Formation tracking control design for uncertain artificial swarm systems under inequality constraints: Leakage and...

The paper proposes a formation tracking control method for the uncertain artificial swarm systems under the inequality constraints. Not only can the agents perform swarm behaviors (e.g., convergence, formation and avoidance of collision), but they can also track the fixed targets in a constrained area (which is formulated as the inequality constraints, such as unilateral constraint and bilateral constraint.). The swarm behaviors are creatively considered as the servo constraints or the control objectives for the swarm agents. Based on the Udwadia-Kalaba (U-K) equation, those prescribed behaviors are realized by a model-based control design (that is the servo constraints force model-based feedforward control). To deal with the inequality constraints in the formation tracking process, a differential homeomorphism transformation is used to relieve the environmental constraints for the swarm agents. Moreover, the uncertainty of the swarm agents (i.e., the parameter uncertainty in modeling and the external disturbances) is considered, which is time-varying and unknown (but bounded). An uncertainty estimation method with dead-zone and leakage term is designed to calculate the possible upper bound of the uncertainty. In virtue of the estimated upper bound of the uncertainty, a robust control is designed for the uncertain swarm agents to obey the prescribed swarm behaviors in the formation tracking task. The system performances of the artificial swarm systems under the proposed control are theoretically guaranteed by a range of rigorous theorems and numerically verified by the simulations of three agents.