Energy shaping nonlinear acceleration control for a mobile inverted pendulum with a slider mechanism utilizing instability

A nonlinear controller for accelerating a mobile inverted pendulum (MIP) with a slider mechanism is proposed. The controller shapes the total energy of the system and utilizes instability of the MIP for acceleration. The body angle and the displacement are controlled to keep states where the MIP is statically unstable, which leads to translational acceleration due to instability of the system. The total energy of the system is shaped to have the minimum at given desired states and the system is controlled to converge to them. The proposed controller can achieve various properties through the energy shaping procedure. Especially 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 and converges to the desired states. The controller also returns the system back to the desired states with state-dependent gains that become large if the system comes close to fall over. Effectiveness of the proposed controller and utilization of instability for the MIP with the slider mechanism are verified through simulations.