cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization

2026-03-03

AI Summary

This work addresses the computational bottleneck in robust trajectory optimization under uncertainty, which arises from large-scale second-order cone programming (SOCP) constraints. To overcome this challenge, the authors propose cuNRTO, a novel framework that deeply integrates GPU parallelism into nonlinear robust trajectory optimization for the first time. cuNRTO introduces two CUDA-based optimization architectures: NRTO-DR employs the Douglas–Rachford splitting method to solve SOCP subproblems in parallel, while NRTO-FullADMM further enhances scalability via the alternating direction method of multipliers. Both leverage custom CUDA kernels, cuBLAS GEMM chains, and sparse direct solvers to accelerate SOCP projections and feedback gain updates. Experiments on a unicycle, quadrotor, and Franka manipulator demonstrate speedups of up to 139.6× over baseline methods, substantially improving real-time performance.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Intelligent Robots: Learning & Optimization for ROB
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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$\times$.

Problem

• robust trajectory optimization
• uncertainty
• Second Order Conic Programming
• computational burden
• autonomous systems

Innovation

• GPU acceleration
• robust trajectory optimization
• SOCP
• ADMM
• CUDA