Trajectory inverse kinematics by conditional density modes

We present a machine learning approach for trajectory inverse kinematics: given a trajectory in workspace, to find a feasible trajectory in angle space. The method learns offline a conditional density model of the joint angles given the workspace coordinates. This density implicitly defines the multivalued inverse kinematics mapping for any workspace point. At run time, given a trajectory in the workspace, the method (1) computes the modes of the conditional density given each of the workspace points, and (2) finds the reconstructed angle trajectory by minimising over the set of modes a global, trajectory-wide constraint that penalises discontinuous jumps in angle space or invalid inverses. We demonstrate the method with a PUMA 560 robot arm and show how it can reconstruct the true angle trajectory even when the workspace trajectory contains singularities, and when the number of inverse branches depends on the workspace location.