Zhang Jiale, Zhao Ruiying, Wu Linlin, Jiao Yuan, Jiao Shengjie
National Engineering Laboratory for Highway Maintenance Equipment, Chang'an University, Xi'an, Shaanxi 710065, PR China.
ISA Trans. 2023 Apr;135:325-338. doi: 10.1016/j.isatra.2022.10.013. Epub 2022 Oct 22.
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.
本文提出了一种针对不等式约束下不确定人工群体系统的编队跟踪控制方法。不仅智能体能够执行群体行为（例如收敛、编队和避碰），而且它们还能在受限区域（被表述为不等式约束，如单边约束和双边约束）内跟踪固定目标。群体行为被创造性地视为群体智能体的伺服约束或控制目标。基于乌德瓦迪亚 - 卡拉巴（U - K）方程，通过基于模型的控制设计（即基于伺服约束力模型的前馈控制）来实现那些规定行为。为了处理编队跟踪过程中的不等式约束，采用微分同胚变换来缓解群体智能体的环境约束。此外，考虑了群体智能体的不确定性（即建模中的参数不确定性和外部干扰），其是时变且未知（但有界）的。设计了一种带有死区和泄漏项的不确定性估计方法来计算不确定性的可能上界。借助估计的不确定性上界，为不确定群体智能体设计了一种鲁棒控制，使其在编队跟踪任务中遵守规定的群体行为。所提控制下人工群体系统的系统性能在理论上由一系列严格定理保证，并通过三个智能体的仿真进行了数值验证。
