Comparative evaluation of robust and optimal controllers for a two-wheeled self-balancing robot under external disturbances

The inherent characteristics of two wheels inverted pendulum (TWIP) robots are unstableness and high sensitivity to external perturbations, which means that effective balance control in the interaction with the real world is a persistent and practically significant challenge. Despite the intensive variety of reported control strategies in the literature, the currently available research is usually based on heterogeneous modeling assumptions, definition of disturbances, controller design and testing protocols. Such diversity prevents the fair comparison and blurs the inherent trade-offs of robustness, complexity, and implementability of various control methods. This gap is filled in this paper where a systematic and reproducible comparative analysis of three representative control approaches to TWIP systems is provided: full-order H infinity control, fixed-structure infinity-PID control and Linear Quadratic Gaussian (LQG) control.Based on the nonlinear TWIP equations of motion and linearized about the upright equilibrium configuration, a disturbance-inclusive dynamic model is obtained to assist in control synthesis. In order to guarantee fairness and repeatability, all controllers have been designed based on the same linearized model of the plant, and tested under the same constraints on actuators and the same disturbance scenarios. Three categories of external disturbances are considered to represent typical real-world interacting conditions experienced in the mobile robotic system: impulsive forces, finite duration disturbances and sustained external inputs. The performance of the controllers is evaluated based on representative time domain performance and robustness metrics under the same evaluation conditions.The outcomes of the simulation prove that the full-order H infinity controller has always the most robust disturbance attenuation, and the highest robustness in all the disturbance scenarios. The fixed-structure H infinity-PID controller is similar in regulation performance but is more practical to implement and it has less complexity of the controller. Contrary to it, the LQG controller is very sensitive to both finite-duration and sustained disturbances when compared to the same noise-free conditions. On the whole, the presented unified framework elucidates the trade-offs between robustness, complexity of controllers and their practical implementation, and a way forward on the selection of disturbance-resilient controllers to be used in the application of two-wheeled inverted pendulum robots.