Research On Motion Control Of Underactuated Unmanned Vehicle With State Constraint

The underactuated system is to drive more degrees of freedom with less control inputs.Underactuated system can not only reduce the cost,weight and volume of the system,but also provide emergency control method in case the actuator failure occurred in the fully actuated system.Therefore,the control problem of under drive mechanical system has been widely concerned in various application cases.The unmanned surface vessel(USV)is commonly equipped with only longitudinal thruster and heading steering device,its sway state is constrained by second-order nonholonomic constraints,could be treated as a typical underactuated system.In operation,it is affected by model perturbation(parameter uncertainty and unmodeled dynamics)and external environment disturbance(wind,wave,current,etc.).Each state has coupling and nonlinear characteristics.In addition,in narrow waterway navigation,formation navigation and multi-agent cooperation navigation,the state or output of the unmanned boat would be strictly constrained,so as to avoid collision or loss of communication due to expected deviation.All of these factors have brought great challenges to the motion control of underactuated USV.Focused on the motion stabilization control and trajectory tracking of the USV with model uncertainty and external disturbance,we introduced the theory of cascaded system,the integrated control strategy of sliding mode with reduced dimension dynamics and kinematics,and the control strategy with additional controllers into the kinematic and dynamic loops.The purpose of this paper is to realize the certainty of motion stability and trajectory controllability of the vessel under integrated disturbance.The non-diagonal USV mathematical model(i.e.the inertia matrix and damping matrix are non-diagonal)is established based on the Newton-Euler method.To ensure the consistency between the model and the actual situation,the necessary model perturbation and external disturbance are included in the model.As the non-diagonal inertia matrix and damping matrix introduced coupling among the states of the system,making the nonlinear characteristics of the underactuated system more prominent.It is difficult to use the linear control theory to solve the control of the nonlinear USV system.In this paper we adoptthe small time local control theory and differential geometry theory,which proves that the underactuated system with strong non-linearity is locally controllable in short time period,and this provides a theoretical basis for the following stabilization control and trajectory tracking control of the USV with state constraints.Firstly,traditional backstepping and Lyapunov methods are introduced tosolve stabilization control of underactuated USV with state constraints.Secondly,robust control law based on adaptive neural network is proposed for the USV stabilization control with state constraints.The complex non-diagonal model is transformed into two cascaded subsystems by global differential homeomorphism transformation and input transformation,and the stability of the cascaded system is proved to be equivalent to that of the original system.Because the stability of the cascade system is equivalent to that of the subsystem with control inputs,this simplifies the controller design and stability analysis.Then an adaptive neural network is proposed to estimate the unknown time-varying disturbance on-line.Based on the results of disturbance estimation,a control law combining barrier Lyapunov function and backstepping method is adopted to optimize the transient response performance.In order to avoid the explosion of dimension and times caused by the backstepping theory to the virtual control input,the first order derivative filter of the virtual variable is obtained by the dynamic surface theory.The simulation results show that the adaptive neural network stabilization control law proposed in this paper is effective and solves the problem of robust stability control of underactuated USV.In order to realize the trajectory tracking control of the USV,a robust control method to generalized dynamic inverse and sliding mode is proposed based on the underactuated characteristics,so that the control purpose can be realized without analyzing the coupling relationship between the states in the under drive system.By introducing the sliding surface,the dynamic equation and kinematic equation of the system are integrated as a whole set,and the dimension of the system could be reduced.The controller is divided into two parts:special solution and auxiliary solution.The selection of auxiliary solution will not affect the stability of underatuated axis.In order to ensure the stability of it,the special solution of the control law is constructed by the generalized inverse theory,in order to ensure the stability of the driving axis,the auxiliary solution which can make the drive axis stable is constructed by introducing the disturbance zero vector matrix with non-singularity.This method does not need to preprocess the model into chain form or the form suitable for reverse step,and does not need to analyze the coupling between various states in detail,so it could be extended to more incomplete systems.It provides a feasible method to solve the control problem of such sort of underactuated system without direct dynamic coupling between the underactuated axis and the actuated axis.Considering underdactuation and robustness of trajectory control of USV,an adaptive neural network observer is proposed,which can accurately estimate both the uncertainty and the states.The observer is independent of the controller,and the estimation results do not depend on the tracking error of the system.The tracking controller is divided into two parts,a kinematic loop and dynamic loop.There are two control strategies to put forward.In the first control strategy,the additional control variable is introduced into the kinematic control to solve the underactuation problem.Then,the sliding mode control is introduced to achieve the finite time convergence of the stabilization error.In the second control strategy,the barrier Lyapunov function is introduced to deal with the problem of tracking error constraints during the kinematic controller design,and the additional control variable is introduced to solve the underactuation problem during the dynamic controller design.The first control strategy does not take into consideration underactuation naturein the dynamic loop,and can be controlled by the existing full drive control method.While the second control strategy ensures the complete information of the kinematic loop and is easy to deal with the state constraints.