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**A recursive technique for tracking control of nonholonomic systems in chained form.**
*(English)*
Zbl 0978.93046

The paper proposes a new design strategy for the tracking problem of a class of nonholonomic control systems in chained form.

First of all, the authors extended a backstepping-based tracking control procedure to the case of nonholonomic chained systems and then solved the semiglobal tracking control problem. They also discuss some special cases where the tracking problem can be globally solved. The proposed recursive methodology is illustrated for two benchmark mechanical systems with nonholonomic constraints, which can be transformed into a dynamic chained form under appropriate change of coordinates and feedback, namely an articulated vehicle and a knife edge moving on a plane. For these two systems the new strategy is also compared with other existing techniques.

The authors also show that the tracking design procedure presented here can be extended to a dynamical extension of the chained form system, which includes systems with a drift term.

First of all, the authors extended a backstepping-based tracking control procedure to the case of nonholonomic chained systems and then solved the semiglobal tracking control problem. They also discuss some special cases where the tracking problem can be globally solved. The proposed recursive methodology is illustrated for two benchmark mechanical systems with nonholonomic constraints, which can be transformed into a dynamic chained form under appropriate change of coordinates and feedback, namely an articulated vehicle and a knife edge moving on a plane. For these two systems the new strategy is also compared with other existing techniques.

The authors also show that the tracking design procedure presented here can be extended to a dynamical extension of the chained form system, which includes systems with a drift term.

Reviewer: M.Fatima Silva Leite (Coimbra)

### MSC:

93C85 | Automated systems (robots, etc.) in control theory |

70F25 | Nonholonomic systems related to the dynamics of a system of particles |

70E60 | Robot dynamics and control of rigid bodies |

70Q05 | Control of mechanical systems |