Abstract
Gaussian Process Motion Planning (GPMP) is a widely used framework for generating smooth trajectories within a limited compute time--an essential requirement in many robotic applications. However, traditional GPMP approaches often struggle with enforcing hard nonlinear constraints and rely on Maximum a Posteriori (MAP) solutions that disregard the full Bayesian posterior. This limits planning diversity and ultimately hampers decision-making. Recent efforts to integrate Stein Variational Gradient Descent (SVGD) into motion planning have shown promise in handling complex constraints. Nonetheless, these methods still face persistent challenges, such as difficulties in strictly enforcing constraints and inefficiencies when the probabilistic inference problem is poorly conditioned. To address these issues, we propose a novel constrained Stein Variational Gaussian Process Motion Planning (cSGPMP) framework, incorporating a GPMP prior specifically designed for trajectory optimization under hard constraints. Our approach improves the efficiency of particle-based inference while explicitly handling nonlinear constraints. This advancement significantly broadens the applicability of GPMP to motion planning scenarios demanding robust Bayesian inference, strict constraint adherence, and computational efficiency within a limited time. We validate our method on standard benchmarks, achieving an average success rate of 98.57% across 350 planning tasks, significantly outperforming competitive baselines. This demonstrates the ability of our method to discover and use diverse trajectory modes, enhancing flexibility and adaptability in complex environments, and delivering significant improvements over standard baselines without incurring major computational costs.
Abstract (translated)
高斯过程运动规划（GPMP）是一种广泛应用于生成平滑轨迹的框架，这对于许多机器人应用中的计算时间限制是一个基本要求。然而，传统的GPMP方法在处理硬非线性约束时往往面临困难，并且依赖于最大后验概率（MAP）解，这忽略了完整的贝叶斯后验分布。这种做法限制了规划多样性并最终影响决策制定能力。最近将Stein变分梯度下降法（SVGD）集成到运动规划中的尝试，在处理复杂约束方面显示出潜力。尽管如此，这些方法仍然面临持续的挑战，例如难以严格强制执行约束和在概率推理问题条件不佳时效率低下。 为了解决这些问题，我们提出了一种新的带有非线性约束的Stein变分高斯过程运动规划（cSGPMP）框架，该框架结合了专门用于硬约束轨迹优化的GPMP先验。我们的方法通过显式处理非线性约束提高了基于粒子的推理效率。这一改进大大扩展了GPMP在需要稳健贝叶斯推断、严格遵守约束和有限时间内计算高效的运动规划场景中的适用范围。 我们在标准基准上验证了我们提出的方法，实现了350个规划任务的平均成功率98.57%，显著优于竞争性基线方法。这表明我们的方法能够发现并利用多种轨迹模式，提高在复杂环境下的灵活性和适应性，并且在不大幅增加计算成本的情况下对标准基线进行了重大改进。 这种方法为机器人系统中的运动规划提供了一种强大的新工具，尤其是在需要遵守硬约束条件的动态环境中显得尤为重要。
URL
https://arxiv.org/abs/2504.04936
