# Simultaneous Prevention of Rotational and Translational Slip for a Humanoid Robot
## 1 Introduction  
Encouraging achievements for humanoid robots, such as stable walking pattern generation [1; 2; 3], dexterous mechanical design [4; 5; 6], and adaptive performance improvement [7; 8; 9], have been made during the last few decades. However, numerous problems concerned with humanoid robots operating in natural environments reliably remain unsolved. One of these problems consists in the prevention of slip during biped walking. Slip may cause humanoid robots to walk unstably or even fall. Therefore, slip prevention is a crucial issue for real-world applications of humanoid robots. Previous studies address that the slip of a humanoid robot during walking is divided into rotational slip and translational slip [10]. Thus, two categories of slip prevention strategies have emerged. On the aspect of rotational slip, many studies focus on the important effects between inertial moments and friction moments. They prevent rotational slipping by balancing the inertial and the friction moments with controlling the movements of the upper body [11; 12; 13; 14]. A class of methods reduced the inertial moments by the arm swing strategy [11; 12]. [PERSON] et al. proposed that the arm swing effectively prevented slipping during biped walking since it reduced vertical ground reaction moment by 63% [11]. [PERSON] et al. found that excessive arm swing in comparison to normal arm swing prevented rotational slipping and increased the biped walking stability dramatically [12]. Another class of methods compensated the inertial moments in yaw to prevent support foot slip as the upperbody movements strategy [13; 14]. [PERSON] et al. decreased the yaw moment by rotating the upper body, which created a secondary moment to counteract the undesired moment [13]. [PERSON], et al. presented a generalized approach for compensating the required yaw moment of the humanoid robot by modifying the motion of the waist joint in order to prevent rotational slipping [14]. Although the above strategies demonstrate the validity of handling the inertial moments to prevent rotational slipping, the calculations for upper body movements are relatively complicated since they are computed from complex robot models. On the aspect of translational slip prevention, most of the studies concentrate on the frictional constraint between the sole of the humanoid robot and the floor. Moreover, they prevent translational slipping by causing the friction which is required for humanoid robot to walk less than the maximum friction that the ground can provide [15; 16; 17; 18; 19; 20]. [PERSON] et al. and [PERSON] et al. developed a gait optimization routine to generate walking patterns. These walking patterns demanded the lowest friction forces for implementation in order to prevent translational slipping [15; 16]. [PERSON] et al. and [PERSON] et al. designed sensors as a measurement system of slip and then adapted the contact points of the robot with the walking surface in order to increase the frictional characteristics [17; 18]. [PERSON] et al. and [PERSON] et al. calculated the frictional force to deduce the quantitative expression of frictional constraint. Constraining the friction of fast walking within the computed constraint could then prevent translational slipping during fast walking [19; 20]. The above methods handled the translational slip phenomenon by reducing the required friction for biped walking or enhancing the friction between the sole of the robot and the ground. However, these methods only consider translational slip, without considering rotational slip, which is important in actual biped walking. In fact, the rotational and translational slip occur at the same time in biped walking, especially in fast walking [19; 21]. Most of the researchers propose methods that only target one of these types of slip. Very few works discuss how to prevent rotational and translational slip simultaneously [11; 12; 13; 14; 15; 17; 19].