arXiv subjects

Adam Evans

Publications and source records attributed to Adam Evans.

4 recordsLinked to original sources

arXiv2026

Polynomial-Based Solutions to Targeting Problems for Onboard Applications

This paper solves the targeting problem focusing on accuracy, computational efficiency, and reliability. The trajectory optimization problem is first recast as a polynomial optimization problem (POP) by leveraging differential algebra to compute high-order Taylor expansions of the nonlinear dynamics and constraints. Moment-sum-of-squares (SOS) optimization is then utilized to solve this POP. A convex formulation based on a second-order expansion of the dynamics is also proposed. For impulsive targeting, the moment-SOS and convex approaches are compared against traditional nonlinear programming (NLP) solvers and map inversion techniques. Results indicate that the moment-SOS approach provides solutions as accurate as traditional NLP, but with the critical advantage of guaranteeing convergence to the global optimum under mild assumptions. Furthermore, the method excels at handling large maneuvers and long propagation times, conditions in which standard linear approximations rapidly degrade. To demonstrate its versatility, the methodology is extended to a continuous low-thrust station keeping (SK) scenario in the Earth-Moon Circular Restricted Three-Body Problem. The algorithm's performance is then evaluated in the presence of significant state errors. The ability to directly handle non-convex constraints and recast complex, nonlinear dynamics into formulations with reliable convergence properties makes the moment-SOS approach suitable for autonomous onboard applications.

math.OC↗

arXiv2026

Exoplanetary Tour Design with Solar Sails: TheAntipodes Results in the GTOC13 Problem

Solar sails present an attractive but challenging propulsion method for large-scale, long-duration trajectory design problems. In 2025, the 13th Global Trajectory Optimization Competition (GTOC13) presented a trajectory design problem involving an exoplanetary solar sailing spacecraft in the fictional Altaira system, where the goal is to collect scientific return from flybys of planets, comets, and asteroids. High-scoring solutions combine combinatorial gravity assist tour design with continuous solar sail trajectory optimization. This paper presents the solution approach developed by the team `TheAntipodes' during GTOC13. The approach combines several search and optimization stages: (1) trade studies to identify competitive entry opportunities, (2) large-scale beam search over ballistic gravity assist tours to identify beneficial planetary structures, (3) resonant targeting strategies for Vulcan flyby sequences, and (4) multi-leg solar sail trajectory refinement using sequential convex programming (SCP). A key component of the refinement process is the use of a lossless control-convex solar sail formulation, which allows for large portions of the trajectory, including all gravity assist geometry and flyby timing, to be optimized simultaneously to maximize score. The resulting trajectory placed third, with a score of 337.878 from 133 scoring flybys, and exhibited a structure broadly similar to those of the other high-scoring solutions. This demonstrates the scalability of methods such as SCP for very large trajectory design problems.

astro-ph.IM↗

arXiv2026

Sample-Free Safety Assessment of Neural Network Controllers via Taylor Methods

In recent years, artificial neural networks have been increasingly studied as feedback controllers for guidance problems. While effective in complex scenarios, they lack the verification guarantees found in classical guidance policies. Their black-box nature creates significant concerns regarding trustworthiness, limiting their adoption in safety-critical spaceflight applications. This work addresses this gap by developing a method to assess the safety of a trained neural network feedback controller via automatic domain splitting and polynomial bounding. The methodology involves embedding the trained neural network into the system's dynamical equations, rendering the closed-loop system autonomous. The system flow is then approximated by high-order Taylor polynomials, which are subsequently manipulated to construct polynomial maps that project state uncertainties onto an event manifold. Automatic domain splitting ensures the polynomials are accurate over their relevant subdomains, whilst also allowing an extensive state-space to be analysed efficiently. Utilising polynomial bounding techniques, the resulting event values may be rigorously constrained and analysed within individual subdomains, thereby establishing bounds on the range of possible closed-loop outcomes from using such neural network controllers and supporting safety assessment and informed operational decision-making in real-world missions.

eess.SY↗

arXiv2025

Learning-Based Stable Optimal Guidance for Spacecraft Close-Proximity Operations

Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability guarantees, which are critical for safety-sensitive aerospace applications. This paper proposes a comprehensive framework that combines control Lyapunov functions with supervised learning to provide certifiably stable, time- and fuel-optimal guidance for rendezvous maneuvers governed by Clohessy-Wiltshire dynamics. The framework is easily extensible to nonlinear control-affine systems. A novel neural candidate Lyapunov function is developed to ensure positive definiteness. Subsequently, a control policy is defined, in which the thrust direction vector minimizes the Lyapunov function's time derivative, and the thrust throttle is determined using minimal required throttle. This approach ensures that all loss terms related to the control Lyapunov function are either naturally satisfied or replaced by the derived control policy. To jointly supervise the Lyapunov function and the control policy, a simple loss function is introduced, leveraging optimal state-control pairs obtained by a polynomial maps based method. Consequently, the trained neural network not only certifies the Lyapunov function but also generates a near-optimal guidance policy, even for the bang-bang fuel-optimal problem. Extensive numerical simulations are presented to validate the proposed method.

eess.SY↗