Swing up Control of Inverted Pendulum on a Cart with Collision by Monte Carlo Model Predictive Control

Monte Carlo Model Predictive Control (MCMPC) is a kind of sample-based MPC methods, which does not require gradient information of cost function. This feature allows us to apply it to systems with non differentiable cost function or discontinuous event taking full advantage of recent parallel computing such as GPU. In this paper, we consider the problem of swing-up stabilization of a cart type inverted pendulum focusing on this feature of MCMPC. The first application is the problem considering the unwinding phenomenon. By applying MCMPC, it is possible to avoid the unwinding phenomenon by directly implementing the feature of the rotation group. The resultant controller thereby is inherently discontinuous. The second application is swing-up stabilization with a model considering collision of the cart with walls. In this case, thanks to the advantage of MCMPC being capable of handling discontinuous events, swinging up can speed up by exploiting the energy by the collision. these are verified by simulations and experiment.