# Locomotion Efficiency Optimization of Biologically Inspired Snake Robots
###### Abstract
Furthermore, several results have been published regarding the design, modeling and control of bio-inspired underwater robots [4]. One of the main characteristics of snake robots is their adaptability to different motion demands. This attribute is extremely important for snake robots, since they have the ability to move over land as well underwater, while the physiology remains the same. Nowadays, different types of underwater vehicles and underwater robotic systems have been used for several challenging subsea inspection and interventions tasks [5]. In addition to the existing underwater robotic solutions, recently, the potential of using bio-inspired underwater snake robots has been studied. Due to their long, flexible and slender body the snake robots can be considered as an interesting alternative solution to improve the efficiency and maneuverability of conventional underwater vehicles [6; 7; 8; 9]. The swimming snake robot as a mobile manipulator arm can be used for several applications such as inspection and maintenance of subsea oil and gas installations accessing tight structures, in biological community and marine archeology. However, several control related challenges must be addressed before we have fully functional swimming snake robots suitable for challenging tasks in highly uncertain subsea environment. An essential problem to be solved is related to the locomotion efficiency of the bio-inspired swimming snake robots. Hence, in this paper, the energy efficiency is studied since it constitutes the main important factor in order to obtain long term autonomy of these type of robots. In [10], gait parameters of a land-based snake robot are obtained to optimize head stability and the speed of the robot simultaneously. However, the energy efficiency is not considered in the optimization framework. In [11], the genetic algorithm (GA) is used to find forward head serpentine gait parameters for a land-based snake robot. However, only the speed of the robot is considered in the optimization in order to find the optimal gait parameters of the head link. Moreover, in [12] gradient-free method is implemented by using [PERSON]'s method in order to optimize the forward velocity of the land-based and swimming snake robots. However, the frequency of the motion pattern has not been included in the optimized parameters. In [13], empirical rules have been derived for underwater snake robots based on extensive simulation studies describing the relationship between the different gait parameters, the power consumption and the achieved velocity for lateral undulation and eel-like motion patterns. Furthermore, in [14], the energy consumption of underwater snake robots (USRs) and remotely operated vehicles (ROVs) have been studied. The obtained comparison results in [14] between USRs and ROVs showed that the USRs are more energy efficient. Experimental results regarding the locomotion efficiency of USRs have been presented in [15], showing the relationship between the gait parameters, the achieved forward velocity and the energy consumption for the lateral undulation and eel-like motion patterns. An optimization framework is proposed in [16] for underwater snake robots. In particular, in [16] the energy efficiency of underwater snake robots was investigated solvinga multi-objective optimization problem for a robot with 10 links. To the best of our knowledge, however, no results have been presented formulating an effective and general optimization framework for bio-inspired snake robots with an arbitrary number of links. In this paper, we consider both the minimization of the power consumption and maximization of the forward velocity, and we propose a framework for solving a multi-objective optimization problem in order to obtain optimal gait parameters. Based on the proposed method, in this paper, we investigate the motion efficiency of both land-based and underwater snake robots using undulatory motion patterns.