Passivity-based control of bicycle robot

Abstract

The paper proposes a control system for bicycle robot based on a passivity-based method. Bicycle robot is a nonlinear, MIMO (multi input - multi output) system. The first input of bicycle robot is the steering torque and and the second input has a relation with the kinetic energy. Its two outputs are the velocity of the steering angle and the velocity of the rolling angle . Bicycle robot is shown to be a passivity system. Consider a control problem which the steering angle tracks a value of zero and the rolling angle tracks a value of zero in order that bicycle robot keeps its vertical balance. We use a new control signal so that the system is passivity with input và output y= , which are the velocity of the steering angle and the velocity of the rolling angle . Stabilization of the equilibrium point at origin uses a PI (proportional integral) passivity-based control. Simulation results are done with Simulink in MATLAB and have good results such as short settling time and small percentage of overshoot. The error of the steering angle comes to 0.01 after two seconds and the error of the rolling angle comes to 0.01 after two seconds. Stability analyses using the passivity theory show that the equilibrium point at origin is asymptotically stable in the case of PI passivity-based control because the system has a positive definite storage function Vb and the derivative of Vb is semi-negative definite and the system is zero-state observable.