In this work, we present an approach to minimizing the time necessary for the end-effector of a redundant robot manipulator to traverse a Cartesian path by optimizing the trajectory of its joints. Each joint has limits in the ranges of position, velocity and acceleration, the latter making jerks in joint space undesirable. The proposed approach takes this nonlinear optimization problem whose variables are path speed and joint trajectory and reformulates it into a bi-level problem. The lower-level formulation is a convex subproblem that considers a fixed joint trajectory and maximizes path speed while considering all joint velocity and acceleration constraints. Under particular conditions, this subproblem has a closed-form solution. Then, we solve a higher-level subproblem by leveraging the directional derivative of the lower-level value with respect to the joint trajectory parameters. In particular, we use this direction to implement a Primal-Dual method that considers the path accuracy and joint position constraints. We show the efficacy of our proposed approach with simulations and experimental results.

翻译：本文提出了一种通过优化关节轨迹来最小化冗余机器人机械臂末端执行器遍历笛卡尔路径所需时间的方法。每个关节在位置、速度和加速度范围上均存在限制，其中加速度限制使得关节空间中的急动现象不可取。所提方法将变量为路径速度和关节轨迹的非线性优化问题重构为双层优化问题。下层子问题为凸优化问题，在固定关节轨迹条件下考虑所有关节速度和加速度约束以最大化路径速度。在特定条件下，该子问题存在闭式解。随后，我们利用下层最优值关于关节轨迹参数的方向导数求解上层子问题。特别地，我们运用该方向实现了考虑路径精度与关节位置约束的原始-对偶方法。通过仿真与实验结果验证了所提方法的有效性。