic systems and tests it in simulation, in this paper, we demonstrate through experimentation, the application of the same method to nonholonomic stochastic Dubin's car type vehicles and achieve convergence to a goal while avoiding workspace boundary. The associated hjb pde is computed off-line using a novel computation method based on an application of the Feynman-Kac Lemma…”