Optimal Control of Soft-Robotic Crawlers Subject to Nonlinear Friction: A Perturbation Analysis Approach

This letter considers the dynamics of a limbless, soft-robotic crawler, modeled as a nonlinear wave equation. Nonlinearities correspond to a sliding friction force modeled as an asymmetric signum function that captures both wet and dry friction effects. A reduced-order model of the dynamics is formed utilizing perturbation method techniques. This reduced-order model is solved analytically and solutions are validated by comparison to numerical solutions for the full dynamics of a soft-robotic crawler in a sewer pipe. This analytic solution to the reduced-order approximation of the dynamics is utilized to derive expressions for the resulting velocity, energy, mileage (efficiency), and engineering stress of a crawler. Assuming actuation that takes the form of a periodic traveling wave, an open-loop control design problem to maximize velocity subject to mileage and stress constraints is formulated and solved numerically. The analytical solutions derived here provide key insights, which can be used in future system and controller co-design of complex crawlers.