Temporal Logic Motion Planning with Convex Optimization via Graphs of Convex Sets

TL;DR

This paper introduces a convex optimization-based method for motion planning with temporal logic, formulated as a shortest path problem in a Graph of Convex Sets, enabling scalable and optimal planning for complex, high-dimensional systems.

Contribution

It presents a novel approach that combines automata-theoretic methods with convex optimization, allowing scalable and globally optimal motion planning under temporal logic constraints.

Findings

Polynomial computational complexity in the number of sample points

Scales to high-dimensional systems like a 30-DoF humanoid

Guarantees soundness and probabilistic completeness

Abstract

Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics. In this paper, we cast Linear Temporal Logic (LTL) motion planning as a shortest path problem in a Graph of Convex Sets (GCS) and solve it with convex optimization. This approach brings together the best of modern optimization-based temporal logic planners and older automata-theoretic methods, addressing the limitations of each: we avoid clipping and passthrough by representing paths with continuous Bezier curves; computational complexity is polynomial (not exponential) in the number of sample points; global optimality can be certified (though it is not guaranteed); soundness and probabilistic completeness are guaranteed under mild assumptions; and most importantly, the method scales to complex specifications and high-dimensional systems, including a 30-DoF humanoid. Open-source code is available at https://github.com/vincekurtz/ltl_gcs.