The increased flexibility of joints and links during movement causes structural deformation, leading to a decrease in task execution accuracy. Therefore, the structural flexibility of the robotic arm must be considered, and achieving high-precision and effective control of the flexible robotic arm also requires consideration of the system's dynamic characteristics. A flexible robotic arm is a highly complex dynamic system, with its dynamic equations exhibiting nonlinearity, strong coupling, and real-variable characteristics. Therefore, establishing a model is crucial for studying the dynamics of flexible arms.
A flexible robotic arm is not only a rigid-flexible coupled nonlinear system, but also a nonlinear system with coupled dynamic and control characteristics, i.e., electromechanical coupling. The purpose of dynamic modeling is to provide a basis for control system description and controller design. The description of a general control system (including state-space description in the time domain and transfer function description in the frequency domain) is closely related to the positioning of sensors/actuators, information transmission from actuators to sensors, and the dynamic characteristics of the robotic arm.
The control of flexible robotic arms generally takes the following forms:
1. Rigidification: Completely ignore the influence of elastic deformation on the rigid body motion of the structure. For example, to avoid excessive elastic deformation from compromising the stability and end-effector positioning accuracy of the flexible robotic arm, NASA's remote-controlled astronaut has a maximum angular velocity of 0.5 deg/s.
2. Feedforward Compensation Method: This method treats the mechanical vibrations caused by the flexible deformation of the robotic arm as deterministic disturbances to the rigid motion and uses feedforward compensation to counteract these disturbances. Bernd Gebler in Germany studied feedforward control of industrial robots with elastic rods and joints. Zhang Tiemin studied a method based on adding zeros to eliminate the dominant poles and instability of the system, and designed a feedforward controller with time delay. Compared with PID controllers, this method can more significantly eliminate residual vibrations in the system. Seering Warren P. et al. have conducted in-depth research on feedforward compensation technology.
3. Acceleration Feedback Control: Khorrami FarShad and Jain Sandeep studied the end-effector trajectory control problem of a flexible robotic arm using end-effector acceleration feedback control.
4. Passive Damping Control: To reduce the influence of relative elastic deformation of the flexible body, various energy-dissipating or energy-storing materials are selected to design the arm structure to control vibration. Alternatively, damping dampers, damping materials, composite damping metal plates, damping alloys, or additional damping structures formed by viscoelastic high-damping materials are all considered passive damping control. In recent years, the use of viscoelastic high-damping materials for vibration control of flexible robotic arms has attracted great attention. Rossi Mauro and Wang David studied the passive control problem of flexible robots.
5. Force Feedback Control Method: The force feedback control of the vibration of the flexible robotic arm is actually a control method based on inverse dynamics analysis. That is, according to inverse dynamics analysis, the torque applied to the driving end is obtained through the given motion of the arm end, and the driving torque is compensated by feedback through motion or force detection.
6. Adaptive Control: A combined adaptive control approach is employed, dividing the system into a joint subsystem and a flexible subsystem. Adaptive control rules are designed using parameter linearization to identify the uncertainties in the flexible robotic arm's parameters. A tracking controller is designed for the flexible robotic arm exhibiting nonlinearity and parameter uncertainty. The controller design is based on robust and adaptive control design using the Lyapunov method. The system is divided into two subsystems through state transitions. Adaptive control and robust control are used to control the two subsystems respectively.
7. PID Control: As the most popular and widely used controller, the PID controller is commonly used in the control of rigid robotic arms due to its simplicity, effectiveness and practicality. It is often used to improve the performance of the PID controller by adjusting the controller gain to form a self-tuning PID controller or by combining it with other control methods to form a composite control system.
8. Variable Structure Control: A variable structure control system is a discontinuous feedback control system, with sliding mode control being the most common type. Its characteristics include: a sliding mode on the switching surface, where the system remains insensitive to parameter changes and disturbances; its trajectory lies on the switching surface, and the sliding phenomenon does not depend on system parameters, exhibiting stable properties. The design of a variable structure controller does not require a precise dynamic model of the robotic arm; the boundary parameters of the model are sufficient to construct a controller.
9. Fuzzy and Neural Network Control: This is a language-based controller that reflects the thought processes of humans during control activities. One of its main characteristics is that the control system design does not require a mathematical model of the controlled object in the conventional sense, but rather the experience, knowledge, and operational data of the operator or expert.
