Real-time Roll Angle Estimation for Two-wheeled Vehicles

An original method for the real-time estimation of the roll angle using low-cost sensors in two-wheeled vehicles is proposed. The roll angle greatly affects the dynamics of singletrack vehicles and its estimation is essential in control systems such as ABS, Traction Control, as well as Curve and Collision Warning, or even active suspensions. The proposed method uses a non-linear Kalman filter, its performances are assessed by using both a set of simulated data from a multibody model and a set of real data collected on an instrumented test vehicle. NOMENCLATURE B distance between laser sensors C road-tyre contact point f non linear equations of motion g gravity acceleration 1 h center of gravity position H observation matrix x I moment of inertia with respect to the roll axis W I overall spin inertia 1 W I rear wheel spin inertia 2 W I front wheel spin inertia I identity matrix K optimal Kalman gain m mass of the vehicle plus rider u longitudinal speed P predicted covariance matrix Q covariance matrix of the process noise 1 r rear tyre radius 2 r front tyre radius t r radius of the tyre cross section R covariance matrix of the observation noise S innovation covariance matrix v observation noise w process noise x vector of state variables z observed variable zL distance of the left laser sensor from ground zR distance of the right laser sensor from ground  swingarm oscillation t  sampling time  wheel spin rotation  pitch angle  roll angle i ideal roll angle X  angular velocity around the X axis of the vehicle Z  angular velocity around the Z axis of the vehicle