Inspired by the line of seminal works on projected path dynamics and time-optimal control of robots, which originated in the 1980s, and recent advances on the computation of safe sets for complex systems in control, we present a new trajectory planning framework for $N$ -link robotic manipulators. Given a path, defined typically in the workspace, we recover the admissible velocity profiles and the realizable corresponding torque profiles that achieve a path traversal. To make this possible, we introduce a new torque feedback parameterization. This enables us to construct the set where the trajectory of the projected path can be confined while reaching a target set with a feasible control action, namely, the reach–avoid set. As a product of this procedure, we develop feedback controllers that guarantee state and input constraint satisfaction, can track reference trajectories, and can handle temporal specifications related, for example, to rendezvous and avoidance setups. Encouraging proof-of-concept experimental evaluation of the theory on a UR10 robotic manipulator suggests the framework can complement and further expand the existing classical approaches.

中文翻译：

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基于安全集的机器人操纵器轨迹规划


受到起源于 20 世纪 80 年代的机器人预测路径动力学和时间最优控制方面的开创性工作以及复杂控制系统安全集计算的最新进展的启发，我们提出了一种新的 $N 轨迹规划框架$ -链接机器人操纵器。给定通常在工作空间中定义的路径，我们恢复实现路径遍历的允许速度分布和可实现的相应扭矩分布。为了实现这一点，我们引入了新的扭矩反馈参数化。这使我们能够构造一个集合，在该集合中，投影路径的轨迹可以被限制，同时通过可行的控制动作达到目标集合，即到达-避免集合。作为该过程的产品，我们开发了反馈控制器，保证状态和输入约束满足，可以跟踪参考轨迹，并且可以处理与交会和回避设置相关的时间规范。鼓励对 UR10 机器人操纵器理论进行概念验证实验评估，表明该框架可以补充并进一步扩展现有的经典方法。