GPU加速非线性最优控制,实时规划效率提升4倍以上
Parallel-in-Time Nonlinear Optimal Control via GPU-native Sequential Convex Programming
- 用GPU原生凸化迭代法替代传统串行求解,实现时间并行
- 在Jetson AGX Orin上达100Hz批量规划,能耗降51%
- 适合嵌入式机器人实时控制,可拓展至多场景优化
实时求解非线性最优控制问题在嵌入式机器人硬件上仍具挑战,传统求解器依赖全局稀疏线性代数或串行递推,难以高效映射到大规模并行处理器。本文提出ucenter,一种GPU原生的序列凸规划(SCP)框架。每轮SCP中,非线性动力学沿参考轨迹线性化,生成的凸子问题通过一致性交替方向乘子法(ADMM)求解。时间分解将全局稀疏KKT分解替换为独立节点密集求解、闭式动态一致性更新及凸约束集上的解析投影。外层SCP循环与内层ADMM子问题均在GPU上执行,实现高效优化。在NVIDIA Jetson AGX Orin边缘平台上评估了四旋翼避障和火星着陆问题。与CPU并行iLQR基线对比,在随机环境中的基准测试显示,该GPU实现达到超过100 Hz的批量规划吞吐量,速度提升4.1倍,能耗降低51%,同时保持低非线性动力学偏差。该框架暴露可复用的GPU并行优化原语,可适用于多种复杂非线性最优控制场景,如基于场景的鲁棒MPC和批量蒙特卡洛生成任务。
原文摘要 · Abstract (English)
Real-time solution of nonlinear optimal control problems remains challenging on embedded robotic hardware, where conventional solvers often rely on global sparse linear algebra or sequential recursions that are difficult to map efficiently to massively parallel processors. This paper presents ucenter, a GPU-native Sequential Convex Programming (SCP) framework for nonlinear optimal control. At each SCP iteration, nonlinear dynamics are linearized around a nominal trajectory, and the resulting convexified subproblem is solved by a consensus Alternating Direction Method of Multipliers (ADMM) scheme. The temporal splitting replaces global sparse Karush-Kuhn-Tucker factorizations with independent per-node dense solves, closed-form dynamic consistency updates, and analytical projections onto convex constraint sets. Both the outer SCP loop and the inner ADMM subproblem are executed entirely on the GPU, enabling efficient optimization. The proposed solver is evaluated on quadrotor obstacle avoidance and Mars powered descent problems using an NVIDIA Jetson AGX Orin edge platform. Benchmarking against a CPU-parallel iLQR baseline in randomized environments reveals that the GPU implementation achieves over 100 Hz batched planning throughput, a 4.1x speedup, and a 51% reduction in energy consumption, while consistently maintaining low nonlinear dynamics defects. The framework exposes reusable GPU-parallel optimization primitives that can be specialized to a wide variety of complex nonlinear optimal control settings, as demonstrated by the scenario-based robust MPC and batched Monte Carlo generation tasks.
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