Abstract: With the continuous expansion of industrial robot applications and the rapid development of modern industries, people expect higher-quality robots, thus placing increasingly higher demands on robot operating speed and precision. Robot control technology is the core to achieving these functions, and its control problems are highly complex. Trajectory tracking control is an important aspect of industrial robot control. This paper systematically introduces the research status and major progress of various algorithms for industrial robot trajectory tracking control, such as PID control, adaptive control, and variable structure control, and provides an outlook on future research directions.
1 Introduction
Industrial robots are a member of the robot family. They are robotic arms or multi-degree-of-freedom robots with multiple joints that are geared towards industrial production. Generally speaking, the main components of an industrial robot are: the robot's mechanical body, the controller used to control the robot's work, the servo drive system used to drive the robot, and the sensing device used to detect changes in various parameters of the robot. It is an automated product that mimics human operation. It can perform automatic control and can also complete various tasks in three-dimensional space through programming. After robots became a new type of production tool for humans, they showed great advantages in improving production efficiency, reducing labor intensity, transforming production forms, and liberating humans from dangerous and harsh working environments [1].
Industrial robots are time-varying, strongly coupled, and nonlinear multi-input/output dynamic systems, making precise control of them an extremely complex problem. The rapid development of modern industry necessitates high-quality robots, and robot control technology is the core of a robot's functionality and a key factor influencing its performance. Control technology significantly constrains the development of robot technology. Therefore, this paper details robot control technologies, elucidates their characteristics, and provides an outlook on future control technologies.
2. Robot Control Technology
The development of robot control theory has roughly gone through three stages: traditional control, modern control, and intelligent control. Traditional control theory mainly includes PID control, feedforward control, and computational torque method; modern control theory mainly includes robust control and variable structure control; intelligent control mainly includes fuzzy control, neural network control, genetic algorithm control, immune algorithm control, adaptive control, iterative learning control, and so on.
2.1 PID Control
PID control is the first control method developed because its algorithm is simple, easy to implement, robust and reliable, and thus widely used [2]. However, there are two main drawbacks when using this method : ① It is difficult to handle the uncertainty in the system model , and it is difficult to make the robotic arm have good dynamic and static qualities. ② The maximum torque that the robotic arm can withstand is limited. When the initial output torque of the controller is too large , there will be limitations to increasing its control coefficient to further improve the system performance.
With the development of computer technology and intelligent control theory, advanced intelligent PID control strategies have been proposed one after another, providing a new approach for the control of complex dynamic uncertain robot systems [3]. Kuc et al. [4] proposed an adaptive PID control method , which consists of an adaptive PID in the feedback loop and an input learning strategy in the feedforward part. In the initial stage, the feedback controller stabilizes the transient response of the robot arm dynamics , and then the feedforward controller calculates the desired driving force to compensate for the nonlinear dynamics of the system . It is compared with the traditional adaptive PID control method . The experimental results show that when all error signals are bounded , this learning control system can better achieve trajectory tracking. Wang Huifang et al. [5] designed a robust adaptive PID control algorithm for the trajectory tracking control problem of uncertain robot systems . This strategy is based on PID control, and based on the sliding mode control idea, it designs an adaptive law that modifies the PID parameters in real time according to the error, and uses a supervisory controller designed based on the Lyapunov function to compensate for the difference between the adaptive PID controller and the ideal controller, so that the system has the set H∞ tracking performance.
Although the PID control method is simple and flexible , due to its inherent drawbacks and the various uncertainties of the robotic arm , many scholars are now combining it with adaptive concepts to address system uncertainties, overcome the shortcomings of PID control , and thus obtain good dynamic and static performance.
2.2 Variable Structure Control
In the field of modern control theory, the main control algorithms are represented by robust control algorithms and sliding mode variable structure control algorithms. These algorithms have introduced the ideas of modern control theory into the field of robot control and have made great progress after many years of development.
