**4.3 Simulation**

We performed a numerical calculation to clarify the correlations among the manipulation time to lift the front wheels, the robot velocity, and the height of the front wheels using (29).

The horizontal axes in **Figure 14(a)**–**(c)** show the manipulation time for lifting of the front wheels, *t* ¼ *tm*, and the vertical axes show the height of the bottom of the front wheels (*y*6), indicating the correlations when the velocity of *Robot A* is *vA* ¼ 0.3, 0.4, and 0.5 km/h, respectively.

When *Robot A* moves at 0.3 km/h and climbs a 0.05-m-high step, 0.228 s is required to lift the bottom of the front wheels to the step height (**Figure 11(a)**), and 0.559 s is the time when the horizontal position of the center of gravity of *Robot A* is the contact position between the rear wheels and the road surface (**Figure 11(b)**). Therefore, *Operator A* must complete the lifting operation in a time between 0.228 and 0.559 s. If *tm* is less than 0.228 s, the bottom of the front wheels (*y*6) will not reach a height of 0.05 m, and if *tm* is greater than 0.559 s, *Robot A* will tip over backward. In **Figure 14(a)**, *t*3, which 0.331 s, is the time between these two events. Thus, operators teleoperate the robots to lift the front wheels of *Robot A* and must stop the incline after 0*:*331 s.

Similarly, *t*<sup>4</sup> and *t*<sup>5</sup> are the times at which *Robot A* moves at 0.4 and 0.5 km/h, respectively, where *t*<sup>4</sup> ¼ 0.248 s and *t*<sup>4</sup> ¼ 0.199 s. The results for *t*<sup>3</sup> and *t*<sup>5</sup> reveal that

*Relationships among the manipulation time (t* ¼ *tm), the velocity of Robot A (vA), and the height of the front*

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

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

*wheels of* Robot A *(y6) for (a) vA* ¼ *0.3 km, (b) vA* ¼ *0.4 km, and (c) vA* ¼ *0.5 km/h.*

*t*<sup>3</sup> is more than 66.33% of *t*5.

**Figure 14.**

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*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote… DOI: http://dx.doi.org/10.5772/intechopen.90162*

**Figure 14.**

**4.3 Simulation**

**Figure 13.**

**Figure 12.**

*Tipping over backward of* Robot A*.*

*Industrial Robotics - New Paradigms*

front wheels using (29).

stop the incline after 0*:*331 s.

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*vA* ¼ 0.3, 0.4, and 0.5 km/h, respectively.

We performed a numerical calculation to clarify the correlations among the manipulation time to lift the front wheels, the robot velocity, and the height of the

*Link touching the front part of* Robot B*, which acts to prevent incline of* Robot A*.*

When *Robot A* moves at 0.3 km/h and climbs a 0.05-m-high step, 0.228 s is required to lift the bottom of the front wheels to the step height (**Figure 11(a)**), and 0.559 s is the time when the horizontal position of the center of gravity of *Robot A* is the contact position between the rear wheels and the road surface (**Figure 11(b)**). Therefore, *Operator A* must complete the lifting operation in a time between 0.228 and 0.559 s. If *tm* is less than 0.228 s, the bottom of the front wheels (*y*6) will not reach a height of 0.05 m, and if *tm* is greater than 0.559 s, *Robot A* will tip over backward. In **Figure 14(a)**, *t*3, which 0.331 s, is the time between these two events. Thus, operators teleoperate the robots to lift the front wheels of *Robot A* and must

The horizontal axes in **Figure 14(a)**–**(c)** show the manipulation time for lifting of the front wheels, *t* ¼ *tm*, and the vertical axes show the height of the bottom of the front wheels (*y*6), indicating the correlations when the velocity of *Robot A* is

*Relationships among the manipulation time (t* ¼ *tm), the velocity of Robot A (vA), and the height of the front wheels of* Robot A *(y6) for (a) vA* ¼ *0.3 km, (b) vA* ¼ *0.4 km, and (c) vA* ¼ *0.5 km/h.*

Similarly, *t*<sup>4</sup> and *t*<sup>5</sup> are the times at which *Robot A* moves at 0.4 and 0.5 km/h, respectively, where *t*<sup>4</sup> ¼ 0.248 s and *t*<sup>4</sup> ¼ 0.199 s. The results for *t*<sup>3</sup> and *t*<sup>5</sup> reveal that *t*<sup>3</sup> is more than 66.33% of *t*5.

In Sections 5 and 6, we discuss the influence of the velocity difference for manipulation of the robots.

### **5. Experiment**

The two robots were teleoperated by individual operators (**Figure 15**). Using joysticks (**Figure 5**), the robots were moved at speeds that were set by the program. Six subjects (five adult males and an adult female) participated as robot operators in the experiments.

