Control Of Underactuated Spacecraft With Nonholonomic Constraints

Underactuated spacecraft is characterized by the fact that there are more degrees of freedom than actuators. From a practical point of view, it is of interest to consider the control problem when some of the actuators have failed for a fully actuated three-axis spacecraft. In fact, control of underactuatd spacecraft is actually an emergency measure in the case of actuator failure. Form the theoretical point of view, as a typical underactuated mechanical system, the research of underactuated spacecraft is helpful to the development of control theory on UMS. In this dissertation, we only focus on the two-input underactuated spacecraft, and a serial of problems are systematically and deeply studied, including the fundamental property analysis, attitude maneuver planning, trajectory tracking and attitude stabilization problems. The main contents of this dissertation are summarized as follows: Firstly, the spacecraft is modeled as an ideal rigid body, and to represent the spacecraft's attitude the Euler angles parameterization is used. Then, the nonholonomic constraints and the fundamental properties of stability, controllability for the two-input spacecraft model are analyzed. All these are the foundation of the latter control system analysis and design.Secondly, the problem of attitude maneuver planning for underactuated spacecraft with nonholonomic constraint is considered. In the special case of axisymmetry, the feasible trajectory generation algorithm is proposed based on the differential flatness property of the spacecraft. The simulation results demonstrate that the obtained trajectories can satisfy the constraints very well, and the small asymmetries do not have a catastrophic effect on the final maneuver orientation. Then, taking into account the actuator saturation, a time-optimal attitude maneuver planning algorithm for general underactuated spacecraft is proposed using the modified Legendre pseudospectral method, in which a relaxation parameter is employed to guarantee the existence of the solution. Moreover, an initial guess generator is developed by particle swarm optimization algorithm to provide a set of feasible initialization solution for the following nonlinear programming problem. Finally, the time-optimal control input is Bang-Bang, and it is clear that the accuracy of the computed solution is diminished at the jump points. Thus, combining the global pseudospectral method and the local pseudospectral method, the distribution of the LGL nodes is changed. We place the knots near those locations at which the control trajectories have large variations, and the total number of LGL nodes is kept as a constant. Simulation results show that, the modified Legendre pseudospectral method can improve the accuracy and feasibility of the computation.Thirdly, a sample-data feedback trajectory tracking algorithm is introduced for underactuated spacecraft, and the open-loop time-optimal trajectory is regarded as a reference. Above all, assuming there exist small initial uncertainty, the model of the underactuated is linearized around the reference trajectory, and in this fashion, the trajectory control problem is cast into a trajectory state regulation problem. Then, based on the online real-time re-planning strategy, the two point boundary value problem is solved by indirect pseudospectral, and a closed-loop analytical solution is gained. Simulation results illustrate that, the reference trajectory can be perfectly tracked by this algorithm. Then, in the presence of disturbances and the actuator saturation, a feedback trajectory tracking algorithm is proposed by real-time re-planning using direct pseudospectral. Further, the differential flatness property for general underactuated spacecraft is extended, such that the open-loop re-optimization can operate online. It is shown that, the real-time re-planning algorithm can follow the reference trajectory as well as finding a more optimal cost function.Last but not least, the stabilization problem of underactuated spacecraft is settled based on infinite optimal control strategy. First of all, a domain transformation is utilized to convert the semi-infinite domain to a half-open, finite interval, and an open-loop attitude stabilization control law is provided by LGR pseudospectral method under the actuator saturation condition. Then, taking into account the external disturbances, the results in Chapter 4 are modified by LGR pseudospectral method, and two attitude stabilization algorithms are explored. One is a free-sampling frequency approach that maximally exploits the computational power, and another based on a fixed sampling frequency that maximally exploits prediction with online optimization to reduce the effects of computational delay. In the absence of computational error, stability is guaranteed by Bellman's Principle of Optimality. Preliminary theoretical analysis ensures practical stability in the presence of computational error and disturbances.