基于加幂积分方法的AUV的点镇定

Point Stabilization for an AUV Based on the Addition of a Power Integrator

针对欠驱动自主式水下航行器(AUV)在水平面的点镇定问题,设计了一种基于加幂积分方法的非光滑控制器.首先,通过极坐标系下的坐标变换避开Brockett必要条件的限制;其次,通过变量代换将变换后的系统分为航向控制和距离控制2个子系统,将高阶系统变为2个低阶系统;然后,对2个子系统分别采用加幂积分方法设计控制器;最后,对于起始点与目标点重合的情况单独采用加幂积分方法设计控制器.通过构造合适的李亚普诺夫函数,证明了欠驱动AUV的速度、距离和角度均能达到期望值.仿真结果验证了所设计控制器的有效性.

In accordance with the point stabilization problem for an underactuated AUV in the horizontal plane,we design non-smooth controllers based on the addition of a power integrator approach. First,we avoid the limitations of Brockett's necessary conditions by using the coordinate transformation of the polar coordinate.Second,we divide the transformed system into heading subsystems and distance subsystems by using variable substitution. Thus,the high-order system is transformed into two low-order systems. Third,we design the controllers for the two subsystems by adding a power integrator. Finally,we design the controllers for the case where the starting point coincides with the target point by adding a power integrator. Through the construction of appropriate Lyapunov functions,the velocities,distances,and angles of an underactuated AUV can converge to the desired values. Simulation results demonstrate the effectiveness of the designed controllers.