Incorporating the nonlinearity index into adaptive-mesh sequential convex optimization for minimum-fuel low-thrust trajectory design

TL;DR

This work tackles minimum-fuel, low-thrust trajectory design by embedding an adaptive-mesh scheme into successive convexification (SCVX) and enhancing it with a nonlinearity-index-guided trust region. It introduces the reparameterization $\tilde{\bm{T}} = \bm{T} s / m$ and an epigraph slack to convexify the objective, while leveraging the state-transition matrix (STM) and, optionally, state-transition tensors (STT) to quantify nonlinearity and regulate step updates. The main contributions are the nonlinearity-index-based trust-region strategy and its demonstration on two benchmarks—the Earth-to-Dionysus heliocentric transfer and a Halo-to-Halo CR3BP transfer—showing improved convergence stability and better fidelity at reduced discretization. The approach holds practical promise for real-time autonomous trajectory optimization by balancing mesh density with nonlinear dynamics to preserve solution quality while limiting computational load.

Abstract

Successive convex programming (SCP) is a powerful class of direct optimization methods, known for its polynomial complexity and computational efficiency, making it particularly suitable for autonomous applications. Direct methods are also referred to as ``discretize-then-optimize'' with discretization being a fundamental solution step. A key step in all practical direct methods is mesh refinement, which aims to refine the solution resolution by enhancing the precision and quality of discretization techniques through strategic distribution and placement of mesh/grid points. We propose a novel method to enhance adaptive mesh refinement stability by integrating it with a nonlinearity-index-based trust-region strategy within the SCP framework for spacecraft trajectory design. The effectiveness of the proposed method is demonstrated through solving minimum-fuel, low-thrust missions, including a benchmark Earth-to-Asteroid rendezvous and an Earth-Moon L2 Halo-to-Halo transfer using the Circular Restricted Three-Body (CR3BP) model.

Figures (6)

• Figure 1: An illustration showcasing nonlinearity index for a two-dimensional problem.
• Figure 2: Summary of the Earth–Dionysus SCVX results: (a) nonlinear vs. linear cost evolution over iterations; (b) optimized 3D trajectory (solid blue) with segmented‐integration verification (dashed red); (c) thrust magnitude profile over normalized time; and (d) spacecraft mass profile over normalized time.
• Figure 3: SCVX performance for the E2D transfer as a function of the number of discretization points $N$: (a) total iterations required for convergence for each configuration; (b) final spacecraft mass (kg) obtained after convergence.
• Figure 4: Four‐panel summary of the Earth–Dionysus SCVX experiment results: (a) nonlinear vs. linear cost evolution over iterations; (b) optimized 3D trajectory (solid blue) with segmented‐integration verification (dashed red); (c) thrust magnitude profile over normalized time; and (d) spacecraft mass profile over normalized time.
• Figure 5: SCVX performance for the CR3BP transfer as a function of the number of discretization points $N$: (a) total iterations required for convergence for each configuration; (b) final spacecraft mass (kg) obtained after convergence.