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

• URL: http://arxiv.org/abs/2607.04310v1
• Date: Sun, 05 Jul 2026 13:46:59 GMT
• Title: GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance
• Abstract summary: In dense environments, where feasible space is limited, the computational workload often dominates the control-cycle runtime.<n>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.<n>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.<n>PSDF-MPC maintains real-time feasibility and robust collision avoidance in dense polygonal environments.
• Score: 2.1993185973565113
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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