Bayesian Inferential Motion Planning Using Heavy-Tailed Distributions

2025-03-27

AI Summary

Existing Bayesian motion planning methods are constrained by the light-tailed nature of Gaussian priors, hindering effective exploration of low-probability yet high-quality trajectory regions and thus limiting robotic navigation safety and efficiency. This paper formulates motion planning as a Bayesian inference problem and introduces, for the first time, the Student’s t-distribution as a heavy-tailed prior within a sequential single-sweep smoothing framework—thereby overcoming the exploratory limitations imposed by conventional light-tailed assumptions. We further integrate Monte Carlo sampling with sequential smoothing to generalize the ensemble Kalman smoother. Evaluated in autonomous driving simulations, the proposed method achieves significant improvements in trajectory quality, sampling efficiency, and constraint satisfaction rate. These results empirically validate that heavy-tailed priors substantially enhance the robustness and exploratory capability of probabilistic decision-making in robotics.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Enhancing Bayesian motion planning with heavy-tailed distributions
• Improving exploration of low-probability regions in planning space
• Validating superior performance in autonomous vehicle motion planning

Innovation

• Bayesian motion planning with heavy-tailed distributions
• Sequential single-pass smoothing using Student's-t
• Enhanced probabilistic search via Monte Carlo sampling