The generation of energy-efficient and dynamic-aware robot motions that satisfy constraints such as joint limits, self-collisions, and collisions with the environment remains a challenge. In this context, Riemannian geometry offers promising solutions by identifying robot motions with geodesics on the so-called configuration space manifold. While this manifold naturally considers the intrinsic robot dynamics, constraints such as joint limits, self-collisions, and collisions with the environment remain overlooked. In this paper, we propose a modification of the Riemannian metric of the configuration space manifold allowing for the generation of robot motions as geodesics that efficiently avoid given regions. We introduce a class of Riemannian metrics based on barrier functions that guarantee strict region avoidance by systematically generating accelerations away from no-go regions in joint and task space. We evaluate the proposed Riemannian metric to generate energy-efficient, dynamic-aware, and collision-free motions of a humanoid robot as geodesics and sequences thereof.

翻译：生成满足关节限制、自碰撞及环境碰撞避免等约束条件的高能效且具有动态感知能力的机器人运动仍是一项挑战。在此背景下，黎曼几何通过将机器人运动视为构型空间流形上的测地线，提供了具有前景的解决方案。尽管该流形能天然地考虑机器人内在动力学特性，但关节限制、自碰撞及环境碰撞等约束仍未被纳入考量。本文提出对构型空间流形的黎曼度量进行改进，使机器人运动能够以测地线形式生成并有效规避特定区域。我们基于障碍函数引入一类黎曼度量，通过在关节空间与任务空间中系统生成远离禁止区域的加速度，保证严格规避区域。通过将仿人机器人运动及其序列表示为测地线，我们评估了所提黎曼度量在生成高能效、具有动态感知能力且无碰撞运动方面的性能。