This dissertation explores aspects of control in rigid-body and robotic systems. The first and second paper analyze the attitude stabilization problem and its generalization to n-dimensional rigid bodies. The third and fourth paper are on cooperative control design for systems that evolve on the n-sphere and related topics such as rigid-body reduced attitude synchronization. The fifth, and final, paper proposes a hybrid systems approach to task-priority based control for mobile manipulation.

he first and second paper concern the problem of attitude tracking by kinematic actuation for a class of almost globally asymptotically stabilizing feedback laws on SO(n). The closed-loop systems are solved exactly for the rotation matrices as functions of time. Exact solutions provide insight into both the transient and asymptotical behavior of a system. Applications of these results are found in model predictive control and in sampled systems. The second paper also solves the optimal control problem of geodesic reduced attitude stabilization subject to full attitude stabilization.

The third and fourth paper concern three cooperative control problems on the n-sphere with applications to reduced attitude synchronization and formation control. The global behavior of a consensus protocol is studied both forwards and backwards in time. The forward time stability properties of all equilibria are characterized for a non-trivial class of graph topologies. The reverse time behavior in the case of cyclic graph topologies results in two types of formations depending on the parity of the number of agents. A third control protocol renders the centroid of agent states constant.

The fifth, and final, paper proposes a hybrid control approach to task priority based planar mobile manipulation, i.e., control on the n-torus. The end-effector path following problem for a nonholonomic mobile manipulator is solved subject to constraints on the input norm, feasible joint configurations, and distance to singularities. The hybrid system is well-posed; there is no Zeno behavior or chattering. A continuous, time-independent feedback law is derived based on the hybrid control design.