Definition of the Mobile Robot

The model considered is that of a unicycle mobile robot (see Fig. 5.2) that has two driving wheels fixed to the axis and one passive orientable wheel that is placed in front of the axis and normal to it [ 19]. 

The two fixed wheels are controlled independently by the motors, and the passive wheel prevents the robot from overturning when moving on a plane. 

It is assumed that the motion of the passive wheel can be ignored from the dynamics of the mobile robot, which is represented by the following set of equations [14]  

Notice that the no-slip condition imposed a nonholonomic constraint described by (5.3), that it means that the mobile robot can only move in the direction normal to the axis of the driving wheels. 

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