Hierarchical control via approximate simulation and feedback linearization

This paper considers the problem of hierarchical trajectory planning and control for a class of nonlinear systems which are feedback linearizable. The proposed hierarchy builds on the notion of approximate simulation relations. We use the diffeomorphic transformation between the feedback linearized system and the nonlinear system, along with the associated interface between the abstraction and the linearization of the concrete system obtained via feedback, to recast the problem of trajectory planning and control for the nonlinear system into a reduced dimensional space. The formal abstraction framework then enables the control to be mapped to the space of the concrete nonlinear system using the feedback linearized system as a “bridge”. Two different hierarchical control architectures are proposed for this framework and the method is demonstrated with a quadrotor system.