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

TL;DR

This paper introduces a novel pseudospectral method utilizing a sparse mesh and Sundman transformation to efficiently solve complex multi-revolution low-thrust space trajectory optimization problems with high accuracy and minimal computation time.

Contribution

It presents a new pseudospectral approach with sparse mesh construction techniques for improved accuracy and efficiency in multi-revolution low-thrust trajectory optimization.

Findings

Achieves high accuracy with few seconds of computation.

Effective in handling various objective functions and perturbations.

Demonstrated on a challenging orbital rendezvous problem.

Abstract

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.