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-

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

Robust Model Predictive Control for Spacecraft Rendezvous with Online Prediction of Disturbance Bounds

IFAC Workshop Aerospace Guidance, Navigation and Flight Control Systems (AGNFCS' 09) Samara, RUSSIA June 30 - July 2, 2009A Model Predictive Controller is introduced to solve the problem of rendezvous of spacecraft, using the HCW model and including additive disturbances and line-of-sight constraints. It is shown that a standard MPC is not able to cope with disturbances. Then a robust Model Predictive Control that introduces the concepts of robust satisfaction of constraints is proposed. The formulation also includes a predictor of the disturbance properties which are needed in the robust algorithm. In simulations it is shown that the robust MPC scheme is able to handle not only additive disturbances (which are the ones used in the formulation) but also large multiplicative disturbances and unmodelled dynamics (due to eccentricity of the orbit of the target spacecraft)

Model predictive control system design and implementation for spacecraft rendezvous

This paper presents the design and implementation of a model predictive control (MPC) system to guide and control a chasing spacecraft during rendezvous with a passive target spacecraft in an elliptical or circular orbit, from the point of target detection all the way to capture. To achieve an efficient system design, the rendezvous manoeuvre has been partitioned into three main phases based on the range of operation, plus a collision-avoidance manoeuvre to be used in event of a fault. Each has its own associated MPC controller. Linear time-varying models are used to enable trajectory predictions in elliptical orbits, whilst a variable prediction horizon is used to achieve finite-time completion of manoeuvres, and a 1-norm cost on velocity change minimises propellant consumption. Constraints are imposed to ensure that trajectories do not collide with the target. A key feature of the design is the implementation of non-convex constraints as switched convex constraints, enabling the use of convex linear and quadratic programming. The system is implemented using commercial-off-the-shelf tools with deployment using automatic code generation in mind, and validated by closed-loop simulation. A significant reduction in total propellant consumption in comparison with a baseline benchmark solution is observed

Robust nonlinear feedback control for Rendezvous in near-circular orbits

The growing development of the space sector has been driving new technologies and innovative methods. One of these methods, the orbital rendezvous, has been around since the 1960s and consists of bringing together two spacecrafts, one of them is passive, named "target", and the other is active, called the "chaser". This second spacecraft, in turn, performs maneuvers with the aid of thrusters in order to reduce the relative distance between the two vehicles until it is approximately zero. Initially, this process was done manually, however, today technology has progressed such that the process can be completely autonomous. At the beginning of the automation of this space maneuver, the concern would only be to complete the mission, however, it has progressed towards improving this automation process taking into account propellant consumption and the amount of time spent to perform it. Thus, the present dissertation aims to develop and implement a robust controller, based on a Lyapunov’s approach, to show its performance, robustness, and effectiveness in an orbital rendezvous mission. By using a linear dynamic system, where the orbital eccentricity of the target is assumed to be a system uncertainty, the nonlinear controller can create a smooth trajectory so that the chaser approaches the target. The results show that this nonlinear controller can find the solution to the problem of rendezvous for short relative distances and low relative speeds as well as for large, always generating smooth paths without overshooting the target. It was also found that even by disturbing the system with uncertainty, the controller can generate a robust trajectory with great results. This type of controller for rendezvous missions, besides being robust and effective, as demonstrated in the obtained results, can generate excellent results for rendezvous between non-circular non-coplanar orbits.O crescente desenvolvimento do setor espacial tem vindo a impulsionar novas tecnologias e métodos inovadores. Um destes métodos, o rendezvous orbital, está presente desde a década de 60, e consiste em aproximar dois veículos espaciais, um deles passivo denominado de “target” e o outro ativo denominado de “chaser”. Este segundo, por sua vez, executa manobras com o auxílio de propulsores de modo a reduzir a distância relativa entre os dois veículos até que esta seja aproximadamente nula. Inicialmente, este processo era feito manualmente, no entanto, atualmente, a tecnologia progrediu de tal forma que o processo consegue ser completamente autónomo. No início da automação desta manobra espacial, a preocupação seria apenas completar a missão, contudo esta progrediu no sentido de melhorar este processo de automação tendo em conta o consumo de propelente e a quantidade de tempo gasto. Desta forma, a presente dissertação tem como objetivo desenvolver e implementar um controlador robusto, baseado numa metodologia de Lyapunov, de modo a mostrar a sua performance, robustez e eficácia numa missão de rendezvous orbital. Ao utilizar um sistema linear dinâmico em que a excentricidade da órbita do “target” se assume como uma incerteza do sistema, o controlador não-linear consegue criar uma trajetória suave, para que o “chaser” se aproxime do “target”. Os resultados obtidos demonstram que este controlador consegue encontrar a solução para o problema de rendezvous tanto para pequenas distâncias e velocidades relativas assim como para grandes, gerando sempre trajetórias suaves sem ultrapassar o “target”. Verifica-se também que, mesmo perturbando o sistema com a incerteza, o controlador consegue gerar uma trajetória robusta com ótimos resultados. Este tipo de controlador para missões de rendezvous, para além de ser robusto e eficaz, como demonstrado nos resultados obtidos, consegue gerar ótimos resultados para rendezvous entre órbitas não-coplanares nãocirculares

Trajectory Control of Rendezvous with Maneuver Target Spacecraft

In this paper, a nonlinear trajectory control algorithm of rendezvous with maneuvering target spacecraft is presented. The disturbance forces on the chaser and target spacecraft and the thrust forces on the chaser spacecraft are considered in the analysis. The control algorithm developed in this paper uses the relative distance and relative velocity between the target and chaser spacecraft as the inputs. A general formula of reference relative trajectory of the chaser spacecraft to the target spacecraft is developed and applied to four different proximity maneuvers, which are in-track circling, cross-track circling, in-track spiral rendezvous and cross-track spiral rendezvous. The closed-loop differential equations of the proximity relative motion with the control algorithm are derived. It is proven in the paper that the tracking errors between the commanded relative trajectory and the actual relative trajectory are bounded within a constant region determined by the control gains. The prediction of the tracking errors is obtained. Design examples are provided to show the implementation of the control algorithm. The simulation results show that the actual relative trajectory tracks the commanded relative trajectory tightly. The predicted tracking errors match those calculated in the simulation results. The control algorithm developed in this paper can also be applied to interception of maneuver target spacecraft and relative trajectory control of spacecraft formation flying

A tutorial on model predictive control for spacecraft rendezvous

This tutorial paper provides a review of recent advances in the field of spacecraft rendezvous using model predictive control (MPC), an advanced optimal control strategy based on on-line constrained optimisation of control inputs based on predictions of future trajectories. Firstly, the rendezvous objectives, and the generic constrained MPC problem formulation are summarised. This is followed by a discussion of how to select the three key ingredients used in an MPC design: the prediction model, the constraints and the cost function. Since MPC implementation relies on finding the solution to constrained optimisation problems in real-time, computational aspects are also briefly examined. The paper concludes with conjecture on ways the use of MPC in this application could be further advanced.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ECC.2015.733072