A Pedaling Torque Observation Approach for Sensorless Electric Bicycles

This study proposes an innovative unknown input observation approach based on Kalman filtering to estimate the cycling torque and provide assistance in electrically powered bicycles. Specifically, a constant and a sinusoidal pedaling torque model are compared, underlining the need for an enhanced mathematical description to improve system performance. Using a nonlinear model of the bicycle longitudinal dynamics, the cycling torque is reconstructed with an Extended Kalman Filter. Also, an online low-computational effort road slope estimation method based on Kalman filtering, that accounts for cornering effect errors, is proposed. The considered approaches, that utilize wheel speed, inertial, and motor current measurements, are tested in an outdoor setting with variable slopes and curves. Differently from the current state-of-the-art, the estimation performances are not only expressed in terms of pedaling torque estimation error minimization. This work presents a novel pedaling power and delivered energy analysis to evaluate the provided electrical assistance and the consequent pedaling effort decrease. The experimental results show that a cycling endeavor reduction, similar to what can be achieved when electrical assistance is provided employing a torque sensor, is possible, especially when relying on improved pedaling modeling.