麦克纳姆轮的机器人移动平台英文文献和中文翻译(7)

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2 System description and problem statement

2.1 Variables in motion equation

Figure 2 shows the prototype robotic system built at Shanghai University. According to kinematic analysis [5],

its motion equation is shown as

& Shuai Guo guoshuai@shu.edu.cn

V ¼ D0W; ð1Þ

1 Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, Shanghai University, Shanghai, People’s Republic

2VX 3

2 —R0 R0 —R0 R0 3

of China

where V ¼ 4VY 5; D0 ¼ 16

R0 R0 R0 R0 7;

44 R0

R0 R0 5

2 Department of Aerospace Engineering, Ryerson University, Toronto, Canada

x0 l0 þL — l0 þL — l0 þL l0 þL

Fig. 1 3D-model of the mobile robot

2x1 3

W ¼ 6x2 7: L is half of the distance from the front axle to

Fig. 3 Mecanum wheel and roller

4 5

the rear axle, l0 the transverse distance from the wheel centers which are also the contact points on the ground to the platform center line, a the mounting angle of the roller, R0 the radius of four wheels; x1, x2, x3 and x4 are angular velocities of the four wheels, respectively. All the param- eters in Eq. (1) are defined in machine design, L = 750 mm, l0 = 615 mm, R0 = 187.5 mm, a = 45°.

Figure 3 is a view of a mecanum wheel and a roller. The roller is fitted on the edge of the mecanum wheel in angle a with its central axis, which can rotate freely around its central axis. The wheel relies on the friction that the roller acts on the ground to move. Because the material of its outer rim is usually rubbers, it will deform under pressure. Figure 4 is a view of distribution of roller outer rim deformation in its transverse section. F is the pressure on the roller, T the driving torque. The radiuses of wheels reduce differently under different pressures. The greater the

Fig. 4 Distribution of roller deformation

pressure, the greater the deformation is. The deformation zone shifts with the action of driving torque and the shifting causes the position of wheel center to change. From the force analysis of mecanum wheel [6], we know that with the wheel rotating, a driving torque is generated by the force in roller axial direction, so the position of the contact points will shift in axial direction. With the deformation of the roller, the R0 and l0 will change.

(a) (b)

Fig. 2 a Prototype robotic system, b motion model

Fig. 5 Motion model of mobile platform

center O in X-direction; R1, R2, R3 and R4 are the radiuses of four wheels, respectively. The direction of the arrow indicates the positive direction.