Dynamic path inversion for a class of nonlinear systems

For a class of Chaplygin-like nonholonomic systems a special motion planning is addressed. Given a path in an n-dimensional space we deduce conditions for which there exist feedforward inputs that cause the system to exactly follow the given path. The posed problem is studied from both local and global viewpoints and a constructive solution is provided by means of a dynamic inversion generator, i.e., a dynamical (inverse) system whose outputs are the sought control inputs. The developed theory may be applied to the maneuver regulation problem to help pursuing aggressive maneuvering of autonomous aerial vehicles. Simulations for 3-dimensional and 2-dimensional path following examples are included.