A Bi-Level Optimization Method for Redundant Dual-Arm Minimum Time Problems

TL;DR

This paper introduces a bi-level optimization approach to minimize the time for a redundant dual-arm robot to follow a path at constant speed by optimizing joint trajectories within physical limits.

Contribution

It formulates the time minimization as a bi-level optimization with a convex lower level and a kinematic upper level, enabling efficient trajectory optimization for dual-arm robots.

Findings

Effective reduction in robot path execution time.

Convex subproblem allows for closed-form solutions.

Numerical results validate the approach's efficiency.

Abstract

In this work, we present a method for minimizing the time required for a redundant dual-arm robot to follow a desired relative Cartesian path at constant path speed by optimizing its joint trajectories, subject to position, velocity, and acceleration limits. The problem is reformulated as a bi-level optimization whose lower level is a convex, closed-form subproblem that maximizes path speed for a fixed trajectory, while the upper level updates the trajectory using a single-chain kinematic formulation and the subgradient of the lower-level value. Numerical results demonstrate the effectiveness of the proposed approach.