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 trajectory tracking and landing. • To testing the new analytic approximation approaches, Inner and Outer, for chance constraints. • To study appropriate MPC algorithms and implement on case-studies. In the first part of the thesis considers deterministic dynamical models of spacecraft are discussed. The first example is about the tracking of trajectory and soft landing on the surface of an asteroid EROS433, this model uses Cartesian coordinates. In the second example, in a similar way to the first example, the trajectory and soft landing is performed on the surface of a celestial body. It is assumed that the celestial body 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 Lander follows 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 Programming Problem (NLP), applying the Runge-Kutta 4th order discretization method, • apply the Quasi-sequential method to the deterministic NLP obtained from the previous 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 now with stochastic variables. To find the control law in each model, the stochastic NMPC was used. The above mentioned approach begins with a chance constrained OCP. The latter is discretized obtaining an NLP. The problem with this NLP, with chance constraints, is that is very difficult to solve in analytic form. So these chance constraints are approached by a different method that exist in the state of the art. This thesis work is focused on approaching the chance constraints through Analytic Approximation Strategies, specifically by the recent: Inner and Outer Approximation methods. The chance constrained MPC is expensive from a computational point of view, but it allows to find a control law for a more reliable trajectory-tracking and soft landing . That is suitable for applications with random disturbances, model inaccuracies, and measurement errors. / Tesis

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 trajectory tracking and landing. • To testing the new analytic approximation approaches, Inner and Outer, for chance constraints. • To study appropriate MPC algorithms and implement on case-studies. In the first part of the thesis considers deterministic dynamical models of spacecraft are discussed. The first example is about the tracking of trajectory and soft landing on the surface of an asteroid EROS433, this model uses Cartesian coordinates. In the second example, in a similar way to the first example, the trajectory and soft landing is performed on the surface of a celestial body. It is assumed that the celestial body 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 Lander follows 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 Programming Problem (NLP), applying the Runge-Kutta 4th order discretization method, • apply the Quasi-sequential method to the deterministic NLP obtained from the previous 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 now with stochastic variables. To find the control law in each model, the stochastic NMPC was used. The above mentioned approach begins with a chance constrained OCP. The latter is discretized obtaining an NLP. The problem with this NLP, with chance constraints, is that is very difficult to solve in analytic form. So these chance constraints are approached by a different method that exist in the state of the art. This thesis work is focused on approaching the chance constraints through Analytic Approximation Strategies, specifically by the recent: Inner and Outer Approximation methods. The chance constrained MPC is expensive from a computational point of view, but it allows to find a control law for a more reliable trajectory-tracking and soft landing . That is suitable for applications with random disturbances, model inaccuracies, and measurement errors. / Tesis