发表机构
PEARL Lab, Dept. of Computer Science, TU Darmstadt; Robotics Institute Germany (RIG)（珍珠实验室，达姆施塔特工业大学计算机科学系; 德国机器人研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究机器人运动规划多模态问题，提出SteinSQP方法，通过约束斯坦变分推理演化粒子集合，用无矩阵原始对偶算法解决子问题，引入优点函数全局化方法，在多任务中表现良好，收敛快且可行性高。
AI 中文摘要
机器人运动规划本质上是多模态的，但经典规划器通常只返回单个解决方案。概率公式通过维持运动分布来解决这一限制。然而在机器人领域，运动样本还必须满足严格约束，这使得运动采样更具挑战性。我们提出了SteinSQP，一种用于多样化可行机器人运动采样的约束斯坦变分推理方法。它通过在核空间SQP子问题中直接嵌入约束来演化相互作用的粒子集合。我们用GPU友好的无矩阵原始对偶算法解决由此产生的约束斯坦 - 牛顿子问题。为使方法全局化，引入了一个联合平衡目标值、约束违反和粒子多样性的集合级优点函数。在五个约束运动规划任务中，SteinSQP返回完全可行的集合，同时保留多样的运动选择。与一阶约束斯坦基线和串行多启动非线性规划相比，SteinSQP在迭代方面显示出更快、更稳健的集合收敛，提高了逐粒子可行性，并在具有挑战性的机器人规模任务上实现了更快的批处理求解时间。
英文摘要
Robot motion planning is inherently multimodal, yet classical planners typically return only a single solution. Probabilistic formulations address this limitation by maintaining a distribution over motions, allowing the planner to reason over multiple low-cost alternatives. In robotics, however, motion samples must also satisfy strict constraints, including collision avoidance, joint limits, contact conditions, and dynamics consistency. These hard requirements make motion sampling substantially more challenging: within a limited planning budget, the ensemble must cover diverse low-cost motions while ensuring that every sample remains feasible under the relevant constraints. We propose SteinSQP (Stein Variational Sequential Quadratic Programming), a constrained Stein variational inference method for diverse feasible robot motion sampling. SteinSQP evolves an interacting particle ensemble, as in Stein variational methods, while embedding constraints directly into a kernel-space SQP subproblem. We solve the resulting constrained Stein-Newton subproblem with a GPU-friendly matrix-free primal-dual algorithm, enabling efficient batched ensemble updates. To globalize the method, we introduce an ensemble-level merit function that jointly balances objective value, constraint violation, and particle diversity. Across five constrained motion-planning tasks, SteinSQP returns fully feasible ensembles while preserving diverse motion alternatives. Compared with first-order constrained Stein baselines and serial multistart nonlinear programming, SteinSQP shows faster and more robust ensemble convergence in terms of iterations, improves particle-wise feasibility, and achieves faster batched time-to-solution on challenging robot-scale tasks.
