Potential field based formation control in trajectory tracking and obstacle avoidance tasks

An approach using potential functions applied to formation control (including aggregation, collision-free goal following behavior, and trajectory tracking one) is proposed. The formation control is considered as a special form of agent aggregation, where the final aggregated form has to constitute a particular previously determined geometrical configuration that is defined by a set of desired interagent distance values. This is achieved by defining an appropriate potential function, which reaches global minimum at the desired shape of formation. The innovation in this paper is the modification of the potential function by adding new parts that take into consideration: (1) the desired orientation of the formation as a whole; (2) obstacle avoidance behavior; and (3) goal following one. The control strategy is based on forcing the motion of the agents along the negative gradient of the potential field and taking into account the agents´ non-holonomic kinematics. The validation of the proposed formation control is confirmed by simulations in MATLAB environment.