Stabilization and synchronization of networked mechanical systems

The main theme of this thesis is coordination and stabilization of a network of mechanical systems or rigid bodies to achieve synchronized behaviour. The idea is to use controls derived from potentials to couple the systems such that the closed-loop system is also a mechanical system with a Lagrangian structure. This permits the closed-loop Hamiltonian to be used as a Lyapunov function for stability analysis.; It is a big challenge to develop a provable, systematic methodology to control and coordinate a network of systems to perform a given task. The control law should be robust enough to handle environment uncertainties, avoid obstacles and collisions and keep the system formation going. The fact that these systems may even have unstable dynamics makes the problem even more interesting and exciting both from a theoretical and applied point of view. This work investigates the coordination problem when each individual system has its own (maybe unstable) dynamics; this distinguishes this work from many other recent works on coordination control where the individual system dynamics are assumed to be single/double integrators.; We build coordination techniques for three kinds of systems. The first one consists of underactuated Lagrangian systems with Abelian symmetry groups lacking gyroscopic forces. Asymptotic stabilization is proved for two cases, one which yields convergence to synchronized motion restricted to a constant momentum surface and one in which the system converges asymptotically to a relative equilibrium.; Next we consider rigid body systems where the configuration space of each individual body is the non Abelian Lie group SO(3) or SE(3). In the SO(3) case, the asymptotically stabilized solution corresponds to each rigid body rotating about its unstable middle axis and all the bodies synchronized and pointing in a particular direction in inertial space. In the SE(3) case, the asymptotically stabilized solution corresponds to each rigid body rotating about its unstable middle axis and translating along its middle axis and the whole network synchronized and moving along a particular direction in inertial space.; We conclude with a brief summary of the results and with a note on numerous directions in which this work can be extended.