The six subjects were labeled *s*<sup>1</sup> to *s*<sup>6</sup> and were divided into three groups, *α*, *β*, and *γ*. Subjects *s*<sup>1</sup> and *s*<sup>2</sup> were the operators in group *α*, subjects *s*<sup>3</sup> and *s*<sup>4</sup> were the operators in group *β*, and subjects *s*<sup>5</sup> and *s*<sup>6</sup> were the operators in group *γ*. Subjects *s*1, *s*3, and *s*<sup>5</sup> operated *Robot A*, and subjects *s*2, *s*4, and *s*<sup>6</sup> operated *Robot B*.

Three experiments were conducted, in which the robot velocities were 0.3, 0.4, and 0.5 km/h. The step height and the friction coefficient were constant at *h* ¼ 0.05 m and *μ* ¼ 0.72.

The subjects understood the step climbing process and learned how to teleoperate the robots before the experiments. The subjects repeated the test 20 times for each experiment, as was explained before the experiments. When either robot was unable to climb the step, the reason for the failure was recorded. The postures of the robots were then corrected, and the operators restarted the test.

The case in which either of the robots was not able to climb the step was taken to be a step climbing failure. The case in which the both robots were able to climb the step was taken to be a step climbing success.

**Tables 1**–**3** show the results of the experiments for the cases in which the moving robot velocities were 0.3, 0.4, and 0.5 km/h, respectively. The numbers listed in the tables are the test numbers when the robots failed to climb the step, and Col.AS, Tip.A, Col.BS, and Tip.B are the reasons for failure. Here, Col.AS, Tip.A, Col.BS, and Tip.B indicate a collision between the front wheels of *Robot A* and the step wall (**Figure 16**), tipping over backward of *Robot A* (**Figure 12**), a collision between the front wheels of *Robot B* and the step wall, and tipping over backward of *Robot B*, respectively. However, as a result of the link touching its body, tipping over backward of *Robot B* did not occur in the experiments (see **Figure 13**).

In the first experiment (**Table 1**: velocity, 0.3 km/h; success, 52 times; failure, eight times), the success rates for groups *α*, *β*, and *γ* were 85, 85, and 90%, respectively. The reason for failure for all of the groups was a collision between the front wheels of *Robot A* and the step wall.

In the second experiment (**Table 2**: velocity, 0.4 km/h; success, 55 times; failure, five times), the success rates for groups *α*, *β*, and *γ* were 100, 75, and 100%, respectively. The reason for failure for all of the groups was collision between the front wheels and the step wall (*Robot A*, four times; *Robot B*, one time). In the third experiment (**Table 3**: velocity, 0.5 km/h; success, 51 times; failure, nine times), the success rates for groups *α*, *β*, and *γ* were 75, 80, and 100%, respectively.

The reasons for failure for the groups were collision between the front wheels of *Robot A* and the step wall (one time), tipping over of *Robot A* (four times), and collision between the front wheels of *Robot B* and the step wall (four times).

**Table 4** lists the ratios for the reasons for failure of the robots to climb the step. The total number of failures for group α was 8 (out of 60 tests), and the total number of failures for groups *β* and *γ* were 12 and 2, respectively (**Tables 1**–**3**).

The most common reason for failure is collision between the front wheels of *Robot A* and the step (59.09%). The second most common reason is collision between the front wheels of *Robot B* and the step (22.73%). Therefore, approximately 82%

**Figure 15.**

**95**

*Step climbing experiment.*

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

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

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote… DOI: http://dx.doi.org/10.5772/intechopen.90162*

**Figure 15.** *Step climbing experiment.*

In Sections 5 and 6, we discuss the influence of the velocity difference for

The two robots were teleoperated by individual operators (**Figure 15**). Using joysticks (**Figure 5**), the robots were moved at speeds that were set by the program. Six subjects (five adult males and an adult female) participated as robot operators in

The six subjects were labeled *s*<sup>1</sup> to *s*<sup>6</sup> and were divided into three groups, *α*, *β*, and *γ*. Subjects *s*<sup>1</sup> and *s*<sup>2</sup> were the operators in group *α*, subjects *s*<sup>3</sup> and *s*<sup>4</sup> were the operators in group *β*, and subjects *s*<sup>5</sup> and *s*<sup>6</sup> were the operators in group *γ*. Subjects

Three experiments were conducted, in which the robot velocities were 0.3, 0.4,

*s*1, *s*3, and *s*<sup>5</sup> operated *Robot A*, and subjects *s*2, *s*4, and *s*<sup>6</sup> operated *Robot B*.

and 0.5 km/h. The step height and the friction coefficient were constant at *h* ¼

