Nonlinear model predictive control of spacecraft relative motion

IFAC-PapersOnLine, 2015

In previous works, the authors have developed a trajectory planning algorithm for spacecraft rendezvous which computed optimal Pulse-Width Modulated (PWM) control signals, for circular and eccentric Keplerian orbits. The algorithm is initialized by solving the impulsive problem first and then, using explicit linearization and linear programming, the solution is refined until a (possibly local) optimal value is reached. However, trajectory planning cannot take into account orbital perturbations, disturbances or model errors. To overcome these issues, in this paper we develop a Model Predictive Control (MPC) algorithm based on the open-loop PWM planner and test it for elliptical target orbits with arbitrary eccentricity (using the linear time-varying Tschauner-Hempel model). The MPC is initialized by first solving the open-loop problem with the PWM trajectory planning algorithm. After that, at each time step, our MPC saves time recomputing the trajectory by applying the iterative linearization scheme of the trajectory planning algorithm to the solution obtained in the previous time step. The efficacy of the method is shown in a simulation study where it is compared to MPC computed used an impulsive-only approach.

Control Engineering Practice, 2012

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 through the use of 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. (P. A. Trodden), [email protected] (A. G. Richards), [email protected] (J. M. Maciejowski) 1 P. A. Trodden is now at

arXiv (Cornell University), 2022

This paper presents a time-constrained model predictive control strategy for the 6 degree-of-freedom (6DOF) autonomous rendezvous and docking problem between a controllable "deputy" spacecraft and an uncontrollable "chief" spacecraft. The control strategy accounts for computational time constraints due to limited onboard processing speed. The translational dynamics model is derived from the Clohessy-Wiltshire equations and the angular dynamics are modeled on gas jet actuation about the deputy's center of mass. Simulation results are shown to achieve the docking configuration under computational time constraints by limiting the number of allowed algorithm iterations when computing each input. Specifically, we show that upwards of 90% of computations can be eliminated from a model predictive control implementation without significantly harming control performance.

2009

A 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).

Journal of Guidance, Control, and Dynamics, 1997

A new approach for the control of a spacecraft with large angle maneuvers is presented. This new approach is based on a nonlinear predictive control scheme which determines the required torque input so that the predicted responses match the desired trajectories. This is accomplished by minimizing the norm-squared local errors between the predicted and desired quantities.

Journal of Guidance, Control, and Dynamics, 2014

The key role of autonomous systems in future space missions has made model predictive control a very attractive guidance and control technique. However, the capability of low-power spacecraft processors to handle the real-time computational load of this technique still needs to be fully established, especially for complex control problems. This paper introduces a method to improve the computational efficiency of model predictive control when applied to the problem of autonomous rendezvous and proximity maneuvering using low-thrust propulsion. To ensure safe trajectories in this scenario, a long control horizon is required and the control problem must be solved at a relatively fast sampling rate. The proposed design addresses such requirements by parameterizing the thrust profile with a set of Laguerre functions. In this setting, the number of control variables can be made significantly smaller than the length of the control horizon, as opposed to standard design methods. By exploiting this property, in combination with multiparametric programming techniques, an explicit control law is derived that is suitable for real-time implementation on simple hardware. The performance of this approach is demonstrated on a small spacecraft mission and compared with that of other control techniques.

Optimal Control Applications and Methods, 2014

In this paper, two nonlinear model predictive control (MPC) strategies are applied to solve a low thrust interplanetary rendezvous problem. Each employs a unique, nonclassical parameterization of the control to adapt the nonlinear MPC approach to interplanetary orbital dynamics with low control authority. The approach is demonstrated numerically for a minimum-fuel Earth-to-Mars rendezvous maneuver, cast as a simplified coplanar circular orbit heliocentric transfer problem. The interplanetary transfer is accomplished by repeated solution of an optimal control problem over (i) a receding horizon with fixed number of control subintervals and (ii) a receding horizon with shrinking number of control subintervals, with a doubling strategy to maintain controllability. In both cases, the end time is left unconstrained. The performances of the nonlinear MPC strategies in terms of computation time, fuel consumption, and transfer time are compared for a constant thrust nuclear-electric propulsion system. For this example, the ability to withstand unmodeled effects and control allocation errors is verified. The second strategy, with shrinking number of control subintervals, is also shown to easily handle the more complicated bounded thrust nuclear-electric case, as well as a state-control-constrained solar-electric case.

IFAC-PapersOnLine, 2019

We propose a non-linear model predictive scheme for planning fuel efficient maneuvers of small spacecrafts that shall rendezvous space debris. The paper addresses the specific issues of potential limited on-board computational capabilities and low-thrust actuators in the chasing spacecraft, and solves them by using a novel MatLab-based toolbox for real-time non-linear model predictive control (MPC) called MATMPC. This tool computes the MPC rendezvous maneuvering solution in a numerically efficient way, and this allows to greatly extend the prediction horizon length. This implies that the overall MPC scheme can compute solutions that account for the long timescales that usually characterize the low-thrust rendezvous maneuvers. The so-developed controller is then tested in a realistic scenario that includes all the near-Earth environmental disturbances. We thus show, through numerical simulations, that this MPC method can successfully be used to perform a fuel-efficient rendezvous maneuver with an uncontrolled object, plus evaluate performance indexes such as mission duration, fuel consumption, and robustness against sensor and process noises.

2011

A robust Model Predictive Controller (MPC) is used to solve the problem of spacecraft rendezvous, using the Hill-Clohessy-Wiltshire model with additive disturbances and line-of-sight constraints. Since a standard (non-robust) MPC is not able to cope with disturbances, a robust MPC is designed using a chance-constrained approach for robust satisfaction of constraints in a probabilistic sense. Disturbances are modeled as Gaussian allowing for an explicit transformation of the probabilistic constraints into simple algebraic constraints. To estimate the distribution parameters a predictor of disturbances is proposed. Both robust and non-robust MPC control laws are compared using the Monte Carlo method, which shows the superiority of the robust MPC.

IEEE Control Systems Letters, 2019

This paper tackles spacecraft optimal control problems in which the cost function is defined by a sum of vector norms, in order to optimize fuel consumption while achieving sparse actuation. An MPC strategy is devised for such type of problems, accounting for different spacecraft maneuvering modes. Closed-loop stability is guaranteed by a conic Lyapunov function, which is employed as a terminal cost in the formulation. A systematic method to construct such function is presented. The proposed design is compared to a standard quadratic MPC scheme on a long-range rendezvous mission.