**3. Cooperative step climbing method**

The proposed method uses the equilibrium of the robots during step climbing. The two connected robots climb a step sequentially. In the present study, stages 1 and 2 indicate the processes in which the front and rear wheels, respectively, of *Robot A* climb the step. Similarly, stages 3 and 4 signify the processes in which the front and rear wheels, respectively, of *Robot B* climb the step (**Figure 9**). The ascent process, as shown in <1>�<16> in **Figure 9**, is described below. The velocities of the robots are constant in the forward direction.

### **3.1 Stage 1**

<1> Both operators perceive the step using the moving images from the cameras on the robots (**Figure 7**). The link height of *Robot A* is set at a high position (**Figure 4**). <2> *Robot B* stops, and *Robot A* moves forward. As a result, the front wheels of *Robot A* are lifted. <3> The operators make both robots move forward while the front wheels of *Robot A* are lifted. <4> When the operators recognize that the front wheels of *Robot A* have passed over the step edge, the operators manipulate the joysticks to adjust the difference in speed between the robots, so that the front wheels of *Robot A* are placed on the upper level of the step. Here, in stages 1 and 2, if *Robot A* is faster than *Robot B*, then the tilt of *Robot A* increases. If *Robot B* is faster than *Robot A*, then the tilt of *Robot A* decreases.

### **3.2 Stage 2**

<5> The operators make the robots continue to move forward. The back wheels of *Robot A* come into contact with the step. <6> *Robot B* pushes *Robot A*. *Robot B*

the speeds of the robots, so that the front wheels of *Robot B* are placed on the upper level of the step. Here, in stages 3 and 4, if *Robot B* is faster than *Robot A*, the tilt of *Robot B* increases. If *Robot A* is faster than *Robot B*, then the tilt of *Robot B* decreases.

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote…*

<13> The operators make the robots continue to move forward. The back wheels of *Robot B* come into contact with the step. <14> *Robot A* pulls *Robot B*. *Robot A* supports the climbing of *Robot B* and *Robot A* prevents *Robot B* from tipping over backward. <15> *Robot B* climbs up onto the step. <16> Once the rear wheels of *Robot B* have reached the upper level of the step, the operators stop each robot.

When *Robot A* climbs a step, the body of the robot inclines, and its front wheels are lifted due to the difference in velocity between the two connected robots. When the robots are manipulated by the operators, the step climbing ability greatly influ-

In this section, we clarify the relationships among the robot incline, the velocity,

**4.1 Relationships among the manipulation time, the velocity, and the height**

In **Figure 10**, Σ*<sup>B</sup>* is the basic coordinate system for the robots, where *p*<sup>0</sup> is the origin as well as the contact position between the rear wheels of *Robot B* and the

*p*2, link position of *Robot B*; *p*3, link position of *Robot A*; *p*4, axis of the rear wheels of *Robot A*; *p*5, axis of the front wheels of *Robot A*; *p*6, tread position of the front

The position vectors for the joints in the coordinate system Σ*<sup>B</sup>* are expressed

*<sup>T</sup>*, <sup>1</sup>*p*<sup>2</sup> <sup>¼</sup> ½ � *lB* <sup>þ</sup> *lLBhLB*

Then, *ϕ<sup>i</sup>* is the angle between Σ*<sup>i</sup>* and Σ*<sup>i</sup>*�1, and Σ<sup>1</sup> is parallel to Σ<sup>0</sup> in *stage 1*.

� �*<sup>T</sup>* (*i* = 1–6). In the local coordinate system, for the case in which

In the basic coordinate system Σ*B*, the homogeneous transformation matrix *<sup>B</sup>T*<sup>4</sup>

(*i* = 1–5) are the joints (*p*1, axis of the rear wheels of *Robot B*;

*<sup>T</sup>*, <sup>2</sup>*p*<sup>3</sup> <sup>¼</sup> ½ � *<sup>d</sup>* <sup>0</sup> *<sup>T</sup>*,

*ϕ*<sup>1</sup> ¼ 0 (1)

*ϕ<sup>i</sup>* ¼ *ϕ*<sup>2</sup> þ *ϕ*<sup>3</sup> (2)

*ϕ*<sup>4</sup> ¼ 0 (3)

*<sup>T</sup>*, and <sup>5</sup>*p*<sup>6</sup> <sup>¼</sup> ½ � *rA* <sup>0</sup> *<sup>T</sup>* (**Figure 10**).

**of the front wheels required to climb the step**

*<sup>T</sup>*, <sup>4</sup>*p*<sup>5</sup> <sup>¼</sup> ½ � *lA* �*RA* <sup>þ</sup> *rA*

P<sup>3</sup>

*<sup>k</sup>*¼<sup>1</sup>*ϕi*, is

X 3

*k*¼1

**3.4 Stage 4**

**4. Theoretical analysis**

*DOI: http://dx.doi.org/10.5772/intechopen.90162*

ences the manipulation time.

and the manipulation time.

ground. In addition, *pi*

wheels of *Robot A*).

<sup>3</sup>*p*4<sup>¼</sup> ½ � *lLA* �*hLA*

<sup>Σ</sup>*<sup>i</sup>* is parallel to <sup>Σ</sup>0, <sup>0</sup>*p*<sup>1</sup> <sup>¼</sup> ½ � <sup>0</sup>*RB*

The incline of *Robot A*,

Here, Σ<sup>4</sup> is always parallel to Σ3:

as *<sup>B</sup>pi*<sup>¼</sup> *xi yi*

Thus,

is as follows:

**87**

supports the climbing of *Robot A*, and *Robot B* prevents *Robot A* from tipping over backward. <7> *Robot A* climbs up onto the step. <8> Once the rear wheels of *Robot A* have reached the upper level of the step, the operators stop each robot.
