Virtual Model Development and Control for an EV3 BallBot Robotic System

In this paper, the virtual model development and control for a BallBot Robotic System (BRS) are addressed. A virtual three-dimensional (3-D) EV3 BRS (EV3BRS) model is here developed through the Simscape™ Multibody™ environment from a BRS designed using the kit LEGO® MINDSTORMS® EV3. The mathematical model from the BRS is obtained through the Euler–Lagrange approach and used as the foundation to develop the EV3BRS Simscape™ model. The electrical model for the motors is derived through Kirchhoff’s laws. To verify the dynamics of the EV3BRS Simscape™ model, a Takagi–Sugeno Fuzzy Controller (TSFC) is designed using the Parallel Distributed Compensation (PDC) technique. Control gains are computed via Linear Matrix Inequalities (LMIs). To test the EV3BRS Simscape™ model under disturbances, an input voltage anomaly is considered. So, adding an H∞ attenuation to the TSFC ensures that the EV3BRS Simscape™ model faces these kind of anomalies. Simulation results confirm that the TSFC with H∞ attenuation improves the performance under anomalies at the input in contrast with the nominal TSFC, although this latter can maintain the body of the system near the upright position also. The dynamics from the EV3BRS Simscape™ model here developed allow us to realize how the real system will behave.