Role of Body Elasticity in Overdamped Undulatory Robot Locomotion

Elongate animals use undulatory body waves to propel themselves through interactions between elastic bodies and the environment. While body elasticity enhances locomotor efficiency in inertial swimmers, its role in highly damped systems like nematodes and snakes is less understood. Elasticity can act locally (affecting a single joint) or over multiple joints (influencing multiple segments, as in snakes' multi-articulated muscles). We study how body elasticity influences actuator energetics in overdamped environments using a theoretical and robophysical Purcell three-link model (BL =0.42m) with local and coupled springs at the two joints. Simulations and theory show that, for the same gait (path in angular configuration space), neither elasticity configuration affects total energy consumption. However, elastically coupled segments redistribute energy across joints by rebalancing joint torques, reducing energy at the head joint and increasing it at the tail. The redistributed energy fraction is determined by the gait's enclosed area and the coupling springs' stiffness. Measurements of motor energy consumption in a robophysical model swimming in a granular medium (6 mm plastic spheres) align with theory regarding the amount of energy that is redistributed for different stiffness of springs. Simulations of an 8-motor swimmer with multiple elastically coupled joints suggest energy redistribution may help elongate animals balance muscle energy use in overdamped environments.