用GPU加速非线性鲁棒轨迹优化,速度提升超139倍。
cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization
- 基于双分裂和ADMM的两种新架构,实现并行化求解
- 在无人车、无人机等模型上实测最快提速139.6倍
- 适合需要实时决策的自动驾驶与机器人系统
鲁棒轨迹优化通过计算满足所有有界扰动下约束的控制策略,使自主系统在不确定性下安全运行。然而,这类问题常导致大规模二阶锥规划(SOCP)约束,计算成本高。本文提出基于CUDA的非线性鲁棒轨迹优化框架cuNRTO,引入两种动态优化架构:NRTO-DR利用Douglas-Rachford分裂法求解NRTO的SOCP子问题,通过并行化锥投影和稀疏直接求解显著降低计算负担;NRTO-FullADMM是新提出的变体,进一步利用问题结构提升可扩展性。我们使用自定义CUDA核实现SOC投影步骤,并用cuBLAS GEMM链完成反馈增益更新。在单轮车、四旋翼无人机和Franka机械臂模型上进行仿真验证,最高提速达139.6×。
原文摘要 · Abstract (English)
Robust trajectory optimization enables autonomous systems to operate safely under uncertainty by computing control policies that satisfy the constraints for all bounded disturbances. However, these problems often lead to large Second Order Conic Programming (SOCP) constraints, which are computationally expensive. In this work, we propose the CUDA Nonlinear Robust Trajectory Optimization (cuNRTO) framework by introducing two dynamic optimization architectures that have direct application to robust decision-making and are implemented on CUDA. The first architecture, NRTO-DR, leverages the Douglas-Rachford (DR) splitting method to solve the SOCP inner subproblems of NRTO, thereby significantly reducing the computational burden through parallel SOCP projections and sparse direct solves. The second architecture, NRTO-FullADMM, is a novel variant that further exploits the problem structure to improve scalability using the Alternating Direction Method of Multipliers (ADMM). Finally, we provide GPU implementations of the proposed methodologies using custom CUDA kernels for SOC projection steps and cuBLAS GEMM chains for feedback gain updates. We validate the performance of cuNRTO through simulated experiments on unicycle, quadcopter, and Franka manipulator models, demonstrating speedups of up to 139.6$\times$. More details are available at https://cunrto.github.io.
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