Energy analysis of worm locomotion on flexible surface

Recent attempts at designing untethered devices for locomotion inside compliant biological vessels, highlighted the requirements for energy efficiency for prolonged duration inside living bodies. Quite a number of studies considered the design and construction of crawling robots but very few focused on the interaction between the robots and the flexible environment. In previous studies, we derived the efficiency, defined as the actual advance divided by the optimal advance, of worm locomotion. In this paper, we analyze the force, minimum energy and power requirements for worm locomotion over flexible surfaces. More importantly, we determine the optimum conditions of locomotion as a function of the number of cells, friction coefficients, stroke length, energy recovery factor, and tangential compliance. Optimality is defined with respect to energy and power requirements. The analytical results are obtained by integrating the force over the actuator motion and alternatively by summing up the overall energy losses due to friction and elastic losses with the surface and the efficient work performed by the robot. The theoretical predictions are compared to numerical simulations modeling worm robots crawling over flexible surfaces and are found in perfect match.