Optimization-based Task and Motion Planning under Signal Temporal Logic Specifications using Logic Network Flow

TL;DR

This paper introduces Logic Network Flow, an optimization framework that encodes STL specifications as polyhedron constraints in network flows, improving planning efficiency and bounds in multi-robot motion planning.

Contribution

It presents a novel encoding of STL constraints as polyhedron constraints within network flows, leading to tighter relaxations and improved computational performance.

Findings

Outperforms Logic Tree in computation time.

Provides better bounds with larger problem sizes.

Scales efficiently with problem complexity.

Abstract

This paper proposes an optimization-based task and motion planning framework, named "Logic Network Flow", to integrate signal temporal logic (STL) specifications into efficient mixed-binary linear programmings. In this framework, temporal predicates are encoded as polyhedron constraints on each edge of the network flow, instead of as constraints between the nodes as in the traditional Logic Tree formulation. Synthesized with Dynamic Network Flows, Logic Network Flows render a tighter convex relaxation compared to Logic Trees derived from these STL specifications. Our formulation is evaluated on several multi-robot motion planning case studies. Empirical results demonstrate that our formulation outperforms Logic Tree formulation in terms of computation time for several planning problems. As the problem size scales up, our method still discovers better lower and upper bounds by exploring fewer number of nodes during the branch-and-bound process, although this comes at the cost of increased computational load for each node when exploring branches.