1. Mobile Robot Motion Control Technology
Mobile robot systems are complex dynamic systems characterized by high nonlinearity and strong coupling. Due to inaccurate measurement and modeling, coupled with load variations and external disturbances, it is difficult to obtain an accurate system model. Therefore, the feedback control law of an accurate model has limitations in practical applications of mobile robots. Commonly used control methods include adaptive control, sliding mode control, robust control, predictive control, optimal control, and intelligent control.
Tracked mobile robots are a type of mobile robot platform with typical nonholonomic constraints, and are affected by more uncertainties compared to wheeled mobile robot platforms. Many factors, such as the mechanical errors of its locomotive, its own mass and moment of inertia, the road surface material and attitude, and the slippage of the tracks on the road surface, all influence the robot's dynamic characteristics. These factors all contribute to the difficulty of controlling the mobile robot.
This driving method necessitates modeling the relative slippage between the tracks and the ground when establishing the robot's kinematic and dynamic models. During robot localization, information such as wheel speed and measurements from other sensors, including angular velocity and acceleration, must be combined using multi-sensor data fusion methods. Motion control requires analyzing the impact of wheel slippage on the robot's dynamic model. Wheeled sliding steering robots can achieve high-speed, precise steering through acrobatic motion control. The four-wheel drive mode of wheeled sliding steering robots allows for acrobatic maneuvers via motion control, enabling the completion of trajectories that are difficult to achieve using conventional techniques.
The DEEC tracked underground search and rescue robot operates in a harsh environment located underground in a coal mine. This environment is highly complex and unpredictable, with the surface material and underground road conditions being highly variable and complex.
2. Active Disturbance Rejection Control Technology
The development of active disturbance rejection controllers began with an important conclusion from a paper discussing how to unify the handling of structural and computational problems of linear systems: the integrator cascade structure of a system is not only the standard structure of a linear system under linear feedback transformation, but also the standard structure of a class of nonlinear systems under nonlinear feedback transformation.
Since the 1970s, Researcher Han Jingqing of the Institute of Systems Science, Chinese Academy of Sciences, through in-depth research on linear system theory, discovered that the integral cascade structure of a system is not only the standard structure of a linear system under linear feedback transformation, but also the standard structure of a class of nonlinear systems under nonlinear feedback transformation. Similarly, for a class of free nonlinear systems, their observers can be designed so that their standard form under nonlinear observation transformation is integral cascade.
In the late 1980s, researcher Han Jingqing further explored the relationship between linear and nonlinear systems. He pointed out that the concepts of linearity and nonlinearity in people's minds mostly come from classical mechanics systems without control input. In classical mechanics systems, people are concerned with describing and interpreting the topological structure of trajectory distribution. For closed systems without input or output, linear and nonlinear systems have completely different topological structures, and the two cannot be arbitrarily transformed. However, control systems have a new structure that classical mechanics systems do not have—control input and feedback, making them open systems. The feedback effect in control systems can destroy most of the original system's topological structure and establish entirely new topological structures. Under state feedback, the invariant properties in the control system are almost reduced to a few integrators and the information channels connecting them; other properties can be set almost arbitrarily. Therefore, the feedback effect in control systems breaks the boundary between linearity and nonlinearity in the sense of classical dynamical systems. Feedback can transform linearity into nonlinearity, and it can also transform many nonlinearities into linearity. From the perspective of feedback control, control systems should no longer be divided into linear and nonlinear systems in the classical sense. For controllable linear systems, some nonlinear characteristics can be set using state feedback. Based on this, researcher Han Jingqing raised a more fundamental question in control theory: should the development of control theory follow the path of model theory or cybernetics? He pointed out that the modern control theory era is the "model theory" era in the history of control theory development. Whether it is a linear or nonlinear system, whether it is the state-space method or the frequency domain method, the mathematical model of the system has become the starting point for analysis and design or the destination for modeling and identification. However, the method of establishing control laws based on models has encountered great challenges in control engineering, with robustness being the most prominent issue. The basic idea of classical regulation theory is not to rely entirely on the mathematical model of the system, but to implement control based on the magnitude and direction of the error between the desired trajectory and the actual trajectory. It is a method of controlling the system by suppressing or eliminating errors based on process errors. He also pointed out that seeking and utilizing certain nonlinear elements with typical characteristics is an important issue, which is the source of the idea for active disturbance rejection controllers.
