Designing Multi-Stage Coupled Convex Programming with Data-Driven McCormick Envelope Relaxations for Motion Planning

TL;DR

This paper introduces a multi-stage optimization framework using data-driven McCormick envelope relaxations to improve motion planning efficiency and interpretability for multi-limbed robots with nonlinear constraints.

Contribution

It presents a novel multi-stage convex programming approach with learned inter-stage coupling constraints tailored for robot motion planning.

Findings

Reduced solve times for complex motion planning tasks

Enhanced interpretability of the optimization process

Validated on a hexapod robot with successful walking and climbing tasks

Abstract

For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with data-driven inter-stage coupling constraints to address the nonlinearity. Both clustering and evolutionary approaches to find the McCormick envelope relaxations are used to find the problem-specific parameters. The learned constraints are then used in the prior stages, which provides advanced knowledge of the following stages. This leads to improved solve times and interpretability of the results. The planner is validated through multiple walking and climbing tasks on a 10 kg hexapod robot.