# C-Legged Hexapod Robot Design Guidelines Based on Energy Analysis
## 3 Model Experimental Validation
### Kinematic Model Validation: Trajectory  
In Figure 16, one can observe how the actual rpms of the system drop for both the open loop and close loop control, but on the close loop control the rpms overshoots straight after this decrease. This overshoot allows the system to catch up, and therefore, making it seem that at the end of the revolution, the system is not lagging Figure 15. In reality, the controller is not able to cope with the nonlinear load variation and is not capable of maintaining the 30 rpms. A more suitable controller, such as a fuzzy or adaptive controller, would allow for different responses at different rotation angles, which would allow for adequate control. Investigating a nonlinear controller for this application is very important for precise control, but is outside the scope of this article. Figure 14: Motion Trajectory Experimental Results obtained with a system of r = 0.02 m throughout one complete revolution compared to the Model Predictions. Figure 15: Graphs showing the evolution of \(y_{h}\) (**left**), and of \(x_{h}\) (**right**) in time throughout two revolutions at 30 rpm in the open loop and in the close loop control, r = 0.015 m.  
The legs dimensions were changed in the two experiments, because during the testing stage, it was noticed that a leg with r = 0.02 m required too much motor torque, which caused the system to lag even more. A reduced leg demands less torque, and therefore, allows the close loop control to be more reactive and meet the reference command sooner. On the other hand, a larger leg implies bigger changes in displacement, and for this reason, this size leg was left for the trajectory validation, shown in Figure 14.  
Energy Model Validation:The image on the left in Figure 17 shows the power consumption of the motor when no load is applied; this power consumption, as previously said, is due to internal resistance, friction losses, and inertial losses. It can be seen that the signal is noisy, but has a very constant average power consumption of 0.104 W. These oscillations could be due to many factors, such as oscillations in the supplying voltage, sensor errors, defects on the motor hardware, etc. It would be interesting to determine if there are some periodic variations associated with defects in the motor hardware that occur on every cycle. If this is the case, an average power consumption depending on the angular position of the motor, which would provide a more precise solution. The image on the right in Figure 17 represents the motor's power consumption when the system is moving, and therefore, a load is applied to the motor shaft. For most of the time, the motor consumption is constant and has the same value as the average power consumption measured when the motor had no load applied. If the average power consumption under no load conditions is subtracted from the curve shown on the right image of Figure 17, the power consumption associated with the energy variations is obtained (Figure 18). This can be compared to the predictions obtained in the previous section (red line in Figure 18). Figure 16: Graph showing the rpms measured by the encoder when in PID control and in the open loop control. Figure 17: Power consumption when motor rotating at w = 30 rpm with no load (**left**), and total power consumption by the motor when moving system m = 0.315 kg, r = 0.15 m, w = 30 rpm (**right**). The predictions estimated a negative power demand during Type I motion as the system has to dissipate GPE, but this has not been detected by the sensors. After revisiting the equations and the equipment to explain this phenomenon, it was noticed that the motor used in the experiments contains a worm gearbox that self-locks to avoid the motor being back-driven [24]. In self-locking worm gears, the torque applied from the load side is blocked and will not drive the worm. This is ideal for applications where loading against the gravitational force is required, but this device will not allow for regenerative braking [25].