Hybrid System Planning using a Mixed-Integer ADMM Heuristic and Hybrid Zonotopes

TL;DR

This paper introduces a novel hybrid system planning framework combining hybrid zonotopes with an ADMM heuristic, improving computational efficiency and convergence in motion planning for autonomous systems.

Contribution

It presents a new set representation and an ADMM heuristic tailored for hybrid zonotopes, enhancing planning efficiency and accuracy over existing methods.

Findings

Lower memory complexity of set representations

Tighter convex relaxations of sets

Faster convergence in hybrid system planning

Abstract

Embedded optimization-based planning for hybrid systems is challenging due to the use of mixed-integer programming, which is computationally intensive and often sensitive to the specific numerical formulation. To address that challenge, this article proposes a framework for motion planning of hybrid systems that pairs hybrid zonotopes - an advanced set representation - with a new alternating direction method of multipliers (ADMM) mixed-integer programming heuristic. A general treatment of piecewise affine (PWA) system reachability analysis using hybrid zonotopes is presented and extended to formulate optimal planning problems. Sets produced using the proposed identities have lower memory complexity and tighter convex relaxations than equivalent sets produced from preexisting techniques. The proposed ADMM heuristic makes efficient use of the hybrid zonotope structure. For planning problems formulated as hybrid zonotopes, the proposed heuristic achieves improved convergence rates as compared to state-of-the-art mixed-integer programming heuristics. The proposed methods for hybrid system planning on embedded hardware are experimentally applied in a combined behavior and motion planning scenario for autonomous driving.