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. While performant, most existing algorithms are highly inefficient as their time complexity grows exponentially with the number of possible actions and objects. Additionally, they only find a single solution to problems in which many feasible plans may exist. To address these limitations, we propose a novel algorithm called Stein Task and Motion Planning (STAMP) that leverages parallelization and differentiable simulation to efficiently search for multiple diverse plans. STAMP relaxes discrete-and-continuous TAMP problems into continuous optimization problems that can be solved using variational inference. Our algorithm builds upon Stein Variational Gradient Descent, a gradient-based variational inference algorithm, and parallelized differentiable physics simulators on the GPU to efficiently obtain gradients for inference. Further, we employ imitation learning to introduce action abstractions that reduce the inference problem to lower dimensions. We demonstrate our method on two TAMP problems and empirically show that STAMP is able to: 1) produce multiple diverse plans in parallel; and 2) search for plans more efficiently compared to existing TAMP baselines.

翻译：许多操作任务（如使用工具或组装零件）的规划通常需要符号推理与几何推理的结合。任务与运动规划（TAMP）算法通常通过在高层任务序列上进行树搜索并验证运动学与动力学可行性来解决此类问题。尽管现有算法性能良好，但其时间复杂度随可能动作与对象数量呈指数增长，导致效率极低。此外，这类算法仅能求解单一路径规划问题，而实际场景中常存在多种可行方案。为突破这些限制，我们提出一种名为Stein任务与运动规划（STAMP）的新算法，该算法利用并行化与可微仿真高效搜索多样化规划方案。STAMP将离散-连续混合的TAMP问题松弛为连续优化问题，并通过变分推断求解。该算法基于梯度变分推断算法——Stein变分梯度下降，以及GPU上的并行化可微物理仿真器高效获取推断梯度。进一步，我们通过模仿学习引入动作抽象，将推断问题降维至更低维度。在两类TAMP问题上的实验表明，STAMP能够：1）并行生成多种多样化规划方案；2）相较于现有TAMP基线方法更高效地搜索规划方案。