Keeping Your Distances: A Distance-Geometric Perspective on Inverse Kinematics
In this talk, I will discuss recent work in my group on the problem of inverse kinematics (IK): finding joint angles that achieve a desired robot manipulator end-effector pose. A wide range of IK solvers exist, the majority of which operate on joint angles as parameters. Because the problem is highly nonlinear, these solvers are prone to local minima (among other troubles). I will introduce an alternate formulation of IK based on distance geometry, where a robot model is defined in terms of distances between rigidly-attached points. This alternative geometric description of the kinematics reveals an elegant equivalence between IK and the problem of low-rank Euclidean distance matrix completion. We use this connection to implement two novel solutions to IK for various articulated robots. The first is a Riemannian optimization-based approach which leverages the structure of the EDM manifold. The second solves a series of convex semidefinite relaxations of the distance-geometric problem. Both methods outperform many existing solvers on a variety of IK problems, some of which incorporate collision avoidance and joint limit constraints. Finally, I will describe a learned IK solver we have recently developed that is able to quickly generate sets of diverse approximate IK results for many different manipulators.
This lecture satisfies requirements for CSCI 591: Research Colloquium.