Error Function Based Kinematic Control Design for Nonholonomic Mechanical Systems

Conference paper

Tracking or following a trajectory at a kinematic level is the most common approach to control nonholonomic systems. The classical feedback approaches may be either local or global. The local approach to feedback control is achieved through the standard linear control design. Convergence is obtained provided that a system, e.g. a vehicle, starts its motion sufficiently close to a desired trajectory. In the global approach, feedback linearization is pursued and it provides asymptotic stability of tracking errors for arbitrary initial states. Both static and dynamic nonlinear feedback linearization may be used in this approach. In this classical kinematic control design using feedback linearization, some additional properties of kinematic models are used. The first property is the chained-form representation. Transformation of the kinematic control model to the chained form simplifies the control design and provides a framework for the direct extension of the controller to vehicles with more complex kinematics [1, 2]. However, this transformation is not strictly necessary. The second property is that the kinematic control model of a system is Chaplygin. Most theoretic control results at the kinematic level are developed for Chaplygin systems; most of them fail for non-Chaplygin systems, which are recognized as systems hard to control [2].

Feedback linearization enables obtaining full-state or input-output linearization. In the latter method an internal dynamics may be left and stability of the internal dynamics must be analyzed separately. Using either linearization, a controller has to be selected in such a way that it provides some kind of the tracking error convergence.

Keywords

Manifold Dinates 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alexander JC, Maddocks JH (1989) On the kinematics of wheeled mobile robots, Int. J. Robot. Res. 8, 15–27.CrossRefGoogle Scholar
  2. 2.
    Bloch AM (2003) Nonholonomic mechanics and control, Springer, New York.MATHGoogle Scholar
  3. 3.
    De Luca A, Benedetto MD (1993) Control of nonholonomic systems via dynamic compensation, Kybernetica 29, 593–608.Google Scholar
  4. 4.
    De Luca A, Oriolo G, Samson C (1998) Feedback control of a nonholonomic car-like robot. In: Laumond J-P (ed.) Robot motion planning and control, Springer, London.Google Scholar
  5. 5.
    Samson C (1995) Control of chained systems: Application to path following and time-varying point stabilization of mobile robots, IEEE Trans. Automat. Contr. 40, 64–77.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.Warsaw University of Technology, Institute of Aeronautics and Applied MechanicsWarsaw
  2. 2.PM—SoftWarsaw

Personalised recommendations