A Constructive Self-balancing Controlled Lagrangian for Wheeled Inverted Pendulum

This work presents a controlled Lagrangian for the wheeled inverted pendulum system in which the upward position of the pendulum becomes a stable nonlinear equilibrium.Unlike the general form of underactuated systems,the configuration variables are not partitioned into actuation and underactuated subsets and instead we show that the energy shaping and matching conditions can be achieved in a constructive procedure.The asymptotic stability is guaranteed by the definiteness of the shaped energy and applying a suitable dissipation.We also apply this self-balancing control to the system which is partially linearized and controlled in the wheel position.The efficiency of the control law along with the wheel positioning is observed by simulation.This work presents a controlled Lagrangian for the wheeled inverted pendulum system in which the upward position of the pendulum becomes a stable nonlinear equilibrium.Unlike the general form of underactuated systems,the configuration variables are not partitioned into actuation and underactuated subsets and instead we show that the energy shaping and matching conditions can be achieved in a constructive procedure.The asymptotic stability is guaranteed by the definiteness of the shaped energy and applying东北大学、IEEE新加坡工业电子分会