Finite Time Formation Control for Multiple Vehicles Based on Pontryagin0s Minimum Principle

研究基于庞特里亚金极小值原理的多运载体有限时间编队问题。运载体刻画为欧氏群切丛上演化的全驱动刚体动力学模型。编队机动时间以及队形的几何结构是由编队任务指定的。对于期望的队形，首先利用庞特里亚金最小值原理给出了开环最优控制。为了克服开环控制对扰动的敏感性并增加针对初始条件不确定性摄动的鲁棒性，在假定运载体间通讯为全联通的模式下，通过反馈将系统当前状态作为初始状态，当前时刻作为初始时刻，进一步将开环控制律转化为闭环形式。为了验证所得结果，给出了平面及空间运载体编队的仿真算例。The paper studies the problem of finite time formation control for multiple vehicles based on Pontryagin0s minimum principle. The vehicle is modeled as a fully actuated rigid body with the dynamics evolving on the tangent bundle of Euclidean group. Both the formation maneuver time and the geometric structure of the formation are specified by the formation task. For the required formation, an open loop optimal control law is derived by using Pontryagin0s minimum principle. In order to overcome the sensitivity of the open-loop control to the disturbance and increase the robustness of the control law to the initial perturbation, the open loop control law is converted to the closed loop form. This is done by feeding the current state back and initializing the control law at the current time, under the assumption that the mode of communication between the vehicles is all-to-all. For demonstration of the result, some numerical examples of formations for both planar and spacial vehicles are included.国家自然科学基金(61374033)资助Supported by National Natural Science Foundation of China中国科学引文数据库(CSCD)140-594