Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

Control of Small Spacecraft by Optimal Output Regulation: A Reinforcement Learning Approach

The growing number of noncooperative flying objects has prompted interest in sample-return and space debris removal missions. Current solutions are both costly and largely dependent on specific object identification and capture methods. In this paper, a low-cost modular approach for control of a swarm flight of small satellites in rendezvous and capture missions is proposed by solving the optimal output regulation problem. By integrating the theories of tracking control, adaptive optimal control, and output regulation, the optimal control policy is designed as a feedback-feedforward controller to guarantee the asymptotic tracking of a class of reference input generated by the leader. The estimated state vector of the space object of interest and communication within satellites is assumed to be available. The controller rejects the nonvanishing disturbances injected into the follower satellite while maintaining the closed-loop stability of the overall leader-follower system. The simulation results under the Basilisk-ROS2 framework environment for high-fidelity space applications with accurate spacecraft dynamics, are compared with those from a classical linear quadratic regulator controller, and the results reveal the efficiency and practicality of the proposed method

Guidance, flight mechanics and trajectory optimization. Volume 12 - Relative motion, guidance equations for terminal rendezvous

Equations of relative motion and guidance for orbital transfer and docking maneuvers in spacecraft rendezvou

Pulse-width predictive control for LTV systems with application to spacecraft rendezvous

This work presents a Model Predictive Controller (MPC) that is able to handle Linear Time-Varying (LTV) plants with Pulse-Width Modulated (PWM) control. The MPC is based on a planner that employs a Pulse-Amplitude Modulated (PAM) or impulsive approximation as a hot-start and then uses explicit linearization around successive PWM solutions for rapidly improving the solution by means of quadratic programming. As an example, the problem of rendezvous of spacecraft for eccentric target orbits is considered. The problem is modeled by the LTV Tschauner–Hempel equations, whose state transition matrix is explicit; this is exploited by the algorithm for rapid convergence. The efficacy of the method is shown in a simulation study.Ministerio de Economía y Competitividad DPI2008–05818Ministerio de Economía y Competitividad MTM2015-65608-

Spacecraft rendezvous by differential drag under uncertainties

At low Earth orbits, differentials in the drag forces between spacecraft can be used for controlling their relative motion in the orbital plane. Current methods for determining the drag force may result in errors due to inaccuracies in the density models and drag coefficients. In this work, a methodology for relative maneuvering of spacecraft based on differential drag, accounting for uncertainties in the drag model, is proposed. A dynamical model composed of the mean semimajor axis and the argument of latitude is used for describing long-range maneuvers. For this model, a linear quadratic regulator is implemented, accounting for the uncertainties in the drag force. The actuation is the pitch angle of the satellites, considering saturation. The control scheme guarantees asymptotic stability of the system up to a certain magnitude of the state vector, which is determined by the uncertainties. Numerical simulations show that the method exhibits consistent robustness to accomplish the maneuvers, even in the presence of realistic modeling of density fields, drag coefficients, the corotation of the atmosphere, and zonal harmonics up to J(8)

Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations

Mathematical formulation of guidance equations and solutions for orbital space mission

Interception and deviation of near Earth objects via solar collector strategy

A solution to the asteroid deviation problem via a low-thrust strategy is proposed. This formulation makes use of the proximal motion equations and a semi-analytical solution of the Gauss planetary equations. The average of the variation of the orbital elements is computed, together with an approximate expression of their periodic evolution. The interception and the deflection phase are optimised together through a global search. The low-thrust transfer is preliminary designed with a shape based method; subsequently the solutions are locally refined through the Differential Dynamic Programming approach. A set of optimal solutions are presented for a deflection mission to Apophis, together with a representative trajectory to Apophis including the Earth escape

Multi-Objective Robust H-infinity Control of Spacecraft Rendezvous

Based on the relative motion dynamic model illustrated by C-W equations, the problem of robust Hinfin control for a class of spacecraft rendezvous systems is investigated, which contains parametric uncertainties, external disturbances and input constraints. An Hinfin state-feedback controller is designed via a Lyapunov approach, which guarantees the closed-loop system to meet the multi-objective design requirements. The existence conditions for admissible controllers are formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimization problem subject to LMI constraints. An illustrative example is provided to show the effectiveness of the proposed control design method