The subjects understood the step climbing process and learned how to teleoperate the robots before the experiments. The subjects repeated the test 20 times for each experiment, as was explained before the experiments. When either robot was unable to climb the step, the reason for the failure was recorded. The postures of the robots were then corrected, and the operators restarted the test. The case in which either of the robots was not able to climb the step was taken to be a step climbing failure. The case in which the both robots were able to climb the

**Tables 1**–**3** show the results of the experiments for the cases in which the moving robot velocities were 0.3, 0.4, and 0.5 km/h, respectively. The numbers listed in the tables are the test numbers when the robots failed to climb the step, and Col.AS, Tip.A, Col.BS, and Tip.B are the reasons for failure. Here, Col.AS, Tip.A, Col.BS, and Tip.B indicate a collision between the front wheels of *Robot A* and the step wall (**Figure 16**), tipping over backward of *Robot A* (**Figure 12**), a collision between the front wheels of *Robot B* and the step wall, and tipping over backward of *Robot B*, respectively. However, as a result of the link touching its body, tipping over backward of *Robot B* did not occur in the experiments (see **Figure 13**).

In the first experiment (**Table 1**: velocity, 0.3 km/h; success, 52 times; failure,

respectively. The reason for failure for all of the groups was a collision between the

In the second experiment (**Table 2**: velocity, 0.4 km/h; success, 55 times; failure,

The reasons for failure for the groups were collision between the front wheels of

**Table 4** lists the ratios for the reasons for failure of the robots to climb the step.

*Robot A* and the step wall (one time), tipping over of *Robot A* (four times), and collision between the front wheels of *Robot B* and the step wall (four times).

The total number of failures for group α was 8 (out of 60 tests), and the total number of failures for groups *β* and *γ* were 12 and 2, respectively (**Tables 1**–**3**). The most common reason for failure is collision between the front wheels of *Robot A* and the step (59.09%). The second most common reason is collision between the front wheels of *Robot B* and the step (22.73%). Therefore, approximately 82%

eight times), the success rates for groups *α*, *β*, and *γ* were 85, 85, and 90%,

five times), the success rates for groups *α*, *β*, and *γ* were 100, 75, and 100%, respectively. The reason for failure for all of the groups was collision between the front wheels and the step wall (*Robot A*, four times; *Robot B*, one time). In the third experiment (**Table 3**: velocity, 0.5 km/h; success, 51 times; failure, nine times), the

success rates for groups *α*, *β*, and *γ* were 75, 80, and 100%, respectively.

manipulation of the robots.

*Industrial Robotics - New Paradigms*

**5. Experiment**

the experiments.

0.05 m and *μ* ¼ 0.72.

step was taken to be a step climbing success.

front wheels of *Robot A* and the step wall.

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### **Table 1.**

*Success rate for step climbing (0.3 km/h), reason for failure, and test number.*


of failures arise from collisions between the front wheels and the step. In other words, if a robot is fitted with an assistance system that is able to detect the distance between the robot and the step, the capabilities of teleoperated robots should be

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

In this section, we discuss the remote operability of the proposed system based

**Figure 17(a)** shows the correlation between the robot velocity and the success rate for step climbing for the three experiments by group (**Tables 1**–**3**). The success rate for group *γ* was high as a whole and increased to 100% at 0.4 and 0.5 km/h. In contrast, the success rate for group *α* increased at 0.4 km/h but decreased at 0.5 km/h. The success rate for group *β* decreased at 0.4 km/h and increased at 0.5 km/h. Therefore, the trends in the experimental results are not consistent. **Figure 17(b)** shows the total success rate at 0.3–0.5 km/h for the three groups (**Tables 1**–**3**). The results of the experiments were different from what we had expected, and the remote operability of the step climbing system did not depend on

*Ratio of successful step climbing: (a) success rate for each group and (b) total success rate for the three groups.*

**6.1 Correlation between the robot velocity and the success rate**

greatly improved.

**Figure 16.**

**6. Discussion**

**Figure 17.**

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on the results of experiments.

*Collision between the front wheels and the step wall.*

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

### **Table 2.**

*Success rate for step climbing (0.4 km/h), reason for failure, and test number.*


### **Table 3.**

*Success rate for step climbing (0.5 km/h), reason for failure, and test number.*


### **Table 4.**

*Ratio of reason for failure of the robots to climb the step (0.3–0.5 km/h).*

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote… DOI: http://dx.doi.org/10.5772/intechopen.90162*

**Figure 16.** *Collision between the front wheels and the step wall.*

of failures arise from collisions between the front wheels and the step. In other words, if a robot is fitted with an assistance system that is able to detect the distance between the robot and the step, the capabilities of teleoperated robots should be greatly improved.
