## 4 Conclusions and Discussion  
In this paper, a novel solution is presented for resolving the problem of multi-gaits for snake-like robots. Serpentine locomotion is the most efficient movement, but snake-like robots cannot move  
Figure 11: (**a**) Experiment on left-turn serpentine locomotion at \(a=\frac{\pi}{3},b=2.4\cdot\pi,c=\frac{\pi}{4}\). (**b**) Experiment on right-turn serpentine locomotion at \(a=\frac{\pi}{3},b=2.4\cdot\pi,c=-\frac{\pi}{6}\).  
Figure 12: (**a**) Multi-wave rectilinear locomotion. (**b**) Obstacle-aided locomotion.  
in narrow spaces. Several works have been conducted on serpentine and rectilinear locomotion. However, only a few mechanisms have been studied for adopting all of the common gaits into the current snake-like framework. To allow a snake-like robot to traverse a wide range of different complex environments, an integrated robot that can perform multi-gait locomotion is proposed. Consequently, a linear translational joint is combined with the swing joint and then applied to rectilinear and serpentine locomotion, respectively. The design of the serpentine locomotion is based on the serpenoid curve, and a distributed control system is used to control the multi-modular robotic unit. Experimental results show that our design has an acceptable performance as both serpentine and rectilinear locomotion correspond well with theoretical analyses. Finally, and perhaps most importantly, a novel obstacle-aided locomotion based on rectilinear locomotion that significantly improves motion efficiency is proposed.  
However, the present study has certain limitations. First, full gait is needed in robot design to achieve the expected performance in a variety of complex environments. We integrated only two basic gaits, and these are insufficient in fulfilling the objective. Second, the gait transition of snake-like robots is a considerable problem in complex environments. Biological snakes can use the most suitable gaits for different environments; however, those utilized by robots are mostly determined by PCs. Thus, locomotion can be invalid when a robot encounters an obstacle while performing the serpentine gait. A sensory-perceptual system is required to help snake-like robots perceive environments and determine locomotion gait, thereby improving the adaptability of the robots. [16] Another issue that is worth studying is the performance of snake-like robots on different surface types. When such a robot moves on smooth ground, the serpentine locomotion may be invalid because of the insufficient radial friction. In this case, utilizing irregularities in the terrain to avoid skidding is a solution for efficient locomotion. Moreover, using the linear translational joint in our design to change body length and shape may allow snake-like robots to adapt to different ground surfaces. In the future, we will integrate concertina and side-winding locomotion to the snake-like robotic gait. We will also adopt the full gait and perception-driven obstacle-aided locomotion for snake-like robots.  
zenodo DOI:10.5281/zenodo.1041033 ([[https://zenodo.org/record/1041033#WfvNTTSGMcY](https://zenodo.org/record/1041033#WfvNTTSGMcY)]([https://zenodo.org/record/1041033#WfvNTTSGMcY](https://zenodo.org/record/1041033#WfvNTTSGMcY))). Video SI: Snake-Like Robot with Fusion Gait.  
The study was funded by the Shanghai Qiming Star Program of the Shanghai Committee of Science and Technology (13 QAI402200). The funding covers the costs of open access publishing.  
[PERSON] and [PERSON] co-organized the work and analyzed the data. [PERSON] and [PERSON] designed and performed the experiments and wrote the paper.  
The authors declare no conflict of interest.