MTNS ’ 98 : Mathematical Theory of Networks and Systems

We consider under-actuated, drift-free, invariant systems on matrix Lie groups and show how motion control results for nilpotent systems can be extended to invariant systems on non-nilpotent Lie groups by applying the technique of nilpotentization. A constructive procedure is presented to compute the required transformations for local representations of systems on three-dimensional Lie groups. It is shown how exponentially stabilizing feedback control laws can be constructed using these transformations .