Yaw Rate and Velocity Tracking Control of a Hands-Free Bicycle

The control of a bicycle has been well studied when a steer torque is used as the control input. Less has been done to investigate the control of a hands free bicycle through the rider’s lean relative to the bicycle frame. In this work, we extend a verified benchmark bicycle model to include a rider with the ability to lean in and out of the plane of the bicycle frame. A multi-input multi-output LQR state feedback controller is designed with the control objective being the tracking of a reference yaw rate and rear wheel angular velocity through the use of rider lean torque and rear wheel (pedaling) torque. The LQR controller is tested on the nonlinear model and numerical simulation results are presented. Conclusions regarding the required lean angle of the rider relative to the bicycle frame necessary to execute a steady turn are made, as well as observations of the effects of right half plane zeros in the transfer function from rider lean torque to yaw rate.© 2008 ASME