# Analysis and Design of a Minimalist Step Climbing Robot
## 4 Design Analysis
In Figure 11, the behavior of the climbing robot during uncontrolled and controlled simulations with active rear wheels is studied. The statistical analyses of variation in the difference of required and allowable torque in the front wheels during controlled and uncontrolled conditions with respect to change in height of step are shown in Table 3. It may be observed that the mean values of required torque on step 1, 2 and 3 are 64.66 Nm, 63.68 Nm and 69.21 Nm, respectively. This implies that, during uncontrolled conditions, more torque is required to overcome a step as compared to the controlled condition. The standard deviation value for each step suggests that the required torque in the uncontrolled condition is always higher than the controlled condition, when simulations are performed with respect to the varying height of the stair. Similarly, negative mean values of allowable torque imply that the allowable torque in an uncontrolled condition is smaller as compared to the controlled condition. Moreover, standard deviation values show that the allowable torque always remain higher in the controlled condition. This reduces the probability of slipping during  
Figure 10: Change in allowable and required torque on the front wheels to overcome a step with respect to the change in height of the step while (**a**) climbing with control and (**b**) climbing without control. Figure 9: Variation of inclination angle of the robot with a change in height of a step at three initial steps of the stair during the operation of climbing up the stairs. The three plots, step 1, step 2 and step 3, represent the variation of inclination angle when the front wheel is at the first, second and third step of the stair, respectively. controlled conditions as compared to the uncontrolled condition. Figure 11a illustrates the variation in allowable and required torque at three initial steps on the front wheels with a change in step height. By comparing the results of an uncontrolled simulation with the active rear wheel (as shown in Figure 11a) and the controlled simulations with the active rear wheel (as shown in Figure 10a), it may be observed that as the step number increases, the required torque to overcome the step in uncontrolled simulations become lesser than compared to the controlled conditions. In Table 4, the mean values and standard deviation values of variation in difference of required and allowable torque in the front wheels during controlled and uncontrolled conditions with active rear wheel and with respect to change in height of step are shown. It may be observed that the mean values of difference in the required torque between uncontrolled and controlled condition are negative and the difference becomes smaller with the increase in step number. By Analyzing the mean values with standard deviation values implies that although the required torque in uncontrolled condition is smaller than the controlled condition at lower steps, as the step number increases, the required torque in the front wheels becomes smaller in the controlled condition as compared to the uncontrolled condition. This phenomenon is observed as the inclination angle of the robot increases with the step number. By analyzing the mean and standard deviation values of allowable torque, it may be observed that as the step number increases, the allowable torque in the controlled condition increases and deviates less than compared to lower step number. In order to understand this behavior, the variations in maximum allowable torque on the rear wheel in both controlled and uncontrolled conditions are plotted and shown in Figure 11b. It may be observed that except for the condition where the front wheels are on the third step and the step height is over 150 mm (approximately), the maximum allowable torque on the rear wheel in the uncontrolled condition is greater than the controlled condition. The torque on the rear wheel pushes the robot, which in turn accounts for the decrease in torque requirement on the front wheels.