Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method
PhD Student, Department of Mechanical and Aerospace Engineering, Princeton University, NJ, USA（普林斯顿大学机械与航空航天工程系博士生）；Assistant Professor, Department of Mechanical and Aerospace Engineering, Princeton University, NJ, USA（普林斯顿大学机械与航空航天工程系助理教授）
Long time-duration low-thrust nonlinear optimal spacecraft trajectory global search is a computationally and time expensive problem characterized by clustering patterns in locally optimal solutions. During preliminary mission design, mission parameters are subject to frequent changes, necessitating that trajectory designers efficiently generate high-quality control solutions for these new scenarios. Generative machine learning models can be trained to learn how the solution structure varies with respect to a conditional parameter, thereby accelerating the global search for missions with updated parameters. In this work, state-of-the-art diffusion models are integrated with the indirect approach for trajectory optimization within a global search framework. This framework is tested on two low-thrust transfers of different complexity in the circular restricted three-body problem. By generating and analyzing a training data set, we develop mathematical relations and techniques to understand the complex structures in the costate domain of locally optimal solutions for these problems. A diffusion model is trained on this data and successfully accelerates the global search for both problems. The model predicts how the costate solution structure changes, based on the maximum spacecraft thrust magnitude. Warm-starting a numerical solver with diffusion model samples for the costates at the initial time increases the number of solutions generated per minute for problems with unseen thrust magnitudes by one to two orders of magnitude in comparison to samples from a uniform distribution and from an adjoint control transformation.
One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajectory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control (MOC) problem that involves optimizing over the initial or final state, subject to state constraints. Drawing on recent developments in reachability analysis subject to state constraints, we show that the proposed MOC problem can be stated as an optimization problem subject to a constraint that involves the sub-level set of the viscosity solution of a quasi-va…
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the…
Convex MPC and Thrust Allocation with Deadband for Spacecraft Rendezvous
Instituto Superior Técnico（高等技术学院）；University of Lisbon（里斯本大学）；Institute for Systems and Robotics（系统与机器人研究所）；School of Science and Technology from the NOVA University of Lisbon（里斯本新大学科学与技术学院）；Lusófona University（卢索福纳大学）；GMV（GMV公司）
This paper proposes an algorithm which can be used in hybrid Coulomb spacecraft formations to minimize propellant by maximizing the amount of force that is generated by Coulomb forces. This problem is difficult due to the nonlinearities inherent in Coulomb's law. The problem is posed as a series of matrix rank minimization problems which can be solved efficiently using a trace heuristic. A numerical example is provided which shows that, using the proposed control allocation algorithm, the amount of propellant required to perform a reconfiguration maneuver is reduced by approximately 40% compar…
We consider the Earth-Venus mass-optimal interplanetary transfer of a low-thrust spacecraft and show how the optimal guidance can be represented by deep networks in a large portion of the state space and to a high degree of accuracy. Imitation (supervised) learning of optimal examples is used as a network training paradigm. The resulting models are suitable for an on-board, real-time, implementation of the optimal guidance and control system of the spacecraft and are called G&CNETs. A new general methodology called Backward Generation of Optimal Examples is introduced and shown to be able to e…
Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such systems, in space applications, could be spacecraft equipped with 1) a variable-$I_{\text{sp}}$, variable-thrust engine or 2) multiple engines each capable of switching on/off independently. To alleviate the challenges that arise when an indirect optimization method is used, a new framework --- Composite Smooth Control (CSC) --- is proposed that seeks smoothness…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and mixed-integer programming, which is prohibitively slow and computationally expensive. This paper targets a fast solution that is capable of real-time implementation onboard spacecraft. To do so, a novel algorithm is developed that blends sequential convex programming and numerical continuation into a single iterative solution process. Inside the algorithm, di…
Todayś world of spaceś primary concern is the uncontrolled growth of space debris and its probability of collision with spacecraft, particularly in the low earth orbit (LEO) regions. This paper is aimed to design an optimized micro-propulsion system, Cold Gas Thruster, to de-orbit the PSLV debris from 668km to 250 km height after capturing process. The propulsion system mainly consists of a storage tank, pipes, control valves, and a convergent-divergent nozzle. The paper gives an idea of the design of each component based on a continuous iterative process until the design thrust requirements a…
Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous
