Constrained Lagrangian-Based, Nonholonomic Modeling and Validation of a Pneumatically Actuated Wheeled Soft Robot

Abstract This article presents three configurations of a pneumatically actuated, symmetric, wheeled soft robot that is able to locomote forwards, backwards, and in a circular trajectory on a planar surface. The robot can achieve 22 cm/s (1.38 body lengths/s) in straight-line speed. We also extend a modeling framework from previous work to express the dynamics of continuum robots and apply it to all three wheeled soft robot configurations. This dynamic model incorporates both holonomic and nonholonomic constraints and is able to capture the locomotion characteristics (configuration and velocity) of the 3D-printed robot. The model is formed by linking discrete rods with inertia, stiffness, and damping derived from constitutive beam bending equations and physical characterization of the robot. This formulation, based on a constrained Lagrangian approach, simplifies the equations of motion by kinematically chaining the rods to resemble the robot body and by constraining the velocity of the segments with wheels. Constraint enforcement is integrated into this formulation to mitigate accumulated errors from numerical integration. The configuration and velocity of the robot are characterized as a function of frequency both in simulation and experimentally, demonstrating a reasonably good match. This work presents and validates a modeling approach that is capable of capturing highly dynamic nonholonomic locomotion of fluid-powered soft robots that current state-of-the-art modeling frameworks cannot.