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 (and some 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 a novel Riemannian optimization-based learned IK solver for articulated robots. This learned model is generative and is able to quickly produce sets of diverse approximate IK results for a variety of different manipulators, while outperforming many existing algorithms.

Bio: 

Prof. Jonathan Kelly leads the Space & Terrestrial Autonomous Robotic Systems (STARS) Laboratory at the University of Toronto Institute for Aerospace Studies. His group carries out research in robotic perception, planning, and manipulation. Prof. Kelly currently holds the Canada Research Chair in Collaborative Robotics, an area that has become a focus of his work. Prior to joining the University of Toronto, he was a postdoctoral fellow in CSAIL at MIT working with Prof. Nick Roy. He received his PhD degree in 2011 from the University of Southern California under the supervision of Prof. Gaurav S. Sukhatme.