eXogenous Kalman Filter for State Estimation in Autonomous Ball Balancing Robots

Abstract

This paper presents discrete-time eXogenous Kalman Filter (XKF) for state estimation in an autonomous Ball Balancing Robot (Ballbot). The Ballbot has four omni-wheels and four motors attached to a ball. The objective is to estimate the position and attitude using measurement from a low cost Inertial Measurement Unit (IMU). To this end, we model the dynamic of the Ballbot as a nonlinear uncertain system. We derive a sufficient condition for stability of the XKF in form of Linear Matrix Inequality (LMI). Experimental tests show the proposed XKF algorithm provide better results than the Extended Kalman Filter (EKF), which is the de facto standard for nonlinear state estimation. The algorithm developed in this paper is written for systems with Lipschitz nonlinearities, which represents a wide class of nonlinearity arising in robotics and autonomous systems.