391 Wheeled Rob 17. Wheeled Robots Guy Campion, Woojin Chung 17.2.5 Characterization of Robot Mobility .. 397 The purpose of this chapter is to introduce, ana- 17.2.6 The Five Classes lyze, and compare the models of wheeled mobile of Wheeled Mobile Robots ............. 398 robots (WMR) and to present several realizations 17.3 and commonly encountered designs. The mobility State-Space Models of Wheeled Mobile Robots ..................... 398 of WMR is discussed on the basis of the kinematic 17.3.1 Posture Kinematic Models ............. 398 constraints resulting from the pure rolling condi- 17.3.2 Configuration Kinematic Models ..... 399 tions at the contact points between the wheels 17.3.3 Configuration Dynamic Models ....... 400 and the ground. According to this discussion it is 17.3.4 Posture Dynamic Models ............... 401 shown that, whatever the number and the types 17.3.5 Articulated Robots ........................ 401 of the wheels, all WMR belong to only five generic classes. Different types of models are derived and 17.4 Structural Properties of Wheeled Robots Models .................... 403 compared: the posture model versus the config- 17.4.1 Irreducibility, Controllability, uration model, the kinematic model versus the and Nonholonomy ....................... 403 dynamic model. The structural properties of these 17.4.2 Stabilizability .............................. 404 models are discussed and compared. These models 17.4.3 Static State-Feedback as well as their properties constitute the back- Linearizability .............................. 404 ground necessary for model-based control design. 17.4.4 Dynamic State-Feedback Practical robot structures are classified according to Linearizability – Differential the number of wheels, and features are introduced Flatness ...................................... 404 focusing on commonly adopted designs. Omnimo- 17.5 Wheeled Robot Structures ..................... 405 bile robots and articulated robots realizations are 17.5.1 Robots with One Wheel ................. 405 described in more detail. 17.5.2 Robots with Two Wheels ............... 405 17.5.3 Robots with Three Wheels ............. 406 17.1 Overview .............................................. 391 17.5.4 Four Robots with Four Wheels ........ 408 17.5.5 Special Applications 17.2 Mobility of Wheeled Robots ................... 392 of Wheeled Robots ....................... 408 17.2.1 Types of Wheels ........................... 392 17.2.2 Kinematic Constraints ................... 394 17.6 Conclusions .......................................... 409 17.2.3 Robot Configuration Variables ........ 396 References .................................................. 410 17.2.4 Restriction on Robot Mobility ......... 396 17.1 Overview Part B 17 The purpose of this chapter is to provide a general Throughout the chapter we make the assumption description of wheeled mobile robots, to discuss their that the wheels satisfy the kinematic constraints rel- properties from the mobility point of view, to intro- ative to the pure rolling conditions at each contact duce several dynamical models necessary for the design wheel/ground, without sliding effects. This implies that of model-based control laws, and to describe the most we assume that the contact forces between the ground commonly encountered realizations of such robots. and the wheels magically take the right values allow-
Part B Robot Structures 392 ing the satisfaction of these conditions; this is an ideal In Sect. 17.3, we present four types of generic state- model In reality the contact forces appear as a conse- space models allowing one to describe robot behavior quence of local sliding, according to phenomenological within each of these five categories, and the relation- contact force models. Using a singular perturbation ships between these models. We introduce kinematic and approach it can be shown however that these sliding dynamic models, whose inputs are, respectively, veloc- effects correspond to fast dynamics, i. e., to dynami- ities and accelerations (or, equivalently input torques), cal effects with characteristic times that are quite short as well as posture or configuration models, correspond- with respect to the dynamics of the global motion of the ing to a minimal description of the robot behavior, or robot, and can therefore be neglected, at least when us- to a full description, including the internal variables, ing the ideal model for control design purpose [17.1] respectively. (Chap. 34). In Sect. 17.4, we present several structural properties The chapter is organized as follows. Section 17.2 of these models, from a control design point of view. We is devoted to the characterization of the restriction first discuss the questions of stabilizability, controllabil- of robot motion induced by these pure rolling condi- ity, and nonholonomy of restricted mobility robots. We tions. We first describe the different types of wheels then discuss the problem of state feedback linearization, used in the construction of mobile robots and derive either input–output linearization by static state feedback, the corresponding kinematic constraints. This allows or full linearization by dynamic extension and dynamic us to characterize the mobility of a robot equipped state feedback. with several wheels of these different types, and we In the last section we present several realizations show that these robots can be classified into only of wheeled mobile robots, with several particular de- five categories, corresponding to two mobility in- vices such as synchronous drive, Swedish wheels, and dices. articulated robots. 17.2 Mobility of Wheeled Robots In this section we describe a variety of wheels and wheel design of a standard wheel. Three conditions should be implementations in mobile robots. We discuss the re- defined for a standard wheel design: striction of robot mobility implied by the use of these wheels and deduce a classification of robot mobility al- 1. the determination of the two offsets d and b lowing one to characterize robot mobility fully, whatever 2. a mechanical design that allows steering motion or the number and type of the wheels. not (i. e., to fix the wheel orientation or not) 3. the determination of steering and driving actuation 17.2.1 Types of Wheels (i. e., active or passive drive) In order to achieve robot locomotion, wheeled mobile Condition 1 is the kinematic parameter design prob- robots are widely used in many applications. In general, lem for a single standard wheel. The parameter d can wheeled robots consume less energy and move faster be either 0 or some positive constant. Parameter b is the than other locomotion mechanisms (e.g., legged robots lateral offset of the wheel and is usually set to zero. In or tracked vehicles). From the viewpoint of control, less a special design, a nonzero b may be selected to obtain control effort is required, owing to their simple mech- pure rolling contact between the wheel and ground with- anisms and reduced stability problems. Although it is out causing rotational slip at the contact point. However, difficult to overcome rough terrain or uneven ground this is rarely used and we mainly consider the case of conditions, wheeled mobile robots are suitable for a large zero lateral offset b . Part B 17.2 class of target environments in practical applications. Condition 2 is a design problem for whether the When we think of a single-wheel design, there are two wheel orientation can be changed or not. If the steering candidates: a standard wheel or a special wheel. A stan- axis is fixed, the wheel provides a velocity constraint dard wheel can be understood as a conventional tire. on the driving direction. Condition 3 is the design prob- Special wheels possess unique mechanical structures in- lem of whether to actuate steering or driving motion by cluding rollers or spheres. Figure 17.1 shows the general actuators or to drive steering or motion passively.
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