GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance

2026-07-05

AI Summary

This work addresses the challenge of real-time local planning in cluttered environments, where conventional optimization-based approaches suffer from high computational overhead due to frequent collision checks. The authors propose a geometrically exact polygonal signed distance function (PSDF) and construct a branch-free, weight-free tensorized geometry pipeline that enables efficient GPU batch computation and automatic differentiation. Integrated into a sequential quadratic programming framework, this pipeline yields PSDF-MPC, a real-time model predictive controller. Notably, the method achieves the first efficient GPU-parallel implementation of PSDF, decouples CPU and GPU workloads, and renders obstacle-avoidance constraint evaluation complexity independent of the number of obstacles. Experiments demonstrate that PSDF surpasses existing methods in both accuracy and efficiency for distance queries, while PSDF-MPC exhibits strong real-time performance and robust collision avoidance in both simulation and physical robot trials.

Abstract

Optimization-based local planning and control require high-rate collision-avoidance constraint evaluation over a prediction horizon. In obstacle-dense environments, where feasible space is limited and the constraints become increasingly complex, the computational workload often dominates the control-cycle runtime. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed Polygonal Signed Distance Function (PSDF) is a geometry-exact signed distance function between a convex polygonal robot footprint and obstacles represented by their boundary edges. It is implemented as a weight-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded into model predictive control by locally linearizing the stage-wise safety constraints within a sequential quadratic programming-based real-time iteration scheme, yielding the PSDF-embedded model predictive controller (PSDF-MPC). The design separates CPU/GPU computation so that the GPU evaluates batched PSDF values and gradients while the CPU solves a sparse quadratic program whose dimension is determined by system dimensions and horizon length, not by obstacle features. Microbenchmarks show that PSDF scales favorably against signed-distance query baselines. Closed-loop simulated and real-world navigation experiments, including comparisons with optimization-based baselines, demonstrate that PSDF-MPC maintains real-time feasibility and robust collision avoidance in dense polygonal environments.

Problem

• collision avoidance
• signed distance function
• real-time control
• optimization-based planning
• computational bottleneck

Innovation

• Polygonal Signed Distance Function
• GPU acceleration
• Model Predictive Control
• Real-time collision avoidance
• Automatic differentiation