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 implementation 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 speedup up to 139.6$\times$.

翻译：鲁棒轨迹优化通过计算满足所有有界扰动下约束条件的控制策略，使自主系统能够在不确定性下安全运行。然而，这些问题通常会产生大规模二阶锥规划约束，其计算成本高昂。本文提出CUDA非线性鲁棒轨迹优化框架，通过引入两种可直接应用于鲁棒决策并在CUDA上实现的动态优化架构。第一种架构NRTO-DR利用Douglas-Rachford分裂法求解NRTO的SOCP内部子问题，通过并行SOCP投影和稀疏直接求解显著降低计算负担。第二种架构NRTO-FullADMM是一种新颖的变体，进一步利用问题结构通过交替方向乘子法提升可扩展性。最后，我们使用定制CUDA内核实现SOC投影步骤，并采用cuBLAS GEMM链进行反馈增益更新，完成了所提方法的GPU实现。通过独轮车、四旋翼飞行器和Franka机械臂模型的仿真实验，我们验证了cuNRTO的性能，其加速比最高可达139.6倍。