In the early 1990s, researcher Han Jingqing dedicated himself to the development of special nonlinear functional units, successfully developing a nonlinear tracking differentiator. He believed that regardless of whether the object is linear, the design philosophy of control systems should shift from linear configuration concepts such as pole placement to nonlinear configurations, because appropriate nonlinear configurations can significantly improve system quality. Based on this, for objects with known models, he presented a method for establishing a nonlinear state observer from the perspective of feedback effects, and used this state observer and nonlinear configuration method to implement state feedback control of nonlinear systems. Numerical simulations show that this nonlinear state observer has strong tracking capability, and the nonlinear configuration of the control system significantly improves the closed-loop quality. This idea can also be extended to systems with unknown object models or systems with known structures and unknown parameters.
Through analysis of the structure and principle of traditional PID controllers, researcher Han Jingqing discovered some existing problems. Based on this, researcher Han proposed a novel nonlinear PID control algorithm by using a tracking differentiator to arrange the transient process, employing appropriate nonlinear combinations and feedback laws, and verifying that this new algorithm has good robustness and adaptability. In the mid-1990s, a class of extended state observers (ESOs) for uncertain objects was obtained by modifying the tracking differentiator in the form of an observer. ESOs can not only obtain the state of uncertain objects but also the real-time actions of internal and external disturbances in the object model. If these real-time actions are compensated into the controller, the integral action in the nonlinear PID can be eliminated. Furthermore, when the controller is used for the control of higher-order objects, a new control law—the nonlinear state error feedback law (NLSEF)—is generated. By analyzing modern control theory and the advantages and disadvantages of PID, and combining modern control theory's understanding of control systems with modern signal processing technology, and drawing on the essence of classic PID, a new type of practical controller—Auto Disturbance Rejection Controller (ADRC)—is formed.
Active disturbance rejection controllers (ADRCs) have undergone more than 30 years of development. Due to their simple algorithms and wide parameter adaptability, they are an effective method for solving control problems involving nonlinearity, uncertainty, strong disturbances, strong coupling, and large time delays. They possess strong adaptability, robustness, and operability, attracting an increasing number of researchers to join the research ranks of ADRC algorithms. Currently, ADRCs have been applied in numerous fields, including motor control, superheated steam temperature control, dynamically tuned gyroscopes, single-stage rotating inverted pendulums, robot control, attitude control of large radio telescope cabins, aircraft attitude control, and ship roll stabilization fins, achieving excellent control results.
Researching the application of active disturbance rejection controllers in ship heading control systems can not only expand the application field of active disturbance rejection controllers, but also effectively improve the control quality of ships, which is of great research significance.
Design of 3DEEC Robot Lateral Motion Active Disturbance Rejection Controller
3.1 General Form of Active Disturbance Rejection Controller for Second-Order Systems
Many controlled objects can be simplified into the following form:
Where w is the external disturbance of the object, u is the control input, b(t) is the control input amplification factor, y is the output, and f(x, w, t) is the object's "total disturbance". For this first-order object, the standard structure of its ADRC controller is generally shown in Figure 1.
Figure 1 Standard structure of ADRC controller
As shown in Figure 1, ADRC consists of three parts: "arrangement of transient process", "nonlinear feedback (NF)" and "extended state observer (ESO)". In the figure, v0 is the control target, v1 is the tracking signal of v0; z1 is the estimate of the system output y, z2 is the estimate of the total disturbance f(x,w,t) of the object; e is the error, u0 is the output of NF, and b0 is the estimate of b(t).
Arrange the transition process:
In a typical control system, the error is directly taken as:
e = v - y
In the formula, v is the set value; y is the system output.
This method of determining the error results in a large initial error, which easily leads to overshoot and is unreasonable. Based on the tolerance of the object, we first arrange a reasonable transient process v1(t), and then take the error as e = v1(t) - y. This is an effective way to resolve the contradiction between the "speed" and "overshoot" of PID, and also a way to improve the "robustness" of the regulator.
