## 1 Introduction  
The decrease of energy usage is recognized as one of the principal goals in industrial and manufacturing areas for economic and climate change mitigation reasons [1]. Energy consumption saving in mechatronic and robotic systems has attracted much interest in both industry and academia [2] due to the need to develop energy-efficient and sustainable infrastructure. The existing approaches for increasing energy efficiency include the development of more efficient energy storage technologies for mobile platforms [3], the use of renewable energy resources [4], and also the deployment of innovative computing techniques for controlling digital infrastructure [5]. Mobile robots serve as a great platform for many various tasks that are difficult, dangerous, or even impossible for humans such as space exploration, underground mining, landmine removal, or disaster relief [6; 7]. Such tasks require robots to act autonomously in most cases and their work environment is incredibly diverse [8]. The nature of such diversity in environments dictates that mobile robots must adapt to these environmentsand not only to one type but a great variety of the terrains. The problem of energy efficiency has been addressed by many different types of robot designs such as flexible (snake-like robots) [9], quadruped robots [10], rovers [11], paddle-driven robots [12], and humanoid robots [13; 14]. Terrain diversity is better overcome by legged robots, as they are a lot more adaptable than wheeled or tracked robots [15; 16; 17] as dictated by nature (there are no wheeled or tracked animals/insets) [18]. Legged robots can more easily adapt to different types of terrain, their roughness, softness, obstacles, gaps, etc. [19]. However, legged robots still have a lot of challenges to overcome in order to be widely used autonomously in many different applications. These challenges include solving problems for foot-terrain interaction [20; 21; 22], gait selection [23; 24], walking patterns [25], body stability/balance [17; 26], speed [27; 28], obstacle avoidance [29; 30], motion planning [31; 32], trajectory planning [33; 34; 35], etc. Robots' autonomy highly depends on their ability to adapt to various types of terrains [36] and their energy efficiency [37; 38]. In some studies, vertebrates and invertebrates were observed leading to results stating that oxygen consumption linearly depends on their locomotion speed [39]. A study on modeling the energy consumption of insects [40] and rats [41] suggests that the main reason for changing gaits is to minimize energy consumption. These results were applied to a 2 g mobile robot by [42] and investigated by calculating the cost of transport (CoT). This parameter assesses energy efficiency to transport any type of animal, insect, fish, bird, vehicle or robot from one point to another. CoT allows comparison of different biological or non-biological systems because it is a dimensionless parameter, and thus is widely used in robotics and biology. However, results obtained from experiments with a 2 g mobile robot [42] showed that CoT is significantly larger than in the existing walking robots when an alternating tripod gait is used. In their next work, they presented results of the locomotion and trajectory control technique for microrobots weighing 1.27 g [43]. The Harvard Ambulatory Micro Robot VP series (HAMR-VP) obtained a CoT of 109 which is still a rather large number. In [44], a method is presented on how to estimate and minimize CoT for legged locomotion. The results of these studies show that it is very important to choose optimal gait to minimize energetic cost. With optimal parameters, CoT is below 1.0 at speeds ranging from 0.1 m/s to 0.35 m/s, but there are no real experiments carried out with either robots or insects. It is difficult to say whether or not results would be the same for walking robots. Real-time control is proposed in [45] where the authors present a model of a realistic quadrupedal walking machine.