# C-Legged Hexapod Robot Design Guidelines Based on Energy Analysis
## 1 Introduction
This gait groups the front and back leg from one side and the central leg from the opposite side to form two tripods. In this gait mode, one tripod is always in touch with the ground, while the other is moving freely in the air, offering increased speed and efficiency. A video simulation of this gait mode generated by implementing the kinematic model developed in this article in MATLAB can be seen in the Supplementary Materials. The six legs synchronized gait mode, offers increased power and is generally used when hill climbing. On the other hand, this gait has reduced speed and reduced energy-efficiency, as at certain periods, the robot will lie on its chassis while the legs continue rotating. Similarly, to the alternating tripod gait, a video simulation of this gait mode can be seen in the Supplementary Materials. Figure 1: C-Legged hexapod robot designed and Manufactured by the Centro de Automática y Robotica de la Universidad Politècnica de Madrid, picture taken by one of the article’s authors [11]. Enhancing the energy-efficiency of legged robots has been a field of great interest and investigation in recent years [14]. These investigations have taken different routes, including (a) designing special robot structures that can reduce the energy consumption [15; 16], (b) optimizing gait modes [13; 17; 18] (c) optimizing foot contact force [14], and (d) energy-efficient trajectory planning [19]. From these four different routes, the majority of the investigations have focused their efforts on optimizing the contact force to increase the robot's efficiency. This type of optimization is based on the fact that over constraints of hexapod robots produce internal forces between contract points that ultimately lead to energy inefficiency and gait instability [14; 20]. Implementing force distribution together with position control algorithms, ensures that adequate torque is applied at each joint reducing the energy wasted in each joint. On the other hand, the main objective of gait optimization is to increase the robots' mobility performance [21], but it has also been proved that optimizing and switching between the different gait modes can save up to 20% [22]. Furthermore, switching between different gait modes can be combined with efficient trajectory planning, and information regarding the terrain can then be used to adequately choose between different gait modes [19]. All of the four optimization techniques have in common the fact that these investigations start with a robot design and their objective is to increase its performance, but it is possible that the design they start with, is inefficient compared to other design possibilities. Therefore, determining and knowing how different design parameters affect the core efficiency of the system is essential to obtain the best design possible, prior to the incorporation of all the different optimizations mentioned above. Given the fact, that many of these investigations start with a design that needs optimization, the energy models are obtained by analyzing the energy consumption of each motor joint using the torque and the angular velocity [14]. In this article, the energy model will be obtained from a more macroscopic perspective and will be understood as the gravitational potential energy (GPE) and kinetic energy (KE) of the robot, allowing a generic hexapod robot to be considered. This offers a novel procedure to obtain the consumption of hexapod robots. The objective of this article is to provide the reader with an understanding of the motion and energy consumption of hexapod robots, together with some design considerations, that will allow energy-efficient C-legged hexapod robots to be developed. To do so, the kinematic model and the energy model of a single C-leg system will be developed to determine the impact of mass, leg radius, and leg's angular velocity on the energy consumption of the system.