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

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, ve locity, and acceleration limits. The problem is reformulated as a bi - level optimization whose lower level is a convex, closed-fo rm 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-lev el value. Numerical results demonstrate the effectiveness of the proposed approach. In several industrial tasks performed by robots, the Cartesian path to be followed by the end-effector requires fewer degrees of freedom than what the manipulator possesses. In many applications [1]-[5], rotation around the attached tool center point (TCP) is considered a free axis, resulting in a kinematically redundant system [6], [7].