Decentralized policies for geometric pattern formation and path coverage
On the reachability of quantized control systems with nonabelian symmetries
A. Arsie and E. Frazzoli
We present the general problem of nonlinear control in the framework of (differentiable) groupoids and thorough some recent results obtained in Algebra we show that for a control system whose symmetry group is a semisimple Lie group (like $SO(3)$), it is possible to achieve a dense subset of the configuration space using just two properly chosen discrete controls. Moreover, this property is robust in the sense that if the two discrete controls are slightly different from the designed ones, the set of achievable states remains dense, while this is not the case in the quantization scheme associated to systems with abelian symmetries.
To appear in Hybrid Systems: Computation and Control, Pisa, Italy, 2007.
