Trajectory Tracking Control Of Underactuated UUV For Autonomic Recovery

After an under-actuated Unmanned Underwater Vehicle completed the mission, it needsto return to the support ship or sub to replay data, download new missions, etc, so therecovery operation of vehicles is an indispensable process. While the motion control is veryimportant technical support for autonomic recovery of Under-actuated UUV, so it has somesignificant value in both theoretic and engineering application to research the motion controlmethod aiming at the process of recovery.This paper analyzes the control and motion characteristics of under-actuated UUV, andsummarizes the present research about tracking control and recovery technology of thevehicles, and based on this, deals with the autonomous recovery mission, considering thecharacteristics of nonholonomic constraints for under-actuated UUV, the strong nonlinear andstrong coupling of dynamic motion model and the uncertainties of hydrodynamic, combinesthe trajectory tracking control with the autonomous recovery of under-actuated UUV. Thenonlinear method was applied to design an advanced trajectory tracking controller, to achievethe tracking mission with “space and time” from the from the start point to the recoveryplatform, which lays the foundation for vehicles completing the recovery mission successfully.The main research contents are as follows:Firstly, the space kinematic model and dynamic model of under-actuated UUV duringthe process of recovery are established, and they are proved to be correct and maneuverablethrough the mechanical simulation of vehicle’s typical movement. Some reasonablehypotheses are put forward according to the physical structure and the work environment ofthe vehicles, and the hydrodynamic parameters which play a dominant role in the spacemotion of under-actuated UUV are reserved. The motion models are simplified to obtainsimplified models of under-actuated UUV motion for3DOF during the process of surfacerecovery and the simple model of under-actuated UUV motion for six degrees of freedomduring the process of underwater recovery. As a premise, the simplification should not affectthe main motion characteristics of the vehicles. And the structure of the trajectory trackingcontroller is simplified consequently.Secondly, the trajectory tracking control method is established by inducting a virtualUUV on the reference trajectory which is the tracking target of the controlled vehicle. Thewhole trajectory tracking control process was departed into two sections, one is the trajectoryplanning of the virtual UUV, and the other one is the tracking of the controlled UUV to the virtual UUV, as a result, the controlled UUV is independent of the reference trajectory, andthe complexity of the trajectory tracking controller is reduced, the control effect is improved.The state variables of the virtual UUV and the controlled UUV are combined to get thetrajectory tracking error, so the trajectory tracking problem of under-actuated UUV istransformed into the trajectory tracking error’s stability and convergence problem. Deals withthe simplified motion model, and at the same time it makes the error equation partly linearizeby inducting auxiliary control variables which reduces the complexity of the controller.What’s more, control theories such as the Back-Stepping techniques as well as Lyapunovfunctions and Young’s inequality and so on mathematical tools are applied to design thecontroller of trajectory tracking in the process of the surface and underwater recovery ofunder-actuated UUV. And the tracking error asymptotic stable converges to the origin toensure the recovery of the vehicle successfully.Then, aiming at the trajectory planning section during the process of surface recovery,according to the truth that the reference points on the reference trajectory have the sameposition with the virtual UUV and the tangent velocity of points is equal to the resultantvelocity of the virtual UUV，the differential equations between the reference trajectoryvariables and the state variables of virtual UUV are established. Combines with the horizontaldynamic model of under-actuated UUV，the expression of the virtual UUV with respect toreference trajectory variables is achieved, thus the reference trajectory information can bemapped to the position and pose information as well as velocity information of virtual UUV,and the trajectory planning work of controlled UUV in horizontal trajectory tracking arecompleted. Dealing with the trajectory planning section during the process of underwaterrecovery, the Frenet-Serret frame, the reference frame, the body-fixed frame and theearth-fixed frame are introduced to transform the attitude angle of the reference points on the3D reference trajectory into the attitude angle of the virtual UUV utilizing the relationshipbetween those frames. At the same time, according to the truth that the reference points on thespace3D reference trajectory have the same position with the virtual UUV and the tangentvelocity of points is equal to the resultant velocity of the virtual UUV，as well as the dynamicmodels of under-actuated UUV motion for6DOF, the expression of the virtual UUV withrespect to3D reference trajectory variables is deduced, thus the space3D trajectory planningwork of the controlled UUV during the process of underwater recovery is completed.Finally, to verify the validity of the trajectory tracking controller, the semi-substantialemulation platform is built. Respectively, the circular trajectory is tracked during the processof surface recovery, and the sinusoidal trajectory for underwater recovery. Simulation results show that the trajectory tracking controller can achieve the surface recovery by trackingcircular trajectory and the underwater autonomic recovery by tracking sinusoidal trajectory,which designed by combining the method of using the virtual UUV as the target of thecontrolled UUV with the Back-Stepping as well as Lyapunov functions. At the same time,3DScene Simulation Computer is used to show the motion state of the vehicle, which improvesthe visual effect of trajectory tracking in the recovery process of under-actuated UUV.