# A Head Control Strategy of the Snake Robot Based on Segmented Kinematics
## 1 Introduction  
Snake robots can adapt to complex environments and move flexibly because of their hyper-redundancy degrees of freedom (DOFs) [1; 2; 3; 4]. However, it needs to obtain information about the surrounding environment if a snake robot wants to work well in a complex environment. Several researchers equip the head of the snake robot with a small camera [5; 6]. The desired image information is needed to obtain from the head camera. Moreover, we need to move the head of the snake robot to a specific position and make it as a manipulator in some scenes. Then the head control strategy of the snake robot is required. [PERSON] et al. proposed the algorithm of head control for the planar snake robot [7] and realized the control of the movement direction of the snake robot head on a plane. Then they further proposed a new head control algorithm in a three-dimensional space by using kinematic redundancy [8]. However, these algorithms are based on the assumption of the velocity constraint, and the assumption is only suitable for the snake robot with wheels. However, snake robots without wheels are also widely studied, and they are more flexible and more adaptable to complex environments than ones with wheels. [PERSON] et al. proposed a head control method of the snake robot based on the serpenoid curve [9], and then they used the zero-moment point (ZMP) method to analyze the stability of the motion of the snake robot. [PERSON] et al. proposed a predefined spiral curve method to control the head of the snake robot [10]. The method is implemented on the snake robot with 3 degrees of freedom joints. However, the predefined spiral curve method limits the range of motion of the head to a certain extent. Moreover, it is not adapted well to these snake robots with single DOF or two DOFs joints. In addition, the method based on serpenoid curve and the predefined spiral curve method cannot achieve control of the arrival of the head of the snake robot to a specific position and posture. To solve these problems, a strategy of the head control of the snake robot based on segmented kinematics is proposed, and it uses the optimization algorithm to enhance the stability of its motion. Moreover, it can give the solution of the joint angles for the specific pose of the head of the robot. In addition, it also solves the problem of the trajectory planning of the overall body for the snake robot. To realize the control strategy, the base part is controlled by the method of discretizing the backbone curve. The specific structure of the snake robot used in this paper is shown in Figure 1. The backbone curve theory is proposed by [PERSON] et al. [11]. In addition, then the backbone curve discretization method is adopted widely [12; 13]. For enhancing the motion stability of the overall body, the backbone curve is designed as a plane arc and the parameters of the arc are also optimized. For the neck part of the robot, we need to determine the desired position and direction of the end link of the neck part by the dexterous workspace of the head part and the desired pose of the head. The method of calculating the dexterous workspace is introduced in the literature [14]. Once the desired position and direction of the end link of the neck part are determined, the optimization algorithm can calculate the joint angles of the neck part. Then the end frame (the frame of the end link) of the neck part is treated as the base frame of the head part, and an inverse kinematics algorithm is selected to solve the joint angles of the head part. Now there are several inverse kinematics algorithms, such as the KDL algorithm [15; 16], the inverse kinematics algorithm based on the optimization [17] and TRAC-IK algorithm [18]. The TRAC-IK algorithm is adopted for its better efficiency and high solution rate. Then all the joint angles of the snake robot are obtained. However, the snake robot will hit the ground if only the trajectory planning in joint space is considered. Thus, a trajectory planning method of the overall body in Cartesian space is proposed.