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Modelling and structural properties The third part of the book is concerned with modelling and control of wheeled mobile robots. A wheeled mobile robot is a wheeled vehicle which is capable of an autonomous motion (without external human driver) because it is equipped, for its motion, with actuators that are driven by an embarked computer. The aim of this chapter is to give a general and unifying presentation of the modelling issues of wheeled mobile robots. Several examples of derivation of kinematic and/or dynamic models for wheeled mobile robots are available in the literature for particular prototypes of mobile robots. Here, a more general viewpoint is adopted and a general class of wheeled mobile robots with an arbitrary number of wheels of different types and actuation is considered. The purpose is to point out the structural properties of the kinematic and dynamic models, taking into account the restriction to robot mobility induced by the constraints. By introducing the concepts of degree of mobility and of degree of steerability, we show that, notwithstanding the variety of possible robot constructions and wheel configurations, the set of wheeled mobile robots can be partitioned in five classes. We introduce four different kinds of state space models that are of interest for understanding the behaviour of wheeled mobile robots. • The posture kinematic model is the simplest state space model able to give a global description of wheeled mobile robots. It is shown that within each of the five classes, this model has a particular generic structure which allows understanding the manoeuvrability properties

C. C. de Wit et al. (eds.), Theory of Robot Control © Springer-Verlag London Limited 1996

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CHAPTER 7. MODELLING AND STRUCTURAL PROPERTIES

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Figure 7.1: Posture coordinates. of the robot. The reducibility, the controllability and the stabilizability of this model are also analyzed. • The configuration kinematic model allows the behaviour of wheeled mobile robots to be analyzed within the framework of the theory of nonholonomic systems. • The configuration dynamic model is the more general state space model. It gives a complete description of the dynamics of the system including the generalized forces provided by the actuators. In particular, the issue of the actuator configuration is addressed, and a criterion is proposed to check whether the motorization is sufficient to fully exploit the kinematic mobility. • The posture dynamic model is feedback equivalent to the configuration dynamic model, and it is useful to analyze its reducibility, controllability and stabilizability properties.

7.1

Robot description

Without real loss of generality and to keep the mathematical derivation as simple as possible, we will assume that the mobile robots under study are made up of a rigid cart equipped with non-deformable wheels and that they are moving on a horizontal plane. The position of the robot in the plane is described as follows (Fig. 7.1). An arbitrary inertial base frame b is fixed