Inverse Kinematics as Low-Rank Euclidean Distance Matrix Completion
This provides a new geometric approach to IK for robotics, though it appears incremental as it builds on existing matrix completion methods.
The paper tackles inverse kinematics (IK) by reformulating it as a low-rank Euclidean distance matrix completion problem, enabling a novel Riemannian optimization-based solution for articulated robots with symmetric joint angle constraints.
The majority of inverse kinematics (IK) algorithms search for solutions in a configuration space defined by joint angles. However, the kinematics of many robots can also be described in terms of distances between rigidly-attached points, which collectively form a Euclidean distance matrix. This alternative geometric description of the kinematics reveals an elegant equivalence between IK and the problem of low-rank matrix completion. We use this connection to implement a novel Riemannian optimization-based solution to IK for various articulated robots with symmetric joint angle constraints.