Research background

In recent years, with the development of robot technology, the application of robot structures with high speed, high precision and high load to weight ratio has attracted much attention in the fields of industry and aerospace. Due to the increase of the flexibility effect of joints and links in the process of movement, the structure is deformed, which reduces the accuracy of task execution. Therefore, the structural flexibility of robot manipulator must be considered, and the system dynamics must also be considered to realize the high-precision and effective control of flexible manipulator. Flexible manipulator is a very complex dynamic system. Its dynamic equation has the characteristics of nonlinearity, strong coupling and real variation. The establishment of its model is very important to study the dynamics of flexible arm. Flexible manipulator is not only a nonlinear system with rigid flexible coupling, but also a nonlinear system with electromechanical coupling. The purpose of dynamic modeling is to provide basis for control system description and controller design. The description of general control system (including state space description in time domain and transfer function description in frequency domain) is closely related to the positioning of sensor / actuator, information transfer from actuator to sensor and the dynamic characteristics of manipulator.

Modeling theory

The dynamic equations of flexible manipulator are mainly established by using the two most representative equations, Lagrange equation and Newton Euler equation. In addition, the variational principle, virtual displacement principle and Kane equation are commonly used. The description of flexible body deformation is the basis of flexible manipulator system modeling and control. Therefore, a certain way is selected to describe the deformation of flexible body, and the description of deformation is closely related to the solution of system dynamic equations.

The deformation of flexible body can be described as follows:

1) Finite element method;

2) Finite segment method;

3) Modal synthesis method;

4) Concentrated mass method.

kinetic equation

Whether continuous or discrete dynamic models, their modeling methods are mainly based on two basic methods: vector mechanics method and analytical mechanics method. Newton Euler formula, Lagrange equation, variational principle, virtual displacement principle and Kane equation are widely used and mature.

control strategy

The flexible manipulator is generally controlled in the following ways:

1) Rigid treatment. The influence of the elastic deformation of the structure on the motion of the rigid body is completely ignored. For example, in order to avoid excessive elastic deformation damaging the stability and end positioning accuracy of the flexible manipulator, the maximum angular velocity of NASA's remote-controlled spacecraft is 0.5deg/s.

2) Feedforward compensation method. The mechanical vibration caused by the flexible deformation of the manipulator is regarded as the deterministic interference to the rigid motion, and the feedforward compensation method is used to counteract this interference. Bernd gebler of Germany studied the feedforward control of industrial robot with elastic rod and elastic joint. Zhang Tiemin studied the method of eliminating the dominant pole and system instability by adding zero, and designed a feedforward controller with time delay. Compared with PID controller, it can eliminate the residual vibration of the system more obviously. Seering Warren P. and other scholars have conducted in-depth research on feedforward compensation technology.

3) Acceleration feedback control. Khorrami farshad and Jain Sandeep studied the end trajectory control of flexible manipulator using end acceleration feedback.

4) Passive damping control. In order to reduce the influence of the relative elastic deformation of the flexible body, various energy consuming or energy storage materials are selected to design the structure of the arm to control the vibration. Or the use of damping shock absorber, damping material, composite damping metal plate, damping alloy or viscoelastic large damping material to form additional damping structure on the flexible beam belongs to passive damping control. In recent years, the application of viscoelastic large damping materials in the vibration control of flexible manipulator has attracted great attention. Rossi Mauro and Wang David studied the passive control of flexible robots.

5) Force feedback control method. The force feedback control of flexible manipulator vibration is actually a control method based on inverse dynamics analysis, that is, according to the inverse dynamics analysis, the torque applied to the driving end is obtained through the given motion at the end of the arm, and the driving torque is feedback compensated through motion or force detection.

6) Adaptive control. The system is divided into joint subsystem and flexible subsystem by using combined adaptive control. The parameter linearization method is used to design adaptive control rules to identify the uncertain parameters of flexible manipulator. The tracking controller of flexible manipulator with nonlinearity and parameter uncertainty is designed. The controller design is based on the robust and adaptive control design of Lyapunov method. The system is divided into two subsystems through state transition. Adaptive control and robust control are used to control the two subsystems respectively.

7) PID control. As the most popular and widely used controller, PID controller is widely used in the control of rigid manipulator because of its simplicity, effectiveness and practicability. It often forms a self-tuning PID controller by adjusting the controller gain or a composite control system combined with other control methods to improve the performance of PID controller.

8) Variable structure control. Variable structure control system is a discontinuous feedback control system, in which sliding mode control is the most common variable structure control. Its characteristics: on the switching surface, it has a so-called sliding mode. In the sliding mode, the system remains insensitive to parameter changes and disturbances. At the same time, its trajectory is located on the switching surface. The sliding phenomenon does not depend on system parameters and has stable properties. The design of variable structure controller does not require an accurate dynamic model of the manipulator, and the boundary of the model parameters is enough to construct a controller.

9) Fuzzy and neural network control. It is a language controller, which can reflect the thinking characteristics of people in control activities. One of its main characteristics is that the control system design does not need the mathematical model of the controlled object in the general sense, but the experience knowledge and operation data of operators or experts.