Perception-Integrated Safety Critical Control via Analytic Collision Cone Barrier Functions on 3D Gaussian Splatting

2025-09-17

AI Summary

To address real-time safe navigation under crowded and extreme conditions (e.g., space robotics), this paper proposes a Collision-Cone Control Barrier Function (CBF) grounded in the analytical geometry of 3D Gaussian lattices. The method constructs a forward collision cone to derive a continuous, closed-form, first-order CBF, enabling tight sensorimotor coupling. Unlike conventional distance-based CBFs, it triggers avoidance earlier, avoids high-order Lie derivatives, ensures control smoothness, and incurs low computational overhead; moreover, it natively supports Minkowski expansion for physical robot modeling. Evaluated on a synthetic 170k-point scene, the approach reduces planning latency to one-third of the baseline, significantly suppresses trajectory jitter, and maintains safety guarantees. This work establishes an efficient and robust safety-critical navigation paradigm for highly dynamic, resource-constrained environments.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We present a perception-driven safety filter that converts each 3D Gaussian Splat (3DGS) into a closed-form forward collision cone, which in turn yields a first-order control barrier function (CBF) embedded within a quadratic program (QP). By exploiting the analytic geometry of splats, our formulation provides a continuous, closed-form representation of collision constraints that is both simple and computationally efficient. Unlike distance-based CBFs, which tend to activate reactively only when an obstacle is already close, our collision-cone CBF activates proactively, allowing the robot to adjust earlier and thereby produce smoother and safer avoidance maneuvers at lower computational cost. We validate the method on a large synthetic scene with approximately 170k splats, where our filter reduces planning time by a factor of 3 and significantly decreased trajectory jerk compared to a state-of-the-art 3DGS planner, while maintaining the same level of safety. The approach is entirely analytic, requires no high-order CBF extensions (HOCBFs), and generalizes naturally to robots with physical extent through a principled Minkowski-sum inflation of the splats. These properties make the method broadly applicable to real-time navigation in cluttered, perception-derived extreme environments, including space robotics and satellite systems.

Problem

• Proactive collision avoidance using analytic barrier functions
• Real-time safety control in cluttered 3D environments
• Efficient perception-integrated navigation for robotic systems

Innovation

• 3D Gaussian Splat collision cone conversion
• Analytic geometry for efficient collision constraints
• Proactive control barrier functions for safer navigation