Control Analysis of a 3D Self-Balancing Inverted Pendulum and Cart System for Stability in the Event of a Sensor Failure

This paper studies and simulates the dynamics and controls for a two-wheeled robotic chassis that successfully and consistently self-balances. Previous approaches to similar models have derived their dynamics from first principles using Newtonian mechanics for a linearized, shared-axle system and Lagrangian mechanics for a linearized, independently-actuated system. As such, the derived dynamics do not often reflect important factors of real world models which are not linear. However, this study specifically focuses on a more complicated system with independently-actuated wheels, for which a sophisticated and realistic dynamic model is derived using non-linearized Lagrangian mechanics. The pendulum and cart movements are each assumed to be planar, and their planes of motion are defined perpendicular to each other. The system’s performance is then analyzed in the simulation environment to determine the effect of various controllers and filters in cases of full and partial state feedback with and without sensor noise. Performance is characterized in terms of pendulum angle relative to the vertical axis and cart trajectory relative to the ground plane, both of which are functions of the voltage-applied force on each wheel independently. A comparison of the results shows that the non-linearized Lagrangian model best fits the true data and yields less uncertainty given a sensor failure. Therefore, the presented study has high intellectual merits compared to existing studies which focus on only linearized models. Based on the deterministic parameters of this study’s non-linearized model, a recommendation is made about which combination of controllers and filters best maintains the system’s stability in the event of a sensor failure returning only partial state feedback.