Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes

TL;DR

This paper introduces a novel motion planning method for autonomous vehicles that leverages reachability analysis and hybrid zonotopes to efficiently satisfy metric temporal logic specifications, enabling real-time decision-making in complex environments.

Contribution

The paper presents a new approach combining reachability analysis with hybrid zonotopes to encode and optimize MTL specifications for motion planning, improving computational efficiency.

Findings

Demonstrates computational advantages over existing methods.

Addresses time-varying environments and disturbances.

Enables multi-agent coordination in motion planning.

Abstract

Metric temporal logic (MTL) provides a formal framework for defining time-dependent mission requirements on autonomous vehicles. However, optimizing control decisions subject to these constraints is often computationally expensive. This article presents a method that uses reachability analysis to implicitly express the set of states satisfying an MTL specification and then optimizes to find a motion plan. The hybrid zonotope set representation is used to efficiently and conveniently encode MTL specifications into reachable sets. A numerical benchmark highlights the proposed method's computational advantages as compared to existing methods in the literature. Further numerical examples and an experimental application demonstrate the ability to address time-varying environments, region-dependent disturbances, and multi-agent coordination.