Controllability and motion control for mechanical systems on Lie groups

Francesco Bullo, CDS, Caltech

This talk focuses on mechanical control systems defined on Lie groups with the Lagrangian equal to kinetic energy, as for example satellites and underwater vehicles. The local controllability properties of these systems are characterized and two algebraic tests are derived in terms of the operation of symmetric product between the input vector fields.

Then, the perturbation method is applied to compute approximate solutions for the system under small amplitude forcing: in-phase signals play a crucial role in achieving motion along symmetric product directions. Finally, various motion control algorithms can be designed to solve, for example, the point to point reconfiguration problem and the exponential stabilization problem. Numerous example illustrate the theoretical results.