cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization

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.

Many robotics problems, including trajectory optimization, inverse kinematics, and contact-rich motion planning, reduce to nonlinear programs (NLPs). Mature NLP solvers such as IPOPT can solve these problems, offering hard constraint satisfaction, optimality guarantees, and favorable scaling with problem dimension. These solvers underpin gradient-based methods in robotics, yet remain CPU-bound and solve only one problem at a time, preventing their integration into GPU-batched learning pipelines. On the other hand, sampling-based approaches such as reinforcement learning, model predictive path integral, and imitation learning have become the core of modern robotics research due to their ability to leverage GPU-batched simulators. These simulators can generate orders of magnitude more dynamics rollouts per second than was previously possible. If a GPU-batched NLP solver existed, it would unlock similar speedups in the number of constrained, locally optimal solutions generated per second. This regime of solving many problems concurrently versus solving a single problem at a time is a key requirement for integrating NLP solvers in modern GPU-batched robotics frameworks. To this end, we introduce jaxipm, the first GPU-batched NLP solver, based on IPOPT, and implemented in JAX. We accomplish this by redesigning IPOPT's algorithm to eliminate control flow with heterogeneous iteration fusion, and by minimizing GPU idle time with iteration level batching. We evaluate jaxipm on a variety of quadrotor nonlinear model predictive control benchmarks, including reference tracking in the presence of obstacles, multi-quadrotor navigation without collision, and navigation in a cluttered environment. We demonstrate up to a $32.85\times$ increase in throughput over IPOPT. Our complete open-source codebase is available at https://github.com/johnviljoen/jaxipm.

Model Predictive Control (MPC) delivers constraint-aware control, but its reliance on online optimization limits its use on systems with fast dynamics, high-dimensional models, or long horizons. Existing GPU implementations typically treat the device as a linear-algebra accelerator, leaving the optimization loop dependent on repeated kernel launches and high-latency memory transfers. This paper introduces CUDA MPC, a GPU-native MPC framework that co-designs the optimization algorithm, execution model, and memory architecture for CUDA hardware. CUDA MPC pairs a parallel-in-horizon alternating direction method of multipliers (ADMM) splitting with a fused CUDA kernel that runs the entire iterative solve on the device. Intermediate optimization variables stay in low-latency, on-chip shared memory, and a localized atomic-flag protocol synchronizes only adjacent horizon blocks, minimizing host intervention, kernel-dispatch overhead, and global-memory traffic. Across six nonlinear robotics benchmarks spanning increasing state dimension and constraint density, CUDA MPC sustains real-time rates at horizons one to two orders of magnitude longer than CPU solvers: it solves an optimization-based collision-avoidance parking problem with 100 s of lookahead within a 0.1 s sampling interval, and is the only solver evaluated that achieves both real-time execution and collision-free coordination for a centralized 10-agent swarm, where acados and CasADi return no feasible solution and require 3.5 s and 4.5 s per solve. Against tensor-framework implementations of the same ADMM splitting, the fused kernel is up to $965\times$ faster.