arXiv subjects

Yilin Zou

Publications and source records attributed to Yilin Zou.

5 recordsLinked to original sources

arXiv2026

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

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.

cs.RO↗

arXiv2026

Optimal Control and Neural Porkchop Analysis for Low-Thrust Asteroid Rendezvous Mission

This paper presents a comparative study of the applicability and accuracy of optimal control methods and neural network-based estimators in the context of porkchop plots for preliminary asteroid rendezvous mission design. The scenario considered involves a deep-space CubeSat equipped with a low-thrust engine, departing from Earth and rendezvousing with a near-Earth asteroid within a three-year launch window. A low-thrust trajectory optimization model is formulated, incorporating variable specific impulse, maximum thrust, and path constraints. The optimal control problem is efficiently solved using Sequential Convex Programming (SCP) combined with a solution continuation strategy. The neural network framework consists of two models: one predicts the minimum fuel consumption ($Δv$), while the other estimates the minimum flight time ($Δt$) which is used to assess transfer feasibility. Case results demonstrate that, in simplified scenarios without path constraints, the neural network approach achieves low relative errors across most of the design space and successfully captures the main structural features of the porkchop plots. In cases where the SCP-based continuation method fails due to the presence of multiple local optima, the neural network still provides smooth and globally consistent predictions, significantly improving the efficiency of early-stage asteroid candidate screening. However, the deformation of the feasible region caused by path constraints leads to noticeable discrepancies in certain boundary regions, thereby limiting the applicability of the network in detailed mission design phases. Overall, the integration of neural networks with porkchop plot analysis offers an effective decision-making tool for mission designers and planetary scientists, with significant potential for engineering applications.

math.OC↗

arXiv2025

Multi-Revolution Low-Thrust Trajectory Optimization With Very Sparse Mesh Pseudospectral Method

Multi-revolution low-thrust trajectory optimization problems are important and challenging in space mission design. In this paper, an efficient, accurate, and widely applicable pseudospectral method is proposed to solve multi-revolution low-thrust trajectory optimization problems with various objective functions and perturbations. The method is based on the Sundman transformation and pseudospectral method, together with a sparse mesh that is monotonic, near-uniformly spaced, and uniformly scattered on the unit circle. Two methods are proposed to construct the mesh: a deterministic method based on rotation mapping; a stochastic method utilizing autocorrelated random sequences. Core mechanisms ensuring the correctness of the method are analyzed, including the dual roles of mesh points as both integration points in the temporal domain and sampling points in the angular domain, the slow dynamics of the system excluding the fast angle variable, and the nearly commutative vector fields generated by applying different control inputs. The method is demonstrated through a multi-revolution low-thrust orbital rendezvous problem. Results show that the proposed method achieves high accuracy with only a few seconds of computational time for challenging problems.

eess.SY↗

arXiv2025

Re-examining the Legendre-Gauss-Lobatto Pseudospectral Methods for Optimal Control

Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau (LGR) points in terms of convergence properties, this paper presents a rigorous re-examination of LGL-based methods. We introduce an augmented formulation that enhances the standard LGL collocation approach by incorporating an additional degree of freedom (DOF) into the interpolation structure. We demonstrate that this augmented formulation is mathematically equivalent to the integral formulation of the LGL collocation method. Through analytical derivation, we establish that the adjoint system in both the augmented differential and integral formulations corresponds to a Lobatto IIIB discontinuous collocation method for the costate vector, thereby resolving the previously reported convergence issues. Our comparative analysis of LG, LGR, and LGL collocation methods reveals significant advantages of the improved LGL approach in terms of discretized problem dimensionality and symplectic integration properties. Numerical examples validate our theoretical findings, demonstrating that the proposed LGL-based method achieves comparable accuracy to LG and LGR methods while offering superior computational performance for long-horizon optimal control problems due to the preservation of symplecticity.

eess.SY↗

arXiv2025

Vectorized Sparse Second-Order Forward Automatic Differentiation for Optimal Control Direct Methods

Direct collocation methods are widely used numerical techniques for solving optimal control problems. The discretization of continuous-time optimal control problems transforms them into large-scale nonlinear programming problems, which require efficient computation of first- and second-order derivatives. To achieve computational efficiency, these derivatives must be computed in sparse and vectorized form, exploiting the problem's inherent sparsity structure. This paper presents a vectorized sparse second-order forward automatic differentiation framework designed for direct collocation methods in optimal control. The method exploits the problem's sparse structure to efficiently compute derivatives across multiple mesh points. By incorporating both scalar and vector nodes within the expression graph, the approach enables effective parallelization and optimized memory access patterns while maintaining flexibility for complex problems. The methodology is demonstrated through application to a prototype optimal control problem. A complete implementation for multi-phase optimal control problems is available as an open-source package, supporting both theoretical research and practical applications.

eess.SY↗