Rolling Locomotion in Soft Robotic Snakes: Modeling, Control, and Experimental Validation
Soft robotic snakes, characterized by continuous body deformation, offer a superior platform for investigating the fundamentals of efficient biological locomotion. This paper introduces a mathematical framework for modeling and analyzing the planar rolling gait of these soft robotic snakes. We leverage principles of continuous deformation and distributed contact dynamics to derive an analytical relationship between the joint parameters of the robot and its resulting rolling velocity. To validate the model and enable practical application, we develop a configuration-space closed-loop controller for accurate trajectory tracking. The stability of the proposed controller is formally confirmed using the input-to-state stability criteria. Simulations and experimental validation demonstrate that the controller achieves accurate trajectory tracking and confirm that the measured rolling speed adheres to the theoretical prediction. These results affirm the effectiveness and accuracy of our gait modeling and control strategy for enhancing the locomotion performance and fundamental understanding of soft robotic snakes. Note to Practitioners—Soft robotic snakes offer unique advantages for applications requiring navigation in cluttered or confined environments, yet their highly compliant bodies and non-linear pneumatic actuation have historically made reliable motion control a significant barrier to deployment. This work addresses that practical need by providing an engineering framework that allows practitioners to command the snake robot to roll at a predictable speed and in a predictable direction, overcoming the unreliability of open-loop actuation. The presented geometric model can be used to estimate forward speed based on desired snake parameters, while the core practical contribution is the closed-loop controller that actively compensates for real-world issues. This controller maintains consistent body curvature despite common challenges like sensor noise, fabrication imperfections, material stiffness variations, and pneumatic delays, all of which typically undermine performance on physical hardware. Validation confirms this approach delivers improved trajectory tracking and more repeatable rolling behavior than current methods. Engineers deploying this framework should note its assumption of planar rolling on relatively uniform terrain and reliance on standard IMU sensing and pneumatic actuation, which may limit performance on highly irregular surfaces or when extreme speed in pressure dynamics is required. This foundation is essential for extending soft snake capabilities toward future, complex behaviors like autonomous navigation and obstacle-aware gaits.