# Anti-Slip Gait Planning for a Humanoid Robot in Fast Walking
## 6 Conclusions  
In order to increase walking speed of the humanoid robot, it is necessary to increase the driving power of the leg joints, which in turn leads to an increase of leg weight. This paper aims to overcome the rotational slip of a motor-driven high-power humanoid robot during its fast walking through a gait planning algorithm with free joints of the waist and arms for multitasking during walking. The main contributions are as follows. Firstly, a 3D three-mass model applicable to fast-walking robots with heavy legs was proposed. Then based on this model, the maximum moment provided by the  
Figure 7: Yaw angle of the robot during walking. It is measured by the IMU. Yaw angle in Case 1 is close to 0. While yaw angles increase in turn in Case 3, Case 2 and Case 4 and they are non-negligible.  
ground friction during walking was calculated, which was then used as a constraint to plan the swing leg motion. After that, the influence of the swing leg on ZMP was calculated, and thus the original reference ZMP trajectory was compensated for to obtain a new one. Based on the compensated ZMP trajectory, the preview control method was adopted to plan the trajectory of the CoM of the inverted pendulum. Finally, the trajectories of all the joints of the legs could be obtained by inverse kinematics.  
In this paper, the effectiveness of the proposed algorithm was verified by simulation, and the conclusions are as follows.  
1. For a humanoid robot with heavy legs, it is the motion of the swing leg that causes rotational slip and strongly affects the overall ZMP of the robot;
2. By using the friction constraint method proposed in this paper to plan the swing leg motion, the maximum walking speed without rotating slip can be obtained;
3. If the ZMP variation caused by the swing leg motion is compensated to the reference ZMP, the actual ZMP of the robot will follow the reference ZMP better, as a result the robot maintains its posture better and the leg lands more stably, avoiding the rotational slip caused by the sole not being attached to the ground;
4. We can only obtain a fast walking gait without rotational slip if we use both the friction constraint method and the ZMP compensation method proposed in this paper sequentially.  
Looking towards future work, some research needs to evolve the off-line methods proposed in this paper to on-line methods, while other research needs to apply these methods to real robots. Since there are model errors between the actual robot and the simulation model, the motors have servo error, and the ground is not an ideal plane, a series of engineering problems in application need to be solved. Furthermore, if the walking distance is long, there will be an accumulation of errors, which means a stability control method is required.  
The following are available online at [[http://www.mdpi.com/2076-3417/9/13/2657/s1](http://www.mdpi.com/2076-3417/9/13/2657/s1)]([http://www.mdpi.com/2076-3417/9/13/2657/s1](http://www.mdpi.com/2076-3417/9/13/2657/s1)), Video S1: Biped Walk in Case 1, Video S2: Biped Walk in Case 2, Video S3: Biped Walk in Case 3, Video S4: Biped Walk in Case 4.  
Conceptualization, methodology, investigation and writing--original draft preparation, F.Z.; conceptualization, validation, writing--review and editing, J.G.  
This research was funded by the National Natural Science Foundation of China, grant number 611175077, the National Research Project, grant number B2220132014 and the National High-Tech R&D Program of China, grant number 2015 AA042201.  
Thanks very much for the guidance from [PERSON] and the help from other colleagues in the Key Laboratory of Biomimetic Robots and Systems.  
The authors declare no conflict of interest.