Nonlinear Dynamics

, Volume 81, Issue 3, pp 1475–1487 | Cite as

Feedback stabilization of a nonholonomic system with potential fields: application to a two-wheeled mobile robot among obstacles

Original Paper


In this paper, a feedback controller for a nonholonomic system with three states and two inputs is derived using an artificial potential function that has no local minima, and the stability of equilibria of the system is analyzed. Although the system with the controller has an infinite number of equilibria due to the nonholonomic constraint, those equilibria except the critical points of the potential function are unstable because of a skew-symmetric component of the controller. When the potential function has critical points of saddle type, the saddles may be stable equilibria in addition to the stable equilibrium at the minimum of the function. The controller is applied to a two-wheeled mobile robot among obstacles and modified by using a time-varying potential function in order to avoid convergence to the saddles. As a result, with the controller, the mobile robot converges to a desired position and orientation without collision with obstacles.


Nonholonomic system Feedback control Lyapunov stability Potential field method 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Systems ScienceKobe UniversityKobeJapan

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