Dynamics-Based Nonlinear Acceleration Control with Energy Shaping for a Mobile Inverted Pendulum with a Slider Mechanism

A nonlinear controller to accelerate a mobile inverted pendulum (MIP) with a slider mechanism is proposed. The concept of this paper is to control translational acceleration and deceleration of the MIP in a dynamically reasonable manner. The body angle and slider displacement are controlled to maintain reference states where the MIP is statically unstable but dynamically stable, which leads to a constant translational acceleration due to instability of the vehicle. The accelerating motion is like a sprinter moving from the crouch start, and it fully exploits the dynamics of the MIP. To achieve it, the total energy of the system is shaped to have the minimum at the given reference states and the system is controlled to converge to them. The controller can achieve various properties through the energy-shaping procedure. In particular, an energy function that will lead to safe operation of the MIP is proposed. The function ensures that motion of the MIP is restricted within predefined regions. The controller also returns the system back to the reference states with state-dependent gains that become large if the system comes close to falling over. The effectiveness of the controller is verified in simulations. Finally, a new physical MIP was constructed, and experiments were carried out with an additional friction compensation method. The results show that the proposed controller works well in the presence of uncertainty, such as noise and modeling errors.