Riemannian Optimization for Distance-Geometric Inverse Kinematics

Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models these robots are typically parametrized by joint angles, generating complicated mapping between robot configuration end-effector pose. Alternatively, kinematic model task constraints can be represented using invariant distances points attached to robot. In this paper, we formalize equivalence of distance-based distance geometry large class constraints. Unlike previous approaches, use connection low-rank matrix completion find solutions completing partial Euclidean through local optimization. Furthermore, parametrize space matrices with Riemannian manifold fixed-rank Gram matrices, allowing us leverage variety mature optimization methods. Finally, show that bound smoothing used generate informed initializations without significant computational overhead, improving convergence. We demonstrate our solver achieves higher success rates than traditional techniques, substantially outperforms them on problems involve many workspace