# Locomotion Efficiency Optimization of Biologically Inspired Snake Robots
## 5 Conclusions  
A general multi-objective optimization framework was presented in this paper. The proposed framework was applied to study the locomotion efficiency for both swimming and land-based snake robots with different numbers of links. The optimal gait parameters were obtained for different configurations of the snake robots. The proposed optimization scheme is general in the sense that it can be used to study the locomotion efficiency for robotic systems using undulatory motion patterns. Using this framework, locomotion efficiency optimization was analyzed for both land-based snake robots moving according to the gait pattern lateral undulation, and for swimming snake robots, using lateral undulation and eel-like motion. In the latter case, the negative work effect was also taken into account. In particular, the energy efficiency of the underwater snake robots was studied using two different equations to calculate power consumption. In the first case, the absolute value of the theoretical joint power was considered as the power consumption, while, in the second case, the benefit of the negative work effect was also considered, i.e., taking into account that the robot is able to recover energy and thus calculating the power consumption using the net joint power. Optimization results for the land-based snake robot were presented considering only the absolute values of the theoretical joint power because of the energy consumption of the ground friction, which does not give a negative work effect. PSO was chosen as a suitable optimization algorithm to acquire the Pareto optimal solutions taking into account the trade-offs between the consumed power and the achieved forward velocity. From the obtained Pareto fronts, we concluded that improving energy efficiency corresponds to the decrements of the forward velocity. Consequently, depending on the control objectives and the available power of the robot, the operators or designers of bio-inspired snake robots can choose the optimal operational point using the Pareto fronts as an informative tool. Furthermore, based on the multi-objective optimization study, we managed to acquire useful insights regarding the optimal values of the gait parameters for both land-based and swimming snake robots. These observations are important to consider in the control and design of snake robots. Investigating the locomotion efficiency of bio-inspired snake robot using other types of sinusoidal motion patterns will be the subject of future work. It is likely that other design parameters could also improve the motion efficiency of the snake robots, and we plan to study the effect of these in future work. Moreover, the proposed optimization framework can also be used for optimizing gaits of biped robots by introducing newly revised optimization variables.  
Figure 11: Optimal gait parameters for the lateral undulation motion pattern for the land-based snake robot: (**a**) 3D plots of optimal gait parameters for robot with \(n=5\) links; (**b**) 3D plots of optimal gait parameters for robot with \(n=10\) links; and (**c**) 3D plots of optimal gait parameters for robot with \(n=20\) links. Colors illustrate different weights of the objective functions[PERSON]  
**Acknowledgments:** Research partly funded by VISTA a basic research program in collaboration between The Norwegian Academy of Science and Letters, and Statoil, and partly supported by the Research Council of Norway through its Centres of Excellence funding scheme, project no. 223254-NTNU AMOS.  
**Author Contributions:** The authors have contributed equally to this work.  
**Conflicts of Interest:** The authors declare no conflict of interest.