Linearized Modeling And Control Of Robotic Bicycle Through Nonlinear Dynamic Model

With the continuous development of science and technology,miniaturized electric driven self-balancing single-track vehicles may provide cities with cheap,safe and energysaving short-distance transportation tools,and then solve the problem of urban pollution,road and parking congestion.In the research of single-track vehicles self-balancing control,steering control is usually based on linear dynamic model,such as the Whipple-CornellDelft benchmark bicycle.The steer control,however,is not effective when bicycle velocity is close to zero.In fact,when the single-track vehicle is at standstill,the steer has little impact on the roll motion of a bicycle body.Therefore,in order to achieve the static balance of the robotic bicycle,one of the feasible ways is to use the mechanical flywheel to provide enough roll torque,so that the vehicle body can be in the static upright balance.However,the high-speed flywheel system will increase the overall power consumption and price of single-track vehicles,which is not conducive to commercialization,and the existence of flywheel system will also make the robotic bicycle unable to achieve sharp turns,thus reducing the applicability of single-track vehicles in complex road conditions.Therefore,in this dissertation we present a method that can balance a robotic bicycle at zero velocity.And because there is no known linear dynamic model which can be directly used in the control of robotic bicycle in the state of large steer angle,based on our earlier work of nonlinear bicycle dynamic model,we developed a novel of linearized dynamic equation near large steer angle.The newly developed linear equation is analyzed for its stability and a Linear Quadratic Regulator(LQR)is designed for balancing the robotic bicycle at zero velocity.Finally,we built a prototype robotic bicycle to verify our design.Both theoretical work and experiment shows the robotic bicycle can achieve its balance at zero velocity with our LQR controller without using either fly-wheel or any other devices that provides roll torque.The detail work of the dissertation is as follows:(1)Firstly,we describe the kinematics of the unconstrained bicycle via generalized coordinates and analyze holonomic and nonholonomic constraints for the front and rear ground contacts.Then the dynamic model of robotic bicycle is built and the Lagrange dynamics of robotic bicycle is obtained.Based on this model,a linearized dynamic equation of the robotic bicycle at 90° handlebar rotation angle was developed.The new developed linear model can realize the static balancing control of the vehicle under 90° handlebars,and it is different from the well-known Whipple-Cornell-Delft linearized benchmark bicycle model which is only applicable at small steer angle and small roll angle.Finally,the observability and controllability of the newly developed linear model are analyzed.(2)With our newly developed linear model,an LQR controller is designed to drive the front wheel motor,and MATLAB simulation is carried out to verify the effectiveness of the LQR control strategy.Simulation experiments show that the LQR controller can quickly and effectively help the single-track vehicle return to the state of static balancing.(3)Design and construction of experimental platform for robot bicycle.A front-wheel drive robotic bicycle experimental prototype under 90° handlebar angle is built,mainly including the design of vehicle mechanical structure,the construction of control system hardware platform and the corresponding software workflow of the balance control system.And the bicycle prototype is used as an experimental platform to carry out the static balance control.Experiments of the test vehicle confirms that the vehicle achieves balance at zero velocity,demonstrating the effectiveness of our control design.