Parallel-in-Time Nonlinear Optimal Control via GPU-native Sequential Convex Programming

TL;DR

This work introduces a fully GPU-native trajectory optimization framework that combines sequential convex programming with a consensus-based alternating direction method of multipliers and demonstrates the solver's extensibility to robust Model Predictive Control by jointly optimizing dynamically coupled scenarios under stochastic disturbances, enabling scalable and safe autonomy.

Abstract

Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic programming algorithms restricts the utilization of massively parallel computing architectures like GPUs. To bridge this gap, we introduce a fully GPU-native trajectory optimization framework that combines sequential convex programming with a consensus-based alternating direction method of multipliers. By applying a temporal splitting strategy, our algorithm decouples the optimization horizon into independent, per-node subproblems that execute massively in parallel. The entire process runs fully on the GPU, eliminating costly memory transfers and large-scale sparse factorizations. This architecture naturally scales to multi-trajectory optimization. We validate the solver on a quadrotor agile flight task and a Mars powered descent problem using an on-board edge computing platform. Benchmarks reveal a sustained 4x throughput speedup and a 51% reduction in energy consumption over a heavily optimized 12-core CPU baseline. Crucially, the framework saturates the hardware, maintaining over 96% active GPU utilization to achieve planning rates exceeding 100 Hz. Furthermore, we demonstrate the solver's extensibility to robust Model Predictive Control by jointly optimizing dynamically coupled scenarios under stochastic disturbances, enabling scalable and safe autonomy.

Figures (7)

• Figure 1: Hierarchical architecture of the proposed parallel-in-time trajectory optimizer.
• Figure 2: The Nvidia Jetson AGX Orin 64GB edge computing platform used for hardware validation.
• Figure 3: Ablation Study Results. Convergence profiles of dynamics defect (Top) and objective cost (Bottom) under varying final penalty parameters $\rho_f$ (Left) and inner ADMM iterations (Right).
• Figure 4: Scalability Benchmark. Computation time (Left) and system throughput (Right) scaling comparison between the 12-core CPU baseline and the proposed GPU solver.
• Figure 5: Hardware Utilization Profiles. Continuous profiling of CPU (overall) and GPU utilization during the batch trajectory optimization tasks. The streaming multiprocessors and maintained an active GPU utilization exceeding 96% across both dynamical environments.