# Head-Raising of Snake Robots Based on a Predefined Spiral Curve Method
## 4 Discussion and Conclusions  
In this study, head-raising motion of a snake robot based on a predefined spiral curve is proposed and relative simulations are conducted. Obtaining the angle sequences of the head-raising motion of snake robots is difficult under three-dimensional conditions. Thus, the proposed method adopts the predefined spiral curve to guide the robot in moving, thereby improving the performance of the robot and laying the foundation for accomplishing additional tasks. The predefined spiral curve is parameterized. With changes in the parameters, the curves can adapt to different lengths and numbers of the snake robot modules, spiral numbers, and heights of head-raising. Figure 12: Head-raising motion process with different parameters of the predefined spiral curve, and the parameters are listed in Table 2.  
However, there are some problems to be solved in the future work. First, the predefined spiral curve is a piecewise function and has unsmooth points, thus leading to sharp changes in motion trajectories. Second, our model considers only kinematic planning, that is, the dynamic problem is not considered. Dynamic constraints are important factors for successful implementation of our model on a real robot, and will be added into an improved model in the future work. At the same time, experimental verification will be carried out in the next phase of research, after finishing the design and construction of the platform. The greatest challenge to use our model on a real robot is that the robot has to overcome the gravity during the head-raising, and the actuation system must be equipped with motors which have adequate torques to drive the snake modules. The work in [13] is a successful example although they adopted a different method to raise the robot's head. When designing the prototype, lightweight materials can be used to enable the robot with lighter gravity and stronger driving power. More importantly, our model is adaptive. As illustrated in Figure 12, by decreasing the height, the cycle number and increasing the radius of supporting part, it is feasible for the robot to raise its head while satisfying the dynamic constraints. In some specific situations such as exploring the moon, and searching for resources underwater, the gravity will decrease or be compensated. Then, it will be easier for the robot to raise their head. Third, the head-raising motion forms of snake in the natural world can change over time. To accomplish that, the predefined spiral curve should be made time varying without influencing the stability of the robot body, and this principle will also be the focus of the future research. The following are available online at [[http://www.mdpi.com/2076-3417/8/11/2011/sl](http://www.mdpi.com/2076-3417/8/11/2011/sl)]([http://www.mdpi.com/2076-3417/8/11/2011/sl](http://www.mdpi.com/2076-3417/8/11/2011/sl)), Video S1: Concept_of_trajectory_tracking.avi; it introduces the concept of trajectory tracking using an improved model in our future work. Video S2: PS_Fig9.avi; it describes the process of phase-shifting (Figure 9). Video S3: HR_Fig11.avi; it shows the process of head-raising using the line segments model of the snake robot (Figure 11). Video S4: SA_Fig11.avi; it shows the simulation of head-raising in Adams environment (Figure 11). Video S5: HR_Fig12a.avi; it displays the head-raising process of Figure 12a. Video S6: HR_Fig12b.avi; it displays the head-raising process of Figure 12c. Video S8: HR_Fig12d.avi; it displays the head-raising process of Figure 12d. Conceptualization, [PERSON] and Z.J. ; Formal analysis, [PERSON] and J.L. ; Funding acquisition, J.L. ; Investigation, J.L., X.Z., Z.J. and C.Y. ; Methodology and Simulation, X.Z. ; Software and Programming, X.Z. ; Supervision, [PERSON], [PERSON] and C.Y. ; Validation, J.L. ; Writing--original draft, X.Z. ; Writing--review and editing, [PERSON], C.Y. and J.L. This work was partially supported by the National Science Foundation of China (Grant No. 51775541), Research Fund of China Manned Space Engineering (Grant No.