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

2025-06-04

AI Summary

This paper addresses the time-optimal trajectory planning problem for redundant dual-arm robots executing a prescribed relative Cartesian path, subject to joint position, velocity, and acceleration constraints while maintaining constant path speed. We propose a novel bilevel optimization framework: the lower level computes the closed-form maximum feasible path speed via convex optimization; the upper level performs iterative time-parameterization using a single-chain equivalent kinematic model, leveraging subgradient information of the lower-level value function. This approach circumvents the computational intractability of conventional nonconvex joint optimization, achieving both efficiency and theoretical rigor. Numerical experiments demonstrate that the method strictly satisfies all kinematic constraints while significantly reducing task completion time, thereby enhancing coordination performance and trajectory feasibility of dual-arm systems.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Constraint Satisfaction and Optimization: Constraint Optimization
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Minimize time for dual-arm robot path following
• Optimize joint trajectories within kinematic limits
• Bi-level optimization for speed and trajectory

Innovation

• Bi-level optimization for dual-arm robots
• Convex closed-form subproblem maximizes speed
• Single-chain kinematics updates trajectory