State-Constrained Rotational and Translational Motion Control with Applications to Monolithic and Distributed Spacecraft
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The main research in this dissertation deals with translationally and rotationally constrained motion planning within aerospace literature. The topology of such a configuration manifold for a rigid body system is fundamentally challenging from a control perspective. This is because a rotational configuration space is a boundless but compact manifold that has no globally continuous feedback control law. This becomes more troublesome when planning a re-orientation in the presence of rotationally constrained zones. This is of paramount importance as these constraints frequently arise in many space science missions such as space telescope or interferometers; it also poses a challenging computational task for the spacecraft's guidance, navigation, and control subsystem. The complexity of such problems is elevated due to the fact that removing the constrained zones from the boundless compact manifold results in a non-convex region. In the first part of this dissertation, a novel guidance algorithm is proposed to handle multiple types of attitude constrained zones. Two types of attitude constrained zones are as developed and we show that such attitude constrained zones can be represented as convex regions. The advantage of the proposed approach hinges upon the development of the novel strictly convex logarithmic barrier potential functional that is subsequently used for constructing two types of control laws. The second part handles the problem of achieving identical orientation for a group of spacecraft in the presence of rotationally constrained zones. A distributed algorithm for consensus of multiple agents is developed where the shared state is assumed to be constrained in a distinct compact convex set and then augment to fit in the constrained reorientation framework presented earlier. This consensus algorithm is applicable when each spacecraft is required to satisfy its own constraints while also synchronizing with other spacecraft. Two sets of simulations of synchronizing space interferometers with identical and independent rotationally constrained zones are presented. In the final part, as an extension to the first part of the dissertation, a general framework for the analysis of rotationally and translationally constrained spacecraft control problems is presented. The general dynamics of the rigid body is addressed in terms of unit dual quaternions parameterizing position- and attitude-dependent variables, and an almost globally stable control law is developed for unconstrained rigid-body dynamics via a convex energy like Lyapunov function. The novelty of a unit dual quaternion based approach hinges on the fact that translationally and rotationally constrained zones can be formulated as convex representable subsets. Moreover, a convex programming approach is proposed to control synthesis of a planet lander that has the aforementioned constrained zones as its mission requirements. The numerical simulations validates that the proposed approach successfully find feasible trajectories satisfying all constraints.