Planning for sequential robotics tasks often requires integrated symbolic and geometric reasoning. TAMP algorithms typically solve these problems by performing a tree search over high-level task sequences while checking for kinematic and dynamic feasibility. This can be inefficient because, typically, candidate task plans resulting from the tree search ignore geometric information. This often leads to motion planning failures that require expensive backtracking steps to find alternative task plans. We propose a novel approach to TAMP called Stein Task and Motion Planning (STAMP) that relaxes the hybrid optimization problem into a continuous domain. This allows us to leverage gradients from differentiable physics simulation to fully optimize discrete and continuous plan parameters for TAMP. In particular, we solve the optimization problem using a gradient-based variational inference algorithm called Stein Variational Gradient Descent. This allows us to find a distribution of solutions within a single optimization run. Furthermore, we use an off-the-shelf differentiable physics simulator that is parallelized on the GPU to run parallelized inference over diverse plan parameters. We demonstrate our method on a variety of problems and show that it can find multiple diverse plans in a single optimization run while also being significantly faster than existing approaches.

翻译：序列化机器人任务规划通常需要符号推理与几何推理的协同处理。传统的任务与运动规划（TAMP）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此类问题。这种方法往往效率低下，因为树搜索产生的候选任务计划通常忽略了几何信息，导致频繁出现运动规划失败，进而需要昂贵的回溯步骤来寻找替代任务方案。本文提出一种名为Stein任务与运动规划（STAMP）的新型TAMP方法，该方法将混合优化问题松弛至连续域。通过利用可微分物理仿真提供的梯度信息，我们能够对TAMP中的离散与连续规划参数进行全局优化。具体而言，我们采用基于梯度的变分推理算法——Stein变分梯度下降——来求解优化问题，从而在单次优化运行中获得解的分布。此外，我们使用现成的可微分物理仿真器（支持GPU并行计算）对多样化的规划参数进行并行化推理。我们在多种问题上验证了所提方法，结果表明：该方法不仅能在单次优化运行中发现多个差异化规划方案，其计算效率也显著优于现有方法。