Unicycles and Two-Wheel Autonomous Ground Vehicles

Abstract

In complement to robotic manipulators, autonomous vehicles form the second large class of robotic systems. In this context, the autonomous or semi-autonomous navigation of unicycle-type and 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 for dexterous maneuvering. In this chapter, a nonlinear optimal control method is developed for solving the stabilization and path following problem of autonomous two-wheel vehicles. In the presented application examples either the kinematic or the joint kinematic-dynamic of the two-wheel vehicle 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 expansion and the computation of the Jacobian matrices of the system’s states-space model. For the approximately linearized model of the two-wheel vehicle 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 two-wheel vehicle converges to the reference setpoints. Through Lyapunov stability analysis the global asymptotic stability properties of the control method are proven In particular, the chapter treats the following topics: (a) Nonlinear optimal control of robotic unicycles, (b) Flatness-based control of robotic unicycles, and (c) Nonlinear optimal control of autonomous two-wheeled vehicles such as motorcycles.