Control law for multiple obstacle avoidance of four-wheeled vehicle with limited steering angle by multilayer minimum projection method

Maintaining control of a mobile robot in a space punctuated by obstacles is known to be a difficult problem. It is generally necessary to avoid such obstacles and find as short a route as possible to a goal. In this paper, we approach such a problem by proposing a design method for a navigation function to a given goal point, assuming that we know the location and shape of the obstacles. We then obtain a control law for a four-wheeled vehicle from a control Lyapunov function extended from this navigation function. Four-wheeled vehicles, such as cars, cannot move sideways due to their nonholonomic constraint. The control law proposed in this paper clears the nonholonomicity and enables us to consider the direction of the vehicle and its steering angle limitation using the backstepping method with our navigation function. We also describe some experimental results of the proposed method for a small four-wheeled vehicle.