Achieving completeness in the motion planning problem demands substantial computation power, especially in high dimensions. Recent developments in parallel computing have rendered this more achievable. We introduce an embarrassingly parallel algorithm for constructing infeasibility proofs. Specifically, we design and implement a manifold triangulation algorithm on GPUs based on manifold tracing with Coxeter triangulation. To address the challenge of extensive memory usage within limited GPU memory resources during triangulation, we introduce batch triangulation as part of our design. The algorithm provides two orders of magnitude speed-up compared to the previous method for constructing infeasibility proofs. The resulting asymptotically complete motion planning algorithm effectively leverages the computational capabilities of both CPU and GPU architectures and maintains minimum data transfer between the two parts. We perform experiments on 5-DoF and 6-Dof manipulator scenes.

翻译：在运动规划问题中实现完备性需要巨大的计算资源，尤其是在高维空间中。并行计算领域的最新进展使得这一目标更易实现。我们提出了一种用于构建不可行性证明的完美并行算法。具体而言，我们基于考克斯特三角剖分流形追踪法，设计并实现了GPU上的流形三角剖分算法。针对三角剖分过程中有限GPU显存资源难以支撑海量内存消耗的挑战，我们创新性地引入了批处理三角剖分策略。与先前构建不可行性证明的方法相比，该算法实现了两个数量级的加速。最终形成的渐进完备运动规划算法有效利用了CPU和GPU架构的计算能力，同时将两部分间的数据传输量降至最低。我们在5自由度和6自由度机械臂场景上开展了实验验证。