Variable structure control is a special type of nonlinear control that can purposefully change the current state of the system during dynamic processes, so that the system can move according to the state trajectory of the pre-set "sliding mode". Therefore, variable structure control is also called sliding mode variable structure control. This control strategy does not require very precise mathematical models for the nonlinearity of the system, the time-varying law of parameters and external disturbances. It only needs to know their range of change to accurately track the trajectory of the system. Therefore, variable structure control has the characteristics of fast response, insensitivity to parameter changes and external disturbances, no need to identify system parameters online, and simple physical implementation [6]. Because the robot system itself is a nonlinear system and there are many unpredictable disturbances, robot control has become one of the main application areas of variable structure control theory in recent years [7]. Reference [8] first used the sliding mode control method to design a variable structure controller for a two-degree-of-freedom robot arm. The experimental results proved that this method can track the time-varying desired trajectory.
This method has its own drawbacks, because when the state trajectory reaches the sliding surface , strictly speaking, it is difficult to slide along the sliding surface toward the equilibrium point , but instead it will traverse back and forth on the upper and lower sides of the sliding surface , which will cause chattering and affect the system control. In the design process of sliding mode, the literature [8] introduced the idea of "boundary layer" and "quasi-sliding mode", and used the saturation function to replace the switching function. Inside the boundary layer, it is a continuous state feedback control, and outside the boundary layer, normal sliding mode control is used, which effectively reduces the chattering. In recent years, many scholars have proposed to combine sliding mode control with fuzzy control, neural network control and other methods to eliminate the chattering problem of robotic arm control input. Magdy [9] combined adaptive fuzzy control with sliding mode control , and fuzzy control provides an effective way to solve the chattering caused by high frequency signals generated by uncertain factors.
In addition , some new sliding mode control methods have been proposed, such as filter-based sliding mode control and disturbance estimation-based sliding mode control. Sliding mode control strategies have been widely applied to the trajectory tracking of robotic arms. Researchers have not only utilized various intelligent algorithms to eliminate chattering problems in sliding mode control , but have also explored new sliding surfaces and control methods , achieving better trajectory tracking performance.
2.3 Adaptive Control
Adaptive control is to compare the performance index of the actual system with the performance index specified by the system, and use the data obtained to correct the controller parameters or control law so that the system can maintain the optimal or suboptimal working state. When the dynamic model parameters of the controlled object change, the adaptive control law can achieve certain performance indicators through timely identification, learning and adjustment, and does not require prior information about unknown parameters. Therefore, it has been widely used in the field of robotics. Reference [10] obtained a control method that can guarantee the global asymptotic stability of the system by utilizing the parameterization characteristics of nonlinear terms in the robot dynamic model. Reference [11] adopted the linear approximation method and designed the controller by combining the linearization of robot dynamics with model reference adaptive control. Reference [12] designed a model-based robust adaptive control method. This control method does not require the system parameters to change slowly, nor does it require knowing what kind of unknown parameters they are. As long as the robot model structure is known, it is convenient for the implementation of the controller.
However, adaptive control has strict requirements for real-time performance and its implementation is relatively complex. Parameter mutations often disrupt the stability of the control system. The convergence characteristics of parameters generally require sufficient continuous excitation, but this condition is difficult to meet in practice. Therefore, adaptive control is usually combined with other algorithms, such as robust adaptive control, sliding mode adaptive control, and fuzzy adaptive control.
