  Planning for many manipulation tasks, such as using tools or assembling
parts, often requires both symbolic and geometric reasoning. Task and Motion
Planning (TAMP) algorithms typically solve these problems by conducting a tree
search over high-level task sequences while checking for kinematic and dynamic
feasibility. This can be inefficient as the width of the tree can grow
exponentially with the number of possible actions and objects. In this paper,
we propose a novel approach to TAMP that relaxes discrete-and-continuous TAMP
problems into inference problems on a continuous domain. Our method, Stein Task
and Motion Planning (STAMP) subsequently solves this new problem using a
gradient-based variational inference algorithm called Stein Variational
Gradient Descent, by obtaining gradients from a parallelized differentiable
physics simulator. By introducing relaxations to the discrete variables,
leveraging parallelization, and approaching TAMP as an Bayesian inference
problem, our method is able to efficiently find multiple diverse plans in a
single optimization run. We demonstrate our method on two TAMP problems and
benchmark them against existing TAMP baselines.
