用厚尾分布提升机器人路径规划的探索能力
Bayesian Inferential Motion Planning Using Heavy-Tailed Distributions
- 用学生t分布替代高斯分布，增强对低概率优质路径的搜索能力
- 在自动驾驶仿真中，采样效率和约束满足率显著优于传统方法
- 适合需要高效探索稀有但高质量解的机器人决策场景
机器人依赖运动规划在执行任务时安全高效地导航。本文研究基于贝叶斯推断的运动规划，即根据规划目标与约束推断运动方案。然而，现有贝叶斯规划方法常难以探索规划空间中的低概率区域，而高质量方案可能存在于这些区域。为此，我们提出使用厚尾分布——特别是学生t分布——来增强概率推断搜索。我们开发了一种新颖的顺序单次平滑方法，将学生t分布与蒙特卡洛采样结合。该方法的一个特例是基于短尾高斯分布的集合卡尔曼平滑。通过自动驾驶车辆运动规划的仿真验证，所提方法在路径规划、采样效率和约束满足方面均优于集合卡尔曼平滑。尽管聚焦于运动规划，本工作也揭示了厚尾分布在机器人概率决策中的广泛潜力。
原文摘要 · Abstract (English)
Robots rely on motion planning to navigate safely and efficiently while performing various tasks. In this paper, we investigate motion planning through Bayesian inference, where motion plans are inferred based on planning objectives and constraints. However, existing Bayesian motion planning methods often struggle to explore low-probability regions of the planning space, where high-quality plans may reside. To address this limitation, we propose the use of heavy-tailed distributions -- specifically, Student's-$t$ distributions -- to enhance probabilistic inferential search for motion plans. We develop a novel sequential single-pass smoothing approach that integrates Student's-$t$ distribution with Monte Carlo sampling. A special case of this approach is ensemble Kalman smoothing, which depends on short-tailed Gaussian distributions. We validate the proposed approach through simulations in autonomous vehicle motion planning, demonstrating its superior performance in planning, sampling efficiency, and constraint satisfaction compared to ensemble Kalman smoothing. While focused on motion planning, this work points to the broader potential of heavy-tailed distributions in enhancing probabilistic decision-making in robotics.
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