Accelerating Signal-Temporal-Logic-Based Task and Motion Planning of Bipedal Navigation using Benders Decomposition

TL;DR

This paper introduces a Benders Decomposition-based method to accelerate task and motion planning for bipedal navigation under Signal Temporal Logic constraints, effectively handling non-convex constraints and reducing computational complexity.

Contribution

The paper presents a novel application of Benders Decomposition to efficiently solve complex hybrid planning problems with nonlinear constraints in bipedal locomotion.

Findings

Faster planning times compared to existing algorithms.

Effective handling of non-convex constraints like kinematic reachability.

Iterative decomposition improves computational tractability.

Abstract

Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer programs (MIP). However, in applications for bipedal locomotion, introduction of non-convex constraints such as kinematic reachability and footstep rotation exacerbates the computational complexity of MIPs. In this work, we present a method based on Benders Decomposition to address scenarios where solving the entire monolithic optimization problem is prohibitively intractable. Benders Decomposition proposes an iterative cutting-plane technique that partitions the problem into a master problem to prototype a plan that meets the task specification, and a series of subproblems for kinematics and dynamics feasibility checks. Our experiments demonstrate that this method achieves faster planning compared to alternative algorithms for solving the resulting optimization program with nonlinear constraints.