A Rapidly-Exploring Random Trees Motion Planning Algorithm for Hybrid Dynamical Systems

TL;DR

This paper introduces HyRRT, a probabilistically complete RRT-based algorithm for motion planning in hybrid dynamical systems, capable of handling both flows and jumps with relaxed assumptions.

Contribution

The paper presents HyRRT, a novel RRT algorithm specifically designed for hybrid systems, with proven probabilistic completeness and applicability to complex systems like walking robots.

Findings

HyRRT is probabilistically complete under mild conditions.

The algorithm effectively handles hybrid dynamics with flow and jump modes.

Application to a walking robot demonstrates its practical utility.

Abstract

This paper proposes a rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HyRRT, randomly picks a state sample and extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. Through a definition of concatenation of functions defined on hybrid time domains, we show that HyRRT is probabilistically complete, namely, the probability of failing to find a motion plan approaches zero as the number of iterations of the algorithm increases. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The motion plan is computed through the solution of two optimization problems, one associated with the flow and the other with the jumps of the system. The proposed algorithm is applied to a walking robot so as to highlight its generality and computational features.