# Online Foot Location Planning for Gait Transitioning Using Model Predictive Control
## 6 Conclusions  
Combining multiple gaits transitioning at various speeds, UPMPC performs better than the HF in all cases. In particular, the gait transitioning between trotting and walking cannot be done by the HF but can be done by UPMPC. Furthermore, it has much better control over yaw and pitch than HF. At most gait transitioning, the mean of absolute values of roll under UPMPC is smaller. UPMPC with fixed parameters is able to accommodate gait transitioning between multiple gaits at a variety of speeds. Despite the use of a simplified model to describe the kinematics and dynamics of the quadruped robot, the UPMPC-planned foot location still meets the requirements for gait transitioning and is better than HF. The use of the uniform foot location not only speeds up the solution, but also converts the problem to be solved into a QP form with a smaller matrix. The coordinates of the foot in the world coordinate system are used as the optimization solution variable more in line with the actual situation. Due to the good migration of the used platform, it is believed that UPMPC can be applied in real systems to meet the need of gait transitioning on real world. Conceptualization, methodology and writing--original draft preparation, X.L. ; writing--review and editing, L.L., H.A. and H.M. All authors have read and agreed to the published version of the manuscript. This work was funded by National Science Foundation of China (No. 61903131) and Outstanding Youth of Department of Education of Hunan Province (No. 20B096) and the China Postdoctoral Science Foundation (No. 2020M683715). Not applicable. The simulation code can be downloaded in [[https://github.com/lxm-1/Mini-Cheetah.git](https://github.com/lxm-1/Mini-Cheetah.git)]([https://github.com/lxm-1/Mini-Cheetah.git](https://github.com/lxm-1/Mini-Cheetah.git)) accessed on 23 August 2021. Figure 12: The figure shows the posture and GRFs of trotting in a gait transitioning to walking at 0.8 m/s. The number 1 in (**a–d**) indicate gait transitioning occuring. The horizontal coordinate of the number 1 in the diagram represents the exact time of the transitioning. The transitioning process is: trotting (0–28.3 s), walking (28.3-final). (**c,d**) only capture the GRFs near the transitioning point to facilitate analysis of the forces, so the transitioning time is not consistent with (**a,b**). All data in the plots are from the same dataset. (**a**) Posture change using the HF at 0.8 m/s gait transitioning. (**b**) Posture change using the UPMPC at 0.8 m/s gait transitioning. (**c**) Change in forward force at 0.8 m/s during gait transitioning. (**d**) Change in lateral force at 0.8 m/s during gait transitioning. (**e**) Comparison of the peak values of roll, pitch and yaw for the two methods after transitioning. The numbers 1, 2 and 3 on the horizontal axis in the graph represent roll, pitch and yaw, respectively. (**f**) Comparison of peak values after transitioning for forward and lateral forces under both methods. The numbers 1 and 2 on the horizontal axis in the diagram represent forward and lateral forces, respectively. Figure A2: The figure shows the posture changes in gait transitioning between flight trotting and walking at 0.4 m/s. The numbers 1 and 2 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 (0–1.88 s (number 1)), walking (1.88–5.12 s (number 2)) and flight trotting (5.12-final). The numbers 1 and 2 in (**b**,**d**,**f**) denote the peak values of the corresponding posture (roll, pitch or yaw) after the gait transitioning. Furthermore, the number 3 indicates the mean of the absolute value of the corresponding posture over the whole time. (**a**) Changes in roll during gait transitioning at 0.4 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 0.4 m/s.