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

arXiv:2607.04310v2 Announce Type: replace Abstract: Optimization-based local planning and control require high-rate evaluation of collision-avoidance constraints over a prediction horizon. Accurately accounting for robot and obstacle geometry in these evaluations can be computationally expensive. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed polygonal signed distance function (PSDF) returns the minimum of exact signed distances between a convex polygonal robot footprint and convex obstacle components represented by their boundary edges. It is implemented as a training-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded in model predictive control by locally linearizing the PSDF-based safety constraint 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 size and sparsity are determined by system dimensions and horizon length rather than obstacle and edge counts. Microbenchmarks show that PSDF scales favorably relative to geometric and learned collision-field baselines. Closed-loop comparisons in simulation, together with real-world navigation experiments, demonstrate that PSDF-MPC operates in real time and achieves collision-free navigation in dense polygonal environments.

Abstract:Optimization-based local planning and control require high-rate evaluation of collision-avoidance constraints over a prediction horizon. Accurately accounting for robot and obstacle geometry in these evaluations can be computationally expensive. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed polygonal signed distance function (PSDF) returns the minimum of exact signed distances between a convex polygonal robot footprint and convex obstacle components represented by their boundary edges. It is implemented as a training-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded in model predictive control by locally linearizing the PSDF-based safety constraint 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 size and sparsity are determined by system dimensions and horizon length rather than obstacle and edge counts. Microbenchmarks show that PSDF scales favorably relative to geometric and learned collision-field baselines. Closed-loop comparisons in simulation, together with real-world navigation experiments, demonstrate that PSDF-MPC operates in real time and achieves collision-free navigation in dense polygonal environments.

Robotics (cs.RO)

arXiv:2607.04310 [cs.RO]

(or arXiv:2607.04310v2 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2607.04310 Focus to learn more arXiv-issued DOI via DataCite

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

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