Model Predictive Control for Spacecraft Rendezvous in Elliptical Orbits with On/Off Thrusters

IFAC Workshop on Advanced Control and Navigation for Autonomous Aerospace Vehicles. 08/06/2015. SevillaIn 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

Trajectory Planning for Spacecraft Rendezvous in Elliptical Orbits with On / Off Thrusters

The 19th World Congress of the International Federation of Automatic Control 2014 Cape Town, SudáfricaIn a previous work, the authors developed a trajectory planning algorithm for spacecraft rendezvous which computed optimal Pulse-Width Modulated (PWM) control signals, assuming that the target was moving in a circular Keplerian orbit. In this paper we extend the algorithm to the case of an elliptical target orbit with arbitrary eccentricity. Since the orbit is elliptical, the linear time-varying Tschauner-Hempel model is used, whose exact solution is possible by using true (or eccentric) anomaly instead of time (which is directly related to both via Kepler's equation). Unlike in the circular case, computing the PWM solution itself requires numerical integration. However, explicit linearization around the computed solution turns out to be possible and is exploited for rapidly improving the solution using linear programming (LP) techniques. The algorithm is initialized by solving the impulsive problem first; the impulses are converted to PWM signals, which are used as an initial guess. Using the explicit linearization and LP, the solution is refined until a (possibly local) optimal value is reached. The efficacy of the method is shown in a simulation study where it is compared to the impulsive-only approach

Trajectory Planning for Spacecraft Rendezvous with On / Off Thrusters

18th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2The objective of this work is to present a trajectory planning algorithm for spacecraft rendezvous that is able to incorporate Pulse-Width Modulated (PWM) control signals. The algorithm is based on linearization around a previously computed solution. To initialize the algorithm, a first solution needs to be obtained. To do so, the trajectory planning problem is solved using Pulse-Amplitude Modulated (PAM) control signals; these are then converted to PWM signals, which are used as an initial guess. Iterating, the solution is refined until an optimal value is reached. Simulations show that this method converges after a few iterations. The algorithm is simple and fast, hence it could be implemented online or used together with a Model Predictive Controller

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)

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-

Transforming triangulations on non planar-surfaces

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.Comment: 19 pages, 17 figures. This version has been accepted in the SIAM Journal on Discrete Mathematics. Keywords: Graph of triangulations, triangulations on surfaces, triangulations of polygons, edge fli

Feedback linearization control for a distributed solar collector field

This article describes the application of a feedback linearization technique for control of a distributed solar collector field using the energy from solar radiation to heat a fluid. The control target is to track an outlet temperature reference by manipulating the fluid flow rate through the solar field, while attenuating the effect of disturbances (mainly radiation and inlet temperature). The proposed control scheme is very easy to implement, as it uses a numerical approximation of the transport delay and a modification of the classical control scheme to improve startup in such a way that results compared with other control structures under similar conditions are improved while preserving short commissioning times. Experiments in the real plant are also described, demonstrating how operation can be started up efficiently.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-04Ministerio de Ciencia y Tecnología DPI2005-0286