通过双层优化提升冗余机械臂轨迹效率，兼顾速度与运动平滑性。
A Bi-Level Optimization Approach to Joint Trajectory Optimization for Redundant Manipulators
- 将轨迹优化拆分为上下两层：上层调参，下层求最大速度
- 在速度与加速度约束下实现路径时间最短，实测加速更快
- 适合需要高速高精度控制的工业机械臂场景
本文提出一种双层优化方法，用于最小化冗余机械臂末端执行器沿笛卡尔路径移动所需的时间。每个关节存在位置、速度和加速度的限制，后两者导致关节空间中的加速度突变（jerks）不可接受。该方法将原本非线性的优化问题（变量为路径速度与关节轨迹）重构为双层结构：下层为凸子问题，在固定关节轨迹条件下最大化路径速度，同时满足所有关节速度与加速度约束；在特定条件下，该子问题具有闭式解。上层则利用下层最优值对关节轨迹参数的方向导数，采用原始-对偶方法优化，同时考虑路径精度和关节位置约束。通过仿真与实验验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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