# Locomotion Efficiency Optimization of Biologically Inspired Snake Robots
###### Abstract
A random velocity is assigned to each particle according to simple mathematical formulae including the experience of the particle itself and its neighborhoods. The position of the particle is updatedusing the obtained new velocity. More specifically, the movement of the particle is influenced by the best experienced position of the particle itself and also the best known position of the swarm. The later helps the swarm to move toward the best solutions. In the PSO algorithm, there is few or no assumption about the optimization problem. Moreover, the gradient information is not required in the optimization procedure. Therefore, there is no limitation about differentiability of the optimization problem. In contrast to GA, PSO acquires memory and saves the experience of good solutions during generations. More importantly, the particles in PSO share the information among the neighborhood. Therefore, the mechanism of constructive cooperation results in a quicker convergence rate. In addition, quite recently, the Reinforcement Learning (RL) method has been applied to address optimization problems in robotics field [27]. To converge to the solution, many objective function evaluations are required in both the PSO and RL methods. However, PSO can use parallel computing to evaluate the objective functions of the particles of each generation. Therefore, it is possible to reduce the computational time significantly. [28] compares the PSO and RL methods applied to solve the obstacle avoidance problem for multi-robotic systems. The results in [28] shows that PSO gives a higher fitness than RL. In this paper, a multi-objective optimization framework is proposed with the overall goal to maximize the achieved forward velocity and simultaneously minimize the average power consumption for bio-inspired snake robots. The optimization problem is solved based on the dynamic model of snake robots proposed in [6; 21; 22]. In particular, multi-objective optimization is used in order to obtain results for lateral undulation and eel-like motion patterns for swimming snake robots with different numbers of links. Furthermore, results are obtained also considering the negative work effect [8] of underwater snake robots. In addition, for land-based snake robots, optimization results are presented for the lateral undulation motion pattern, which is the most common motion pattern for this type of robot. In [29], a multi-objective optimization method for objectives with input-dependent noise is proposed and applied to optimize the speed and head stability of the sidewinding gait of a snake robot. The energy efficiency of land-based snake robot with 16 links is studied in [30] by comparing the energy efficiency of sidewinding locomotion with that of lateral undulation and sinus-lifting motion. The multi-objective optimization approach is presented in [10] for land-based snake robots to optimize the head stability and speed, simultaneously. The dynamic model of the robot was considered as a black-box model. The speed was simply defined by the center of mass displacement after a given time. In order to consider the head stability, the estimated area through which the desired focal point swept was minimized. In [10], surrogate models are obtained by running a few experiments, while the objective functions are also optimized, simultaneously. Therefore, adding more optimization variables to the problem may lead to an increase in the number of experiments. In this paper, however, we propose to use a dynamic model of snake robots instead of a black-box model. Consequently, we reduce the cost of experiments. Moreover, we also consider minimizing the power consumption in our proposed optimization framework. Furthermore, the proposed optimization method obtains the optimal parameters giving the most efficient motion pattern for both land-based and swimming snake robots. The obtained results thus provide interesting insights regarding the control and the design of bio-inspired snake robots. The rest of this paper is structured as follows.