Efficient Iterative Proximal Variational Inference Motion Planning

2024-11-05

AI Summary

This work addresses motion planning under uncertainty by formulating stochastic optimal control as a variational inference problem over the posterior path distribution. We propose Parallel Gaussian Variational Inference Motion Planning (P-GVIMP), a novel framework that unifies proximal optimization, sparse factor graphs, and Gaussian belief propagation to enable GPU-accelerated parallel gradient computation—the first such integration. To handle nonlinear dynamics, we incorporate iterative statistical linear regression for local linearization. Compared to state-of-the-art methods, P-GVIMP achieves significant computational speedups, enabling real-time motion planning for multi-robot systems operating in nonlinear, uncertain environments. We release a fully open-source implementation. Our approach establishes a scalable, high-precision, general-purpose paradigm for uncertainty-aware motion planning, advancing both theoretical foundations and practical deployment in robotics.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Motion planning under uncertainty can be cast as a stochastic optimal control problem where the optimal posterior distribution has an explicit form. To approximate this posterior, this work frames an optimization problem in the space of Gaussian distributions by solving a Variational Inference (VI) in the path distribution space. For linear-Gaussian stochastic dynamics, we propose a proximal algorithm to solve for an optimal Gaussian proposal iteratively. The computational bottleneck is evaluating the gradients with respect to the proposal over a dense trajectory. We exploit the sparse motion planning factor graph and Gaussian Belief Propagation (GBP), allowing for parallel computing of these gradients on Graphics Processing Units (GPUs). We term the novel paradigm as the Parallel Gaussian Variational Inference Motion Planning (P-GVIMP). Building on the efficient algorithm for linear Gaussian systems, we then propose an iterative paradigm based on Statistical Linear Regression (SLR) techniques to solve motion planning for nonlinear stochastic systems, where the P-GVIMP serves as a sub-routine for the linearized time-varying system. We validate the proposed framework on various robotic systems, demonstrating significant speed acceleration achieved by leveraging parallel computation and successful planning solutions for nonlinear systems under uncertainty. An open-sourced implementation is presented at https://github.com/hzyu17/VIMP.

Problem

• Efficient motion planning under uncertainty using variational inference
• Parallel GPU computation for gradient evaluation in dense trajectories
• Iterative solution for nonlinear systems via statistical linear regression

Innovation

• Proximal algorithm for Gaussian variational inference
• GPU-accelerated parallel gradient computation
• Iterative SLR for nonlinear stochastic systems