10 a review of models and structures for wheeled mobile robots four case studies

A Review of Models and Structures for Wheeled Mobile Robots:

Four Case Studies

Ramiro Vel´azquez and Aim´e Lay-Ekuakille

Abstract— This paper reviews the mathematical models of

four commonly encountered designs for wheeled mobile robots

(WMR). These designs belong to two generic classes of wheeled

robot structures: differential-drive and omnimobile. First, the

two wheel differential-drive model is presented to show how

zero turning radius is achieved with only bidirectional move￾ment. Three particular designs are addressed: the popular

two-active-fixed wheels and one-passive-caster wheel, a simple

belt-drive, and sprocket-chain system. Next, the model for

omnimoble robots with Swedish wheels is presented to illustrate

holonomic omnidirectional motion. All four models are based

on physical parameters easily measured and are useful to

understand the internal dynamics of these WMR and to

accurately visualize their motion in 2D environments. They

can be therefore used as a practical reference to predict the

accessibility of physical prototypes to selected places and to

test different algorithms for control, path planning, guidance,

and obstacle avoidance.

I. INTRODUCTION

Understanding how wheeled mobile robots (WMR) move

in response to input commands is essential for feedback

control design and many navigation tasks such as path

planning, guidance, and obstacle avoidance.

Campion and Chung classified in [1] the mobility of WMR

into five generic structures corresponding to a pair of indices

(m, s): mobility degree m and steerability degree s. The first

one refers to the number of degrees of freedom the WMR

could have instantaneously from its current position without

steering any of its wheels while the second refers to the

number of steering wheels that can be oriented independently

in order to steer the WMR. These five classes are:

• Type (3,0) robots or omnidirectional robots have no

steering wheels (s=0) and are equipped only with

Swedish or active caster wheels. They have full mobility

in the plane (m=3), which means that they are able

to move in any direction without any reorientation.

Representative examples of such robots are [2] and [3].

• Type (2,0) robots have no steering wheels (s=0) but

either one or several fixed wheels with a common

axle. The common axle restricts mobility to a two￾dimensional plane (m=2). Examples of type (2,0) robots

are [4] and [5].

• Type (2,1) robots have no fixed wheels and at least one

steering wheel. If there is more than one steering wheel,

R. Vel´azquez is with the Mechatronics and Control Systems Lab

(MCS), Universidad Panamericana, 20290, Aguascalientes, Mexico. Con￾tact: [email protected]

A. Lay-Ekuakille is with the Department of Innovation

Engineering, Universit`a del Salento, 73100, Lecce, Italy. Contact:

[email protected]

their orientations must point to the same direction (s=1).

Therefore, mobility is restricted to a two-dimensional

plane (m=2). An example is the synchronous drive

WMR in [6].

• Type (1,1) robots have one or several fixed wheels

on a common axle and also one or several steering

wheels, with two conditions for the steering wheels:

their centers must not be located on the common

axle of the fixed wheels and their orientations must

be coordinated (s=1). Mobility is restricted to a one￾dimensional plane determined by the orientation angle

of the steering wheel (m=1). Examples of this type are

the tricycle, the bicycle, and the car-like WMR.

• Type (1,2) robots have no fixed wheels, but at least two

steering wheels. If there are more than two steering

wheels, then their orientation must be coordinated in

two groups (s=2). Mobility is restricted to a one￾dimensional plane (m=1) determined by the orientation

angles of the two steering wheels.

This paper particularly address type (3,0) and (2,0) robots.

Taking as example our own prototypes (and some practical

lessons learned from their implementation), we derive the

mathematical models of four commonly encountered designs

for these two types of WMR.

The rest of the paper is organized as follows: in Sec￾tion 2, the popular two wheel differential-drive model is

obtained using the general two-active-fixed wheels and one￾passive-caster wheel structure. Next, two other differential￾drive designs are presented to illustrate some other efficient

locomotion systems: a simple belt-drive system which shows

how frictional forces transfer torque to generate motion and

a sprocket-chain system which offers another method for

transferring motion when frictional forces are insufficient

to transfer power. In Section 3, the omnimobile robot with

Swedish wheels is analyzed. The resulting model shows how

holonomic omnidirectional motion is achieved. Finally, the

conclusion summarizes the paper main concepts.

II. DESIGNS AND PROTOTYPES

Let us start addressing type (2,0) robots. There are many

design alternatives; however, the two-wheel differential-drive

robot is by far the most popular design.

Let us consider our prototype IVWAN (Fig. 1(a)). Its

mechanical structure is based on a differential-drive con￾figuration consisting of two independently controlled front￾active wheels and one-rear-caster wheel (Fig. 1(b)). Active

wheels are driven by two high-power DC motors which allow

IVWAN to achieve a maximum speed of 20 km/hr.

The 15th International Conference on Advanced Robotics

Tallinn University of Technology

Tallinn, Estonia, June 20-23, 2011

978-1-4577-1159-6/11/$26.00 ©2011 IEEE 524