# Anti-Slip Gait Planning for a Humanoid Robot in Fast Walking  
Fangzhou [PERSON]  
1  
[PERSON]  
1 School of Mechatronical Engineering, Intelligent Robotics Institute, Beijing Institute of Technology, Beijing 100081, China Key Laboratory of Biomimetic Robots and Systems, Ministry of Education, Beijing 10  
weight of the leg is ensured [10]. However, the hydraulic system has shortcomings such as liquid leakage, high noise and a complicated system, so its further development is not optimistic. The other option is to use high-power motors or multiple motors in parallel. This configuration is easier with little noise, which is then employed in many laboratories. Figure 1 shows a typical motor-driven humanoid robot model. The robot has 6 degrees of freedom for each leg and a six-dimensional force-torque (F-T) sensor for each ankle. In addition, there is always an inertial measurement unit (IMU) fixed inside the chest. P2, HRP-5P, BHR-5, et al. have the similar leg configuration and sensors [4; 5; 6]. In this type of structure, since the motor must be placed inside or near its corresponding joint, and the harmonic drive gear associated with it is also heavy, the weight of the leg is greatly increased. When the robot is walking fast, the swing leg creates a large yaw moment on the support leg. When a moment generated by the friction between the ground and the sole is insufficient to offset this yaw moment, rotational slip occurs to the robot. Rotational slip is very harmful, specifically, it will make the robot deviate from a predetermined travel route and motion state, causing the robot to become unstable or even tip over. Therefore, it is necessary to overcome the rotational slip by using motion planning or a control algorithm to improve the stability of fast walking. Traditional methods are to compensate for the yaw moment by planning motions of some joints. According to the recordings in current papers, rotation of the waist in the yaw direction is utilized to compensate the moment in some cases [11; 12], or swinging of the arms is used to generate the reverse torque [13; 14], or both of these two are employed at the same time [15; 16]. Each method above could have certain effects, but joints of waists or arms that are used in these systems for moment compensation can't be planned for other tasks, which weakens the ability to multi-task while walking. To address these problems, [PERSON] et al. proposed an on-line compensation scheme for the yaw moment, which allows using the motion of every single link of the robot to contribute to the compensation, and achieved good results in the simulation of the kicking action [17; 18]. However, this method could only be used for force-controlled robots, and there is no simulation or experiment applied to the robots' walking. Therefore, none of the above methods satisfy the needs of fast-walking robots in real life. To overcome the shortcomings of these methods mentioned above, in this paper, we try to find a gait  
Figure 1: Typical motor-driven humanoid robot. They always have an inertial measurement unit (IMU) fixed inside the chest and a six-dimensional force-torque (F-T) sensor for each ankle. Each leg has 6 degrees of freedom (DoFs): (**a**) Simulation model; (**b**) DoF configuration. pattern with optimized yaw moment to satisfy the friction constraints. Joints of waist or arms are not used when gait planning, so they can be planned for other tasks. In order to calculate the friction constraints and plan for the walking pattern, we need a reasonable calculation model. Multi-link model provides high precision, but it's too complicated to use to meet the needs of real-time control. An inverted pendulum model or inverted pendulum flywheel model is simple in structure and convenient in calculation, but they can only be applied to robots with lightweight legs [11; 19]. That's because the mass of the inverted pendulum model is concentrated at one point, which is called the center of mass (CoM) and is usually mapped into the chest of the robot.