2.4 Other control methods
In recent years, artificial intelligence technology has made great progress and has been applied to the field of robotics. Intelligent control no longer relies on mathematical models in the system design process, gets rid of the constraints of nonlinearity, and provides a new means to solve the trajectory control problem of uncertain robots, which has great theoretical value and application prospects. In the trajectory tracking control problem, fuzzy control [13 , 14] and neural network control [15] are mainly used. Fuzzy control uses the control experience of experts to make up for the unfavorable factors such as nonlinearity and uncertainty in the dynamic characteristics of robots. It does not rely on the mathematical model of the object and has strong robustness. Fuzzy control itself also has some shortcomings, such as poor ability to synthesize quantitative knowledge. Once the control rules and membership functions are determined, they cannot be modified, thus limiting its adaptive ability. Moreover, the establishment of fuzzy rules is a very tricky problem, and the control effect is usually not ideal. The online learning function of neural network control method makes it have good robustness in the face of various disturbances and model errors, and it is increasingly valued in the application of nonlinear system control. However, because this control strategy requires online or offline learning, it occupies a lot of system resources and will seriously reduce the real-time performance of motion control. In some literature [16 , 17], these two control methods are often combined for the control of nonlinear systems. The guiding idea is to use the learning ability of neural networks to achieve the purpose of adjusting fuzzy control. This not only gives fuzzy control a certain degree of adaptive ability, but also gives neural networks reasoning and inductive ability.
3. Discussion and Outlook
Based on the robot control technologies summarized above, it can be seen that in the development and application of various algorithms, and considering the characteristics of the robotic arm itself, there are still some issues worth discussing . This paper believes that the following aspects deserve further research:
(1) Current robot control technologies are highly dependent on the kinematic model, dynamic model , and dynamic model of the robot and the object being manipulated. When using model-based control methods, the parameters in the system are generally required to be accurate . However, in the application of multi-robot systems in unstructured environments, it is usually impossible to obtain all the information of the object being manipulated. Even so, the selected control strategy is required to complete the given control task. Therefore , it is of great practical significance to study adaptive control strategies with a fixed model structure but time-varying parameters , or control methods that can estimate the parameters of the object being manipulated online. For example, adaptive control can effectively estimate unknown robot dynamic parameters, and variable structure control is an effective robust control method that is insensitive to bounded disturbances and parameter changes. Combining the advantages of adaptive control and variable structure control, adaptive control is used to identify the uncertain parameters of the system online, and non-parametric uncertainties and estimation errors are eliminated by using variable structure terms. As the identified parameters converge, their robustness gain decreases. Under the premise of maintaining the same stability, this algorithm improves the robustness of the smooth control law to the unknown dynamic characteristics of the system.
(2) The design of the controller should be less dependent on the parameter information of the measuring joint . Generally, control methods require simultaneous measurement of position and velocity signals . The velocity signal is usually obtained by differentiating the position signal or by a velocity measuring instrument . The former method is prone to mixing position measurement error and noise , while the latter method greatly increases the cost of the controller. Using filters to generate pseudo-tracking error signals to avoid measuring velocity , or designing velocity observers to estimate velocity, are current research trends . However, after adding filters or observers, it is still necessary to ensure the stability of the closed-loop system.
(3) Stability analysis of nonlinear systems has always lacked a fixed method , especially for complex robot systems, where it is often difficult to construct the Lyapunov function of the system to prove the stability of the control method. Therefore, research on robot stability problems not only has practical application value , but also has important research significance for the development of stability analysis theory for nonlinear systems.
(4) Most current research focuses on continuous-time systems , while relatively little research is done on discrete-time systems. In discrete robotic arm systems , continuous excitation is sometimes required to stabilize the system , but how to obtain such continuous excitation remains a problem that needs to be solved.
(5) At present, many control methods are based on computer simulation experiments . There are relatively few experiments on real robotic arm systems , and most of them are limited to planar robots such as SCARA and Puma-560 . Extending the tracking target of the controller design to three or even six degrees of freedom in space has certain practical significance.
4. Conclusion
The problem of robot trajectory tracking control has attracted increasing attention. As the above introduction and analysis show , theoretical research on robot trajectory tracking control will trend towards combining various control methods, comprehensively utilizing the characteristics of various algorithms to effectively achieve robot tracking control, thus better serving humanity. In conclusion, with the development of control theory, signal processing, and many other disciplines, research on robotic arm trajectory tracking control will continue to advance.
