# Online Foot Location Planning for Gait Transitioning Using Model Predictive Control
## 5 Results
### UPMPC vs. HF
However, there is no difference in the mean of absolute value between the two methods. This means that both methods require essentially the same size force over the whole time. There is no considerable difference between the two methods in regards to forward forces or lateral forces. Combined with the change of posture, the UPMPC uses the same force to achieve smaller posture peak and mean of absolute values of posture over the whole time. Therefore, the UPMPC enables better control of posture. The UPMPC helps the quadruped robot to perform better in gait transitioning tasks at 0.8 m/s. The overall oscillations in posture are also smaller. However, it still cannot avoid the oscillation of posture at the moment of transitioning. The better effect of UPMPC has been demonstrated. Figure 7: The figure shows the posture changes in gait transitioning between flight trotting and walking at 0.8 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: flight trotting (0–2.27 s (number 1)), walking (2.27–5.27 s (number 2)), flight trotting (5.27–8.77 s (number 3)), walking (8.77–11.81 s (number 4)), flight trotting (11.81–15.20 s (number 5)) and walking (15.20-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 0.8 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 0.8 m/s. (**c**) Changes in pitch during gait transitioning at 0.8 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 0.8 m/s. (**e**) Changes in yaw during gait transitioning at 0.8 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 0.8 m/s. Figure 9 is the posture change during gait transitioning between flight trotting and trottting at 1.2 m/s. The transitioning points are marked by the numbers 1, 2, 3, 4 and 5 in the figure. In Figure 9, many parts are overlapped. At three transitioning points, the peak of the roll using UPMPC is slightly larger than that of HF in Figure 9. However, the HF does not show a clear advantage over the UPMPC in reducing the peaks values. The mean of absolute value of the two methods is basically the same. For a slightly larger peak values than the HF, the UPMPC has the same mean of absolute value. It shows that the UPMPC allows the quadruped robot to recover stable from the postural oscillation of the transitioning more quickly. Despite the small peak values, the HF requires a longer time of posture oscillation to remove the effects of the transitioning. Therefore, it cannot be stated which method is really better for roll control. In Figure 9, both methods have a large  
Figure 8: The figure shows the force changes in gait transitioning between flight trotting and walking at 0.8 m/s. The numbers 1, 2, 3, 4 and 5 in (**a**,**c**) indicate gait transitioning occuring. The horizontal coordinate of these numbers in the diagram represents the exact time of the transitioning. The transitioning process is: flight trotting (0–1.37 s (number 1)), walking (1.37–4.54 s (number 2)), flight trotting (4.54–7.86 s (number 3)), walking (7.86–11.05 s (number 4)), flight trotting (11.05–14.33 s (number 5)) and walking (14.33-final). The numbers 1, 2, 3, 4 and 5 in (**b**,**d**) denote the peak values of the corresponding forward forces or lateral forces after the gait transitioning. Furthermore, the number 6 indicates the mean of the absolute value of the corresponding forces over the whole time.