Nonlinear Optimal Control for the Wheeled Inverted Pendulum System. Issue 1 (16th April 2019)

• Record Type: Journal Article
• Authors: Rigatos, G.; Busawon, K.; Pomares, J.; Abbaszadeh, M.
• Is Part Of: Robotica. Volume 38:Issue 1(2020)
• Page Start: 29
• Page End: 47
• Publication Date: 2019-04-16
• Subjects: Wheeled inverted pendulum, -- Nonlinear optimal control, -- H-infinity control, -- Approximate linearization, -- Taylor series expansion, -- Jacobian matrices, -- Riccati equation, -- Lyapunov analysis, -- Global stability; Robots -- Periodicals; 629.89205
• DOI: 10.1017/S0263574719000456
• Languages: English
• ISSNs: 0263-5747

Abstract

Summary: The article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system's strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal ( H -infinity) feedback controller is developed. The controller's gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the H -infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.