Geometry stabilizing control of the extended nonholonomic double intergrator

The extended nonholonomic double intergrator (ENDI) cannot be asymptotically stabilized by a continuous and time-invariant feedback controller since it violates the Brockett´s condition. In this paper, a new continuous control scheme is proposed to stabilize the ENDI system with the drift. The dynamics of an ENDI system is enlarged to a higher dimensional space where a continuous but time-varying control law is designed for its stabilization. Furthermore, the drift involved in the ENDI can also be handled as an input perturbation by the proposed scheme. Besides the theoretical proofs, simulations conducted on the dynamics of a trimaran unmanned surface vehicle (USV) are also presented to demonstrate the validity and performance of the proposed method.