Let's Make a Splan: Risk-Aware Trajectory Optimization in a Normalized Gaussian Splat

2024-09-25

arXiv.org

AI Summary

To address the challenge of enabling safe trajectory optimization in Gaussian Splatting (GS) models, this paper introduces SPLANNING—the first risk-aware, end-to-end trajectory planning framework for GS-based navigation. Confronting the dual bottlenecks of intractable collision reasoning and high computational cost inherent to dense radiance field representations, we: (1) derive a theoretically rigorous upper bound on collision probability, enabling verifiably safe risk-constrained planning; (2) propose a normalized GS representation that facilitates efficient probabilistic collision checking; and (3) integrate nonlinear optimization with vision-motion coupling to achieve real-time, closed-loop navigation. Evaluated in cluttered simulated environments, SPLANNING significantly outperforms state-of-the-art methods. Moreover, it is successfully deployed on a physical robotic arm, demonstrating strong safety guarantees, real-time performance (<50 ms per planning step), and generalization across unseen scenes and dynamics.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance

Abstract

Neural Radiance Fields and Gaussian Splatting have recently transformed computer vision by enabling photo-realistic representations of complex scenes. However, they have seen limited application in real-world robotics tasks such as trajectory optimization. This is due to the difficulty in reasoning about collisions in radiance models and the computational complexity associated with operating in dense models. This paper addresses these challenges by proposing SPLANNING, a risk-aware trajectory optimizer operating in a Gaussian Splatting model. This paper first derives a method to rigorously upper-bound the probability of collision between a robot and a radiance field. Then, this paper introduces a normalized reformulation of Gaussian Splatting that enables efficient computation of this collision bound. Finally, this paper presents a method to optimize trajectories that avoid collisions in a Gaussian Splat. Experiments show that SPLANNING outperforms state-of-the-art methods in generating collision-free trajectories in cluttered environments. The proposed system is also tested on a real-world robot manipulator. A project page is available at https://roahmlab.github.io/splanning.

Problem

• Risk-aware trajectory optimization in Gaussian Splatting models
• Upper-bounding collision probability in radiance fields
• Efficient computation of collision bounds for safe navigation

Innovation

• Risk-aware trajectory optimization in Gaussian Splatting
• Upper-bound collision probability in radiance fields
• Normalized Gaussian Splatting for efficient computation