Offline optimal planning of trajectories for redundant robots along prescribed task space paths is usually broken down into two consecutive processes: first, the task space path is inverted to obtain a joint space path, then, the latter is parametrized with a time law. If the two processes are separated, they cannot optimize the same objective function, ultimately providing sub-optimal results. In this paper, a unified approach is presented where dynamic programming is the underlying optimization technique. Its flexibility allows accommodating arbitrary constraints and objective functions, thus providing a generic framework for optimal planning of real systems. To demonstrate its applicability to a real world scenario, the framework is instantiated for time-optimality on Franka Emika's Panda robot. The well-known issues associated with the execution of non-smooth trajectories on a real controller are partially addressed at planning level, through the enforcement of constraints, and partially through post-processing of the optimal solution. The experiments show that the proposed framework is able to effectively exploit kinematic redundancy to optimize the performance index defined at planning level and generate feasible trajectories that can be executed on real hardware with satisfactory results.

翻译：冗余机器人在预设任务空间路径上的离轨最优轨迹规划通常分解为两个连续过程：首先通过任务空间路径逆解获得关节空间路径，随后为该路径赋予时间规律。若两个过程相互分离，则无法优化相同的目标函数，最终只能得到次优结果。本文提出一种统一方法，以动态规划为核心优化技术。该方法的灵活性允许容纳任意约束条件与目标函数，从而为真实系统的最优规划提供通用框架。为验证其在现实场景中的适用性，以Franka Emika的Panda机器人为例，面向时间最优性对该框架进行了实例化。针对真实控制器上执行非平滑轨迹时存在的典型问题，部分通过在规划层级施加约束解决，部分通过对最优解进行后处理缓解。实验表明，该框架能够有效利用运动学冗余优化规划层级定义的性能指标，生成可在真实硬件上执行且结果满意的可行轨迹。