Dynamical Analysis of an Undulatory Wheeled Locomotor: a Trident Steering Walker

This paper presents a novel methodology of dynamical analysis of an undulatory wheeled locomotor: a trident steering walker based on Lagrangian mechanics. The trident steering walker moves by undulatory locomotion in which it transforms its periodic changes in shape into its displacement and it is a mechanical system subject to nonholonomic constraints in which all wheels roll without slipping on a horizontal plane. The dynamical equations of the trident steering walker consist of the Euler-Lagrange equations and the time derivatives of the equations of the nonholonomic constraints. The nonholonomic constraints are especially incorporated through the Lagrangian undetermined multipliers. I demonstrate the effectiveness of a dynamical control law which is derived from a path-following feedback kinematical control law previously designed by the author by performing a path-following motion in which the trident steering walker follows a third-order Bezier curve path. The dynamical equations are numerically integrated and the simulated state variables of Lagrangian mechanics exactly correspond with those of a commercial multibody dynamics simulator, LMS Virtual. Lab Motion. Therefore, the validity of the dynamical analysis of Lagrangian mechanics is verified by the comparison with the commercial multibody dynamics simulator.