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.

翻译：许多操作任务（如使用工具或组装零件）的规划通常需要同时进行符号化推理与几何推理。任务与运动规划算法通常通过在高层次任务序列上进行树搜索，同时检查运动学与动力学可行性来解决这些问题。然而，随着可能动作和物体数量的增加，搜索树的宽度可能呈指数级增长，导致效率低下。本文提出一种新颖的任务与运动规划方法，将离散-连续混合规划问题松弛为连续域上的推理问题。我们的方法STAMP（斯坦任务与运动规划）通过并行化可微物理仿真器获取梯度，利用基于梯度的变分推理算法——斯坦变分梯度下降——来求解该新问题。通过引入离散变量的松弛化、并行化计算，并将任务与运动规划视为贝叶斯推理问题，我们的方法能够在单次优化运行中高效找到多个多样化规划方案。我们在两个任务与运动规划问题上验证了该方法，并与现有基线算法进行了对比实验。