Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification

-- Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. T o enable this, we present two novel frameworks for applying principles of constrained optimization to the new variational inference algorithm Stein variational gradient descent. Our general framework supports multiple types of constrained optimizers and can handle arbitrary constraints. We demonstrate on a variety of problems that we are able to learn to approximate distributions without violating constraints. Specifically, we show that we can build distributions of: robot motion plans that exactly avoid collisions, robot arm joint angles on the SE(3) manifold with exact table placement constraints, and object poses from point clouds with table placement constraints. Estimating uncertainty defines a core problem in robotics. In robotic perception, where partial observability and noise are prominent, it is often desirable to reason about the world in a probabilistic way [1]. Because robot motion and sensing is imperfect, there is an entire distribution of possible states of the system. Instead of trying to estimate the pose of a robot, for example, we approximate the distribution over possible poses. Modern robots might have uncertainty about their own pose, future states produced by a motion plan or poses and shapes of objects in the scene.