Tightening Mixed-Integer Convex Relaxations for Efficient Temporal Logic Motion Planning via Logic Network Flow

Xuan Lin, Jiming Ren, Yandong Luo, Weijun Xie, Ye Zhao

Keywords: Task and motion planning, temporal logic, mixed-integer programming

TL;DR: Logic Network Flow (LNF) is a novel formulation for temporal logic specifications with provably tighter convex relaxations and fewer constraints than standard Logic Tree approaches.

Abstract: This paper proposes an optimization-based task and motion planning framework, named ``Logic Network Flow," that integrates temporal logic specifications into mixed-integer programs for efficient robot planning. Inspired by the Graph-of-Convex-Sets formulation, temporal predicates are encoded as polyhedron constraints on each edge of a network flow model, instead of as constraints between nodes in traditional Logic Tree formulations. For temporal logic motion planning with piecewise-affine dynamic systems, comprehensive experiments demonstrate computational speedups of up to several orders of magnitude. Hardware demonstrations validate real-time replanning capabilities under dynamically changing environmental conditions. The project website is at \url{https://logicnetworkflow.github.io/}.

Submission Number: 45