Transcription and optimization of an interplanetary trajectory through quantum annealing

Abstract

This study employed a quantum-annealing framework to solve spacecraft trajectory optimization problems. Quantum annealing belongs to the field of quantum computing and is a promising technique for tackling hard binary optimization problems by employing quantum annealers. To address the optimal control of a trajectory using quantum annealing, a transcription procedure was introduced to express the problem in the binary optimization form required. The proposed procedure leverages the pseudospectral method to discretize the trajectory and represents the dynamical constraints as algebraic equality constraints at specific nodes. Subsequently, both a linearization procedure and binary representation strategy for the real-valued variables of the problem were presented, leading to the quadratic binary unconstrained optimization form. The quantum-annealing-based method was tested in the context of an interplanetary low-thrust transfer from the Earth to Mars. First, we discussed which instances of the problem, especially in terms of their dimensions, are implementable on currently available quantum annealers; then, a solution was sought by employing annealers from D-Wave systems. Solutions from hybrid solvers that combine classical and quantum resources, and fully quantum solvers were explored. The results demonstrate the validity of the transcription approach, demonstrate the ability of the hybrid solver to tackle the case-study problem, and highlight the promising features and current limitations of practical trajectory optimization with quantum annealing.