A nonlinear optimal control approach for autonomous motorcycles

The safety of driving two-wheel vehicles, such as motorcycles, can be significantly improved through electronic control of the their stability properties. This will also allow for precise path following and capability for dexterous maneuvering. In this article, a nonlinear optimal control method is developed for solving the stabilization and path following problem of autonomous motorcycles. The joint kinematic and dynamic model of the motorcycle undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control algorithm. The linearization takes place using Taylor series series expansion and the computation of the Jacobian matrices of the system's states-space model. For the approximately linearized model of the motorcycle an H-infinity feedback controller is designed. The computation of the feedback gain of the controller requires the repetitive solution of an algebraic Riccati equation, taking again place at each time-step of the control method. The concept of the control method is that at each time instant the system's state vector is made to converge to the temporary equilibrium, while this equilibrium is shifted towards the reference trajectory. Thus, asymptotically the state vector of the motorcycle converges to the reference setpoints. Through Lyapunov stability analysis the global asymptotic stability properties of the control method are proven.