A Continuous Control for Stabilizing the Extended Nonholonomic Double Integrator
The extended nonholonomic double integrator (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 without 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. Besides the theoretical proofs, simulations conducted on the dynamics of a mobile robot are also presented to demonstrate the validity and performance of the proposed method.
Long Chen, Yongkang Zhang, Aixing Feng, Zhenying Xu, Boquan Li and Han Shen
Y. Peng et al., "A Continuous Control for Stabilizing the Extended Nonholonomic Double Integrator", Key Engineering Materials, Vol. 464, pp. 217-220, 2011