A Continuous Control for Stabilizing the Extended Nonholonomic Double Integrator: Theory and Simulation Results
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.
Y. Peng et al., "A Continuous Control for Stabilizing the Extended Nonholonomic Double Integrator: Theory and Simulation Results", Applied Mechanics and Materials, Vols. 44-47, pp. 3987-3991, 2011