# C-Legged Hexapod Robot Design Guidelines Based on Energy Analysis
## 1 Introduction  
In recent years, the development and investigation of a large variety of mobile robots used in a wide diverse set of applications have been enhanced by electronics cost reduction, increased microchips computational capabilities, and intelligent and flexible manufacturing [1]. Mobile robots can be classified by the environment in which they work: land (UGVs), air (UAVs), or underwater (AUVs) [2]. Land robots can be further classified by their locomotion, which can be wheeled, tracked, or legged. Wheeled robots have the ability to reach high speeds with low power consumption and can be guided by controlling few degrees of freedom, but their ability to overcome obstacles is limited [3]. For this reason, although wheeled robots are the most prominent, tracked and legged robots offer motion advantages over the former in unstructured environments [4, 5]. It is important to recall that most parts of the earth and other planet's surfaces are inaccessible to conventional wheeled robots, due to the uneven terrain and obstacles, and therefore, there is a need to develop new mobile robots with enhanced mobile capacities. These natural terrains, on the other hand, offer a great opportunity for legged robots to demonstrate their terrain adapting capabilities [6]. The increased obstacle overcoming capabilities of legged robots can be explained by the fact that this type of robot does not require a continuous support surface, but uses a discrete footh for each foot, enhancing their mobility [7]. On the other hand, the speeds achieved by legged robots are much lower, and energetically this type of robot is very inefficient. This is an important drawback in modernrobotics as the battery energy-storing capabilities, and their heavy weight is a limiting design criterion [7]. Thus, it is critical for robots to be energy-efficient to maximize battery performance. Moreover, generally speaking, legged, robots have more actuators, making them difficult to build and demand complex control algorithms. Legged robots are biologically inspired, and their design tries to replicate the walking motion of animals in nature: One leg robots are inspired by kangaroos, two-legged robots by bipeds, four legs on quadrupeds, and more than four legs are inspired by insects. The number of legs might be an evident classification criterion, but it is important to realize that the number of legs will also determine the gait stability, which can be static or dynamic. Robots with static gaits are always balanced as the robot weight vector always remains within the polygon formed by the legs in touch with the ground [8]. As a general rule, the more legs, the more stable the robot will be, but this will give rise to slow, inefficient, and complex legged robots. In this paper, a hexapod robot will be considered, more specifically a C-leg shape hexapod robot. Hexapod robots are one of the most statically stable legged robots, and possess great flexibility, while standing or moving [9]. This stability combined with a simple C-leg design with only one degree of freedom per leg, offers a balanced trade-off between the increased mobility capabilities of legged robots and the robustness and high speeds of conventional wheeled robots [10]. Figure 1 shows a C-legged hexapod robot designed and manufactured by the Universidad Politecnica de Madrid. One of the most well-known C-legged hexapod robots is RHex [12]. This project was funded by the Defense Advanced Research Projects Agency (DARPA) and involved many universities, such as the University of Michigan, McGill University, University of California, amongst others. The synchronization possibilities of the six individual legs give rise to a variety of different gaits which determine the motion of the robot [13]. The two most common gaits are the alternating tripod gait mode and the six legs synchronized gait mode [10]. The alternating tripod gait mode is the standard walking/running gait used by Rhex.