On the Design of Region-Avoiding Metrics for Collision-Safe Motion Generation on Riemannian Manifolds

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.