Computation of forward stochastic reach sets: Application to stochastic, dynamic obstacle avoidance

TL;DR

This paper introduces an efficient method to compute the forward stochastic reach set and its probability measure for nonlinear systems, enabling probabilistic obstacle avoidance in robotics, especially with convex obstacle shapes.

Contribution

The paper presents a novel approach to compute FSR sets with probability measures for nonlinear stochastic systems, facilitating probabilistic collision avoidance in robotics.

Findings

Method successfully computes FSR sets for nonlinear systems.

Convexity of FSR is guaranteed for convex obstacle shapes.

Demonstrated effectiveness in multi-obstacle avoidance scenarios.

Abstract

We propose a method to efficiently compute the forward stochastic reach (FSR) set and its probability measure for nonlinear systems with an affine disturbance input, that is stochastic and bounded. This method is applicable to systems with an a priori known controller, or to uncontrolled systems, and often arises in problems in obstacle avoidance in mobile robotics. When used as a constraint in finite horizon controller synthesis, the FSR set, and its probability measure facilitates probabilistic collision avoidance, in contrast to methods which presume the obstacles act in a worst-case fashion and generate hard constraints that cannot be violated. We tailor our approach to accommodate rigid body constraints, and show convexity is assured so long as the rigid body shape of each obstacle is also convex. We extend methods for multi-obstacle avoidance through mixed integer linear programming (with linear robot and obstacle dynamics) to accommodate chance constraints that represent the FSR set probability measure. We demonstrate our method on a rigid-body obstacle avoidance scenario, in which a receding horizon controller is designed to avoid several stochastically moving obstacles while reaching the desired goal. Our approach can provide solutions when approaches that presume a worst-case action from the obstacle fail.