用于实时碰撞避免的GPU加速多边形符号距离函数
GPU-Accelerated Polygonal Signed Distance Functions for Real-Time Collision Avoidance
浏览论文内容
中文总结 AI 辅助
研究在密集障碍物环境中实时碰撞避免问题，提出多边形符号距离函数（PSDF），通过张量化几何管道实现GPU加速，嵌入模型预测控制，设计分离CPU/GPU计算，实验证明其有效性。
中文摘要 AI 辅助
基于优化的局部规划和控制需要在预测范围内高速评估碰撞避免约束。在障碍物密集环境中，计算工作量常主导控制周期运行时间。所提出的多边形符号距离函数（PSDF）是凸多边形机器人足迹与由其边界边表示的障碍物之间的几何精确符号距离函数。它被实现为无权重、无分支的张量化几何管道，支持批量GPU执行和自动微分。PSDF通过在基于序列二次规划的实时迭代方案中局部线性化阶段安全约束而嵌入模型预测控制，产生PSDF嵌入模型预测控制器（PSDF-MPC）。该设计分离了CPU/GPU计算，使得GPU评估批量PSDF值和梯度，而CPU求解一个稀疏二次规划，其维度由系统维度和预测范围长度决定，而非障碍物特征。微基准测试表明PSDF与符号距离查询基线相比具有良好的扩展性。闭环模拟和实际导航实验，包括与基于优化的基线的比较，表明PSDF-MPC在密集多边形环境中保持实时可行性和强大的碰撞避免能力。
英文摘要
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.
发表机构
- School of Mechanical Engineering, Yonsei University（延世大学机械工程学院）
机构由 AI 辅助整理，请以论文原文为准。
