Navigation Function-Based Control of Multiple Wheeled Vehicles

In this paper, a collision-free navigation method for a group of autonomous wheeled vehicles is investigated. The position and orientation information of individual vehicles is transformed to navigation variables, which are the distance left to the goal position, the angle made by the orientation of the vehicle at the goal position and the vehicle-to-target (v-to-t) vector, and the angle made by the heading direction of the vehicle and the v-to-t vector. As a Lyapunov function for deriving a smooth control law that drives all the vehicles from an initial configuration to a goal configuration, a new navigation function that incorporates the squared norm of the navigation variables, the boundaries of collision-free areas, and the angles made by the vehicle heading direction and the vehicle-to-obstacle (v-to-o) vectors is proposed. The asymptotic stability of the closed-loop system is proved. The effectiveness of the developed algorithm is illustrated through three simulations (three vehicles in a free environment, three vehicles in the presence of a static obstacle, and eight vehicles operating along a corridor) and two experiments (static and moving obstacles avoidance). The proposed algorithm has been implemented on a real forklift and the navigation of the forklift from an arbitrary initial configuration to a goal configuration while avoiding collisions has been demonstrated.