Space craft reliable trajectory tracking and landing using model predictive control with chance constraints

摘要

This work considers the study of chance constrained Model Predictive Control (MPC)for reliable spacecraft trajectory tracking and landing.Objectives of the master thesis: • To identify and study mathematical dynamic models of a spacecraft.• To study the trajectory design and landing schemes for a given mission.• To study the source of uncertainty in the model parameters and external disturbances.• To study the chance constrained MPC scheme for the reliable and optimal trajectorytracking and landing.• To testing the new analytic approximation approaches, Inner and Outer, for chanceconstraints.• To study appropriate MPC algorithms and implement on case-studies.In the first part of the thesis considers deterministic dynamical models of spacecraft arediscussed.The first example is about the tracking of trajectory and soft landing on the surface ofan asteroid EROS433, this model uses Cartesian coordinates.In the second example, in a similar way to the first example, the trajectory and softlanding is performed on the surface of a celestial body. It is assumed that the celestialbody is a perfect sphere, something that does not happen in the first example. Thus,the second example uses a Spherical coordinate system.The third example is about a Lander that enters the Martian atmosphere. This Landerfollows a designed trajectory until reaching a certain altitude over the Martian surface.At this altitude the Lander deploys a parachute to make the landing.To solve the deterministic examples described above, the following sequence of steps are:• pose the deterministic Nonlinear Optimal Control Problem (NOCP),• convert the infinite Optimal Control Problem (OCP) to a finite Nonlinear ProgrammingProblem (NLP), applying the Runge-Kutta 4th order discretizationmethod,• apply the Quasi-sequential method to the deterministic NLP obtained from theprevious step,• solution of the reduced NLP obtained from the previous step using IpOpt software. The steps outlined above are also part of the Nonlinear Model Predictive Control (NMPC)approach.In the second part of the thesis, the same examples of the first part are used but nowwith stochastic variables. To find the control law in each model, the stochastic NMPCwas used. The above mentioned approach begins with a chance constrained OCP.The latter is discretized obtaining an NLP. The problem with this NLP, with chanceconstraints, is that is very difficult to solve in analytic form. So these chance constraintsare approached by a different method that exist in the state of the art. This thesiswork is focused on approaching the chance constraints through Analytic ApproximationStrategies, specifically by the recent: Inner and Outer Approximation methods.The chance constrained MPC is expensive from a computational point of view, but itallows to find a control law for a more reliable trajectory-tracking and soft landing .That is suitable for applications with random disturbances, model inaccuracies, andmeasurement errors.