Constrained Gaussian Process Motion Planning via Stein Variational Newton Inference

2025-04-07

AI Summary

Traditional Gaussian process motion planning (GPMP) struggles to rigorously enforce hard nonlinear constraints and fails to fully exploit the diversity and robustness inherent in Bayesian posteriors. To address issues of imprecise constraint enforcement, inefficient variational inference, and ill-conditioned posterior approximations, this paper proposes constrained Stein variational Gaussian process motion planning (cSGPMP). Our framework is the first to integrate Stein variational Newton optimization into GPMP, coupled with constraint-aware GP prior modeling, particle-adaptive gradient correction, and a hard-constraint projection mechanism. Evaluated on 350 standard benchmark tasks, cSGPMP achieves a mean success rate of 98.57%, significantly outperforming baseline methods. It simultaneously improves constraint satisfaction accuracy, variational inference efficiency, and trajectory diversity—while maintaining real-time performance—thereby extending the applicability of GPMP to safety-critical, low-latency robotic motion planning under stringent constraints.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Enforcing hard nonlinear constraints in GPMP
• Improving efficiency in poorly conditioned probabilistic inference
• Enhancing planning diversity with Bayesian posterior consideration

Innovation

• Stein Variational Newton Inference for constraints
• GPMP prior for trajectory optimization
• Efficient particle-based inference under constraints