The video provided shows two experimental results of a controlled Ball-on-Wheel system, each subjected to a different filtering and control method. The objective is to robustly stabilize the system's unstable equilibrium. In particular, the first part of the video demonstrates the real-time application of a Recursive Possibilistic Particle Filter (RPPF) combined with a min-max Model Predictive Control (MPC) scheme. For comparison, the second part of the video showcases the performance of an Extended Kalman Filter (EKF) paired with a nominal MPC scheme.

The hardware setup consists of a ball and a wheel, with the wheel driven by a NEMA 23 stepper motor coupled with a DMT 5505 motor controller. The translational displacement of the ball is measured by two time-of-flight sensors, processed by an ESP32 microcontroller. This microcontroller also facilitates communication with an external PC and transmits control commands following from the considered estimation and control schemes to the motor controller.

Notably, the second scheme, i.e., EKF combined with nominal MPC, relies solely on a single state estimate, accounting only for uncertainties of aleatoric nature. In contrast, the proposed scheme (RPPF and min-max MPC) shown in the first part of the video also considers uncertainties of epistemic nature. It does so by capturing all possible system states through a possibilistic particle filter. For control decisions, the set of all possible states in the current time step is reduced to the worst-case subset, enabling robust stabilization of the the unstable equilibrium via an implicit control law embedded within the min-max MPC framework.

A quantitative analysis of both schemes, as well as further details on the proposed method, hardware setup, and utilized parameters, can be found in the related publication associated with this video.