New Math Trick Lets Robot Arms Move More Smoothly Around Obstacles

Thomas Cohn and colleagues present a new approach to planning trajectories for robot manipulators under kinematic equality constraints, which restrict feasible motions to a measure-zero submanifold of the configuration space. Because the vast majority of inverse kinematics (IK) functions are computed by automated meta-solvers like IKFast and are difficult to modify for differentiability, the authors instead compute gradients of analytic IK parameterizations by leveraging the inverse function theorem to recover the desired gradients from the ordinary forward kinematic Jacobian. They also present a least-squares domain extension and an optimization-amenable description of the reachability constraint, which preserves gradient signal outside the reachable workspace. They demonstrate the approach through numerical experiments and downstream tasks, including a hardware demonstration of an RB-Y1 picking up a box and placing it on a table.