Analysis and Optimization of Sinus Lifting in Snake Robots
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Snake robots have been around for decades. The study on snake robots started in 1946 when Gray performed a mathematical analysis on the biological snake. Hirose followed his course and developed the world's first snake robot in 1972, named ACM III. A number of snake robots have been developed ever since, as they have a huge potential in many fields due to their special shape and mobility, such as, for example in search and rescue missions. A snake is a vertebrate, an animal with a backbone. It possesses different kinds of locomotion, depending on the environment around it. The most common motion pattern is lateral undulation, where the snake slides along the ground, propagated by waves from the head to the tail of the snake. A sub-type or modification of lateral undulation is sinus lifting. This unique feature is different, as the snake lifts parts of its body at specific places during the movement to obtain a faster motion. This locomotion is interesting, as a real snake shifts its motion from pure lateral undulation to sinus lifting. Different sinus lifting methods have been looked at, including a theoretical analysis of the motion pattern. Averaging theory, which uses the average of the system to find a simplified solution for the original system, has been applied to the snake robot model. The average acceleration found by the method was applied to find the optimally tuned parameters for the sinus lifting methods. Simplifying assumptions were made in order to calculate the average acceleration and make the system easier to analyse and compute. The most important of them is that the snake is considered ``held back", making the mass centre stationary and the velocity zero. By applying the average acceleration to the system, the optimization for some of the sinus lifting methods was found. One method could not find the optimally tuned parameter, thus making the results difficult to analyse. The reason for this is unclear, but, the simplifying assumption that the centre of mass is stationary is known to not hold in real life. This may be a possible explanation as to why the model could not find the correct parameter. The snake robot in this model consists of a number of links, and the snake was further applied different normal forces, depending on where links are lifted. The force from a lifted link is variably distributed on the grounded links, depending on how close to the lifted link they are. This may result in that the optimally tuned parameters could not be found for any of the sinus lifting methods. These results can be due to the simplifying assumption of the mass centre, as it is still considered to be non-moving. It can also have to do with how the normal forces are implemented. Sinus lifting has proven to be a more efficient locomotion than pure lateral undulation, and should therefore be applied to future snake robots. Averaging theory can help simplify the snake robot system, making it easier to handle and implement. However, the method needs to be researched further when including the mass centre to be moving for finding more coinciding results, making sure that the averaging method can be applied to all snake robot systems.