Modeling and state estimation of a Micro Ball-balancing Robot using a high yaw-rate dynamic model and an Extended Kalman Filter

The state estimation and control of a ball-balancing robot under high yaw rate is a challenging problem due to its highly nonlinear 3D dynamic. The small size and low-cost components in our Micro Ball-Balancing Robot makes the system inherently very noisy which further increases the complexity of the problem. In order to drive the robot more aggressively such as translating and spinning at the same time, a good state estimator which works well under high yaw rates is required. This paper presents the derivation of a high yaw-rate Ball-Balancing Robot dynamic model and the implementation of said model in an Extended Kalman Filter (EKF) using raw on-board sensor measurements. The EKF using the new model is then compared to a Kalman Filter which uses a linearized dynamic model. The accuracy of the attitude estimates and the controller performance under high yaw rates were verified using a motion capture system.