Research On The Trajectory Tracking And Formation Control For Underactuated Surface Vehicles

Due to the low transportation cost and large transportation volume,it is well known that the largest transport guarantee for world trade is ocean transportation.In marine transportation,the ship is its main transportation carrier,and ship transportation is the fundamental guarantee of international trade.With the development of international trade,growth of trade volume,and the rise of large-scale ocean-going container ships,modern smart ships that can adapt to long-distance and large-capacity are increasingly favored by international trade.In addition,with the improvement of naval equipment technology and the technical sharing between the military and civilian,the ship motion control technology has attracted lots of attention in marine control community.In the development of ship motion control,due to no actuator is used for the control of sway motion directly,compared to fully-driven ships,the research on underactuated ships is more challenging.The underactuated ship control system has nonlinear characteristics,such as strong coupling and model uncertainties,and it has external time-varying disturbances and ship manipulation constraints.In the research field of underactuated ships,single-vessel control and formation control are two major topics.Among these,single-vessel control is the foundation.However,with the developing trend of the diversity of ship tasks,ship formation control derived from single-vessel control has increasingly attracted the attention of the academic community.Compared with single-ship control,formation control is widely used in marine search and rescue,resource exploration,oceanography,marine science examination,ship rescue and ocean replenishment.Therefore,the research on the trajectory tracking and formation control for underactuated surface vehicles is not only an important topic to master the independent intellectual property rights,but also conforms to the national strategic requirements of China's maritime power.In this paper,the nonlinear control feature of underactuated surface vehicles is analyzed based on the three-degree-of-freedom ship motion model.Combining the ship model uncertainties and disturbance time-varying characteristics,the research on trajectory tracking and formation control for underactuated surface vehicles is proposed.The main contents of this paper are as follows:First,due to the complex problem of taking the derivative of the virtual control law and environmental disturbances of the ship motion control,a robust adaptive PI sliding mode control and parameter estimation scheme is proposed.By introducing a virtual velocity variable,the trajectory tracking control problem is transformed into a control error stabilization problem,and in order to overcome the complex problem of system virtual control law derivation,a PI sliding mode control strategy combined with backstepping technique is proposed.In addition,through the design of the distributed scalar function,a specific scheme for the controller design of the system is given,and the design principle of the control system is presented intuitively.The upper bound estimation of disturbances control is used to deal with the system's external unknown disturbances.Finally,through the design of the closed-loop system controller,the uniformly ultimately bounded stable of the closed-loop system is obtained.Second,considering the requirement of engineering applications,in the existing works,when we design a controller to solve the trajectory tracking problem of underactuated surface vessel with adaptive PD sliding mode and parameter estimation control method,it will involve the existences of first-order derivatives of environmental disturbances,however,this may not be satisfied in practical engineering.In addition,in the field of trajectory tracking control of underactuated surface vessels,when using sliding mode control methods,many existing works are designed the sliding mode surface based on the symbol function,which can bring the chatting of the closed-loop system with the discontinuity of the sliding surface.Therefore,this paper proposes a control algorithm based on PI sliding mode control and upper bound estimation of disturbances.The control law which based on the continuous mode design can be divided into two parts.An equivalent control law to deal with tracking errors and model uncertainties,then a disturbance control law to solve the problem of environmental disturbances.When dealing with unknown disturbances outside the control system,an upper bound estimation of disturbances method can effectively avoid problems such as the first-order derivatives of environmental disturbances,which makes the control algorithm more powerful in practical engineering.Thirdly,a novel trajectory tracking control method is designed to relax the assumption of passive boundedness in sway motion.Through constructing the virtual control,the mathematical relationship between virtual control and sway velocity is established.Then,by using the coordinate transformation,it can transform the system trajectory tracking problem into a control error stabilization problem.In order to realize the control of system error and virtual control law,the controller is designed by the adaptive PI sliding mode and parameter estimation method.Finally,the stability of the closed-loop system is proved by Lyapulov stability,and the stabilization characteristic of the virtual control error is obtained.By using the mathematical relationship between the virtual control and the sway velocity,it can be proved that passive boundedness in sway motion.Therefore,we can effectively avoid such assumptions and indirectly prove that it satisfies the control system design requirements.Finally,based on the study of single-ship trajectory tracking control,the paper extends the research to the leader-follower formation control of underactuated surface vehicles.Due to the model uncertainties and environmental disturbances of the leader-follower formation control of underactuated surface vehicles,a parameter estimation and upper bound estimation based sliding mode control scheme is proposed.In the design of the controller,a parameter estimation and upper bound estimation is developed to solve the problem of unknown plant parameters and the environment disturbances,which can reduce the dependence of ship modes,and improve the control accuracy.Furthermore,in order to reduce the speed measurement equipment cost and the network burden caused by system information transmission,this paper proposed an adaptive control law to compensate for the leader velocities information,which can reduce the dependence of leader formation.At the end of this paper,the contributions of this paper are summarized.We give a research plan in our future work,where how to solve the mechanism of multi-static or slow time-varying obstacles avoidance and the optimization problem will be taken into account.