# Online Foot Location Planning for Gait Transitioning Using Model Predictive Control
## 5 Results
### UPMPC vs. HF
(**a**) Change in forward force at 0.8 m/s. (**b**) Comparison of the peak values of forward force after transitioning and mean of the absolute values of forward force in the whole time for the two methods at 0.8 m/s. (**c**) Change in lateral force at 0.8 m/s. (**d**) Comparison of the peak values of lateral force after transitioning and mean of the absolute values of lateral force in the whole time for the two methods at 0.8 m/s. change in pitch at the instant of transitioning. The pitch using UPMPC has a smaller peak. It can be clearly seen from Figure 9b. At the same time, the mean of absolute values of pitch using the UPMPC is also smaller than that using the HF. Therefore, the UPMPC has better control for pitch. In Figure 9d, the yaw of both methods has some variation. In contrast to the UPMPC, HF does not control yaw well. Yaw gradually deviates from the stable value as gait transitioning occurs. The yaw using UPMPC also deviates, but its deviation under multiple gait transitioning is much smaller than HF in Figure 9f. Thus, the UPMPC has better control for yaw. Stability of posture is a prerequisite for the stable movement of a quadruped robot. Figure 10a,b shows the foot-end force of the left front leg planned by the MPC during the transitioning process. In Figure 10a, the vast majority of the curves from both methods overlap. A clear feedback is also obtained in Figure 10c. It was not possible to clearly determine which method had a smaller peak value of the forward force after gait transitioning. The mean of absolute values are also essentially the same. The forces are essentially the same under both methods. From the peak values, the lateral forces planned by UPMPC become significantly smaller than those of HF in Figure 10d. During the whole transitioning process, the lateral forces of HF are significantly greater than those of the UPMPC. Comparing to HF, the robot with the UPMPC has less posture change during gait transitioning, along with same forward forces and less lateral forces over the whole time at the speed of 1.2 m/s. The gait transitioning task is done better by the UPMPC. This indicates that the UPMPC selects a better location for the landing point. Combining the forces and posture, UPMPC's results are much better than HF's. Figure 9: _Cont._  
Figure 10: _Cont._  
Figure 9: The figure shows the posture changes in gait transitioning between trotting and flight trotting at 1.2 m/s. The numbers 1, 2, 3, 4 and 5 in (**a**,**c**,**e**) indicate gait transitioning occuring. The horizontal coordinate of these numbers in the diagram represents the exact time of the transitioning. The transitioning process is: trotting (0–4.66 s (number 1)), flight trotting (4.66–7.87 s (number 2)), trotting (7.87–11.36 s (number 3)), flight trotting (11.36–14.38 s (number 4)), trotting (14.38–17.88 s (number 5)) and flight trotting (17.88-final). The numbers 1, 2, 3, 4 and 5 in (**b**,**d**,**f**) denote the peak values of the corresponding posture (roll, pitch or yaw) after the gait transitioning. Furthermore, the number 6 indicates the mean of the absolute value of the corresponding posture over the whole time. (**a**) Changes in roll during gait transitioning at 1.2 m/s. (**b**) Comparison of the peak values of roll after transitioning and mean of the absolute values of roll in the whole time for the two methods at 1.2 m/s. (**c**) Changes in pitch during gait transitioning at 1.2 m/s. (**d**) Comparison of the peak values of pitch after transitioning and mean of the absolute values of pitch in the whole time for the two methods at 1.2 m/s. (**e**) Changes in yaw during gait transitioning at 1.2 m/s. (**f**) Comparison of the peak values of yaw after transitioning and mean of the absolute values of yaw in the whole time for the two methods at 1.2 m/s.