Recently, several approaches have attempted to combine motion generation and control in one loop to equip robots with reactive behaviors, that cannot be achieved with traditional time-indexed tracking controllers. These approaches however mainly focused on positions, neglecting the orientation part which can be crucial to many tasks e.g. screwing. In this work, we propose a control algorithm that adapts the robot's rotational motion and impedance in a closed-loop manner. Given a first-order Dynamical System representing an orientation motion plan and a desired rotational stiffness profile, our approach enables the robot to follow the reference motion with an interactive behavior specified by the desired stiffness, while always being aware of the current orientation, represented as a Unit Quaternion (UQ). We rely on the Lie algebra to formulate our algorithm, since unlike positions, UQ feature constraints that should be respected in the devised controller. We validate our proposed approach in multiple robot experiments, showcasing the ability of our controller to follow complex orientation profiles, react safely to perturbations, and fulfill physical interaction tasks.

翻译：近期，多种方法尝试将运动生成与控制集成于同一环路中，以使机器人具备传统时间索引跟踪控制器无法实现的反应式行为。然而，这些方法主要关注位置控制，忽略了在许多任务（如拧螺丝）中至关重要的朝向部分。本文提出一种闭环调节机器人旋转运动与阻抗的控制算法。给定表示朝向运动计划的一阶动力系统与期望的旋转刚度曲线，该方法使机器人能够按照期望刚度所指定的交互行为跟踪参考运动，同时实时感知当前朝向（以单位四元数表示）。由于单位四元数具有位置变量所不具备的约束条件，我们基于李代数构建算法以确保控制器遵循这些约束。通过多项机器人实验验证，该方法能够跟踪复杂朝向曲线、安全响应扰动并完成物理交互任务。