In practical engineering problems, there is often a need to extract continuous and differential signals from discontinuous or noisy measurement signals. In the past, linear differentiators and linear filters were used, but these methods still could not satisfactorily solve the problem. The tracking differentiator uses nonlinear functions to achieve a smooth approximation of the generalized derivative of the input signal.
The tracking differentiator is a signal processing component. The active disturbance rejection controller (ADRC) primarily utilizes its tracking characteristics and ability to extract differential signals to manage the transient response of the input signal and extract the differential signal. Specifically, when the input signal undergoes abrupt changes, the tracking differentiator can provide the controller with a smooth output signal as input, ensuring continuous change in the control output and preventing overshoot due to sudden input changes, thus enhancing system stability. The tracking differentiator provides an achievable dynamic performance index for the closed-loop system; this index is no longer a steady-state expected value for the controlled object, but rather a curve that can be tracked in real time. Furthermore, the tracking differentiator can also perform filtering when external disturbances exist in the input signal.
Extended State Observer
The extended state observer, proposed by Han Jingqing in 1995, is a novel state observer that can track the state variables of the system at each order, estimate the total effect of the unmodeled dynamics and external disturbances of the system, and compensate for the unmodeled dynamics and external disturbances of the system. It uses nonlinear elements to realize the dynamic feedback linearization of nonlinear systems and is the core of the active disturbance rejection controller.
For the system equations
As can be seen, Equation (3-19) has the same form, that is, the feedforward compensation of the extended state transforms the nonlinear uncertain system into the standard form of the linear system: the integral cascade type.
As can be seen, the extended state observer treats the nonlinear dynamics, model uncertainties, and external disturbances contained in the controlled system as extended states and observes and estimates them in real time. It uses a feedforward link to compensate for the extended state observations, thereby realizing the feedback linearization of the nonlinear system.
For second-order systems
Nonlinear error feedback
First, let's introduce the nonlinear function fal. In practical control engineering, the adage "large error, small gain; small error, large gain" is commonly used. And what about nonlinear functions...?
Figure 3. Schematic diagram of the nonlinear function fal
Figure 4. Structure diagram of the active disturbance rejection controller
Thus, the three components of an Active Disturbance Rejection Controller (ADRC) are derived: a Tracking Differentiator (TD), an Extended State Observer (ESO), and a Nonlinear State Error Feedback (NLSEF). The Tracking Differentiator (TD) orchestrates the transient response, enabling fast, overshoot-free tracking of the system input signal and providing a good differential signal. The Extended State Observer (ESO) estimates the system state, model, and external disturbances, and is the core of the ADRC. By transforming the nonlinear, uncertain object with unknown external disturbances into a cascaded integrator, the Extended State Observer allows for the design of an ideal controller based on the state error feedback. By employing a suitable nonlinear configuration for the state error feedback, a nonlinear state error feedback control law is realized. The automatic estimation and compensation of disturbances is the most crucial aspect, hence the name "Active Disturbance Rejection Controller."
ADRC Discrete Algorithm
Discretizing the above theory yields the following discretization formulas for each component of ADRC:
Arrange the transition process
3.2 Design of DEEC Robot Lateral Motion Controller
DEEC Robot Kinematics Equations
The DEEC robot uses three high-power Maxthon brushed DC motors: one to drive the tracked arm and two to drive the left and right tracked wheels. The robot's maximum moving speed is 1 m/s, and its maximum turning speed is 60°/s. It can achieve zero-radius turning as well as turning within a specified radius. Since this section primarily analyzes the lateral motion of the robot body, the influence of the tracked arm is not considered; the model only considers the left and right tracked wheels. To enhance the robot's intelligence, we model it. For lateral control, we develop corresponding control algorithms based on this model.
The motion curve of the robot model is shown in Figure 5. In Figure 5, XOY is the Earth-fixed reference coordinate system, which is a right-handed coordinate system; coordinate O is the starting point of the robot's motion; the robot moves from point O to point M (the movement of the robot's geometric center) after time t. From this, the following relationship can be derived:
Conclusion
ADRC technology plays an important role in the design of the motion controller for the DEEC robot. Based on this, this paper elaborates on the design of the DEEC robot's lateral controller and tunes the operating parameters to achieve good control results.
