A New Configuration of Two-Wheeled Inverted Pendulum: A Lagrangian-Based Mathematical Approach

This work presents a novel design of two-wheeled vehicles. The proposed design provides the vehicle with more flexibility in terms of the increased degrees of freedom which enable the vehicle to enlarge its working space. The additional translational degree of freedom (DOF), offered by the linear actuator, assists any attached payload to reach higher levels as and when required. The model of the system mimics the scenario of double inverted pendulum on a moving base. However, it is further complicated due to the addition of a one more (DOF). As adding more degrees of freedom to the system increases the degree of complexity, Lagrangian dynamic formulation is used, due to its relative simplicity, to derive the system dynamics. The new developed configurations is of great importance in various applications including self balance robots, wheelchairs on two wheels, stability analysis of multi segment gaits and multi links cranes etc. In order to maintain the system nonlinear characteristics, the system model is derived with the consideration of the joints friction based on the Coulomb friction model. An investigation is carried out on the impact of the joints damping on the stability of the system. KeywordsLagrangian formulation, modelling and simulation , double inverted pendulum.