Control method, system and controller of three-degree-of-freedom robot arm, and storage medium

Abstract

The application discloses a control method and system of a three-degree-of-freedom mechanical arm, a controller and a storage medium, and relates to the technical field of industrial robot control. The method comprises the following steps: collecting actual values of positions of joints of the three-degree-of-freedom mechanical arm, and obtaining speed estimation values and disturbance estimation values according to the actual values of the positions and current control signals by using a nonlinear state observer; taking the deviation of the actual values of the positions from an expected trajectory as a starting point, constructing Lyapunov functions and designing control laws based on the speed estimation values and the disturbance estimation values by using a backstepping method; and controlling the three-degree-of-freedom mechanical arm according to a target control signal output by a final control law. Time-dependent gain functions determined by a predetermined convergence time are introduced in the nonlinear state observer, the construction of the Lyapunov functions and the design of the control laws, and each control law is used to make the first-order time derivative of a corresponding Lyapunov function negative. Therefore, fast and accurate trajectory tracking can be realized within the predetermined convergence time, and overshoot can be strictly avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial robot control, and particularly relates to a control method and system of a three-degree-of-freedom mechanical arm, a controller and a storage medium. BACKGROUND

[0002] In industrial assembly applications, a three-degree-of-freedom mechanical arm needs to achieve high-precision and high-stability motion control. However, the traditional PID (Proportional-Integral-Derivative) control or conventional servo control method often has obvious overshoot and oscillation problems. The overshoot of the end position of the mechanical arm not only reduces the positioning accuracy, but also may cause safety risks such as collision, workpiece damage or assembly failure. Especially when the target position is close to the physical boundary or safety constraint, a single overshoot may cause a serious accident.

[0003] Research shows that using a non-overshoot control strategy can effectively avoid the trajectory from overshooting the target position, thereby improving the safety and operation reliability of the system. At the same time, in order to meet the requirements of high-speed assembly operations on response speed, modern motion control technology tends to pursue finite time convergence, that is, to converge the tracking error to zero within a predetermined time. Fixed-time or preset-time convergence control not only provides faster dynamic response, but also has stronger robustness, which can effectively suppress model uncertainty and external disturbances.

[0004] Therefore, how to ensure fast convergence while achieving non-overshoot or average non-overshoot motion has become a key problem to be solved in the field of industrial robot control. SUMMARY

[0005] The present application aims to provide a control method and system of a three-degree-of-freedom mechanical arm, a controller and a storage medium, to achieve fast and high-precision trajectory tracking within a predetermined convergence time, strictly avoid overshoot, and have strong robustness to uncertainty and external disturbances, thereby improving the safety and reliability of the mechanical arm in precision assembly tasks.

[0006] In a first aspect, embodiments of the present application provide a control method for a three-degree-of-freedom robot arm, comprising the following steps: collecting actual values of positions of joints of the three-degree-of-freedom robot arm, and obtaining estimated values of velocities and estimated values of disturbances of the joints by using a nonlinear state observer according to the actual values of the positions and a current control signal of the three-degree-of-freedom robot arm; taking deviations of the actual values of the positions of the joints from a desired trajectory as first-level tracking errors, and using a backstepping method to start from the first-level tracking errors, to construct Lyapunov functions and design control laws based on the estimated values of the velocities and the estimated values of the disturbances step by step; and controlling the three-degree-of-freedom robot arm according to a target control signal output by a final-level control law to track the desired trajectory; wherein a time-dependent gain function is introduced in the nonlinear state observer, the construction of the Lyapunov functions at each level, and the design of the control laws at each level, the time-dependent gain function is determined by a predetermined convergence time, and the design purpose of the control laws at each level is to make a first-order time derivative of a corresponding Lyapunov function negative definite, and the time-dependent gain function is determined by , , .

[0007] In some embodiments, the nonlinear state observer adopts a sliding mode observer or an extended state observer.

[0008] In some embodiments, the nonlinear state observer is represented by the following formula:

[0009] ;

[0010] wherein, respectively represent estimated values of positions, velocities and disturbances of the joints, respectively represent derivatives of , represents a gain of the nonlinear state observer, represents an approximate matrix of , represents the time-dependent gain function, , represents an inertia matrix, represents the current control signal.

[0011] In some embodiments, the final-level control law is represented by the following formula:

[0012] ;

[0013] wherein, represents a target control signal output by the final-level control law, is a constant; , ; , , ; , represents a first level control law; , is a constant, represents a derivative of a desired trajectory ; represents an adaptive gain, represents a positive constant, f represents the lumped disturbance value, represents , represents a first derivative of , a th derivative of .

[0014] In some embodiments, the method further comprises: at the end of each control period, updating a time variable t = t + Ts, where Ts represents a sampling period; when , determining an output of the target control signal as , where, represents a proportional feedback gain matrix, represents the desired trajectory, represents the position actual value, represents a preset threshold value.

[0015] In a second aspect, embodiments of the present application provide a control system of a three-degree-of-freedom robot arm, comprising: a signal acquisition module configured to acquire position actual values of joints of the three-degree-of-freedom robot arm; a state observer configured to obtain velocity estimation values and disturbance estimation values of the joints according to the position actual values and a current control signal of the three-degree-of-freedom robot arm by using a nonlinear state observer; a backstepping control module configured to take deviations of the position actual values of the joints from a desired trajectory as first level tracking errors, and to construct Lyapunov functions and design control laws based on the velocity estimation values and the disturbance estimation values by using a backstepping method with the first level tracking errors as a starting point; and an execution module configured to control the three-degree-of-freedom robot arm according to a target control signal output by a final level control law to track the desired trajectory; wherein a time-dependent gain function is introduced in the nonlinear state observer, construction of the Lyapunov functions at each level, and design of the control laws at each level, the time-dependent gain function is determined by a predetermined convergence time, and a design purpose of the control laws at each level is to make a first order time derivative of a corresponding Lyapunov function negative definite, and the time-dependent gain function is represented as , represents the predetermined convergence time, .

[0016] In a third aspect, an embodiment of the present application provides a controller, comprising a memory, a processor, and a computer program stored in the memory, and when the computer program is executed by the processor, the control method of the three-degree-of-freedom robot arm in the first aspect is implemented.

[0017] In some embodiments, the controller is a digital signal processor or a microcontroller.

[0018] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, having a computer program stored thereon, and when the computer program is executed by a processor, the control method of the three-degree-of-freedom robot arm in the first aspect is implemented.

[0019] The control method, system, controller, and storage medium of the three-degree-of-freedom robot arm in the embodiments of the present application, when controlling the three-degree-of-freedom robot arm, first collect actual values of positions of joints of the three-degree-of-freedom robot arm, and use a nonlinear state observer to obtain estimated values of speeds and disturbances of the joints according to the actual values of the positions and a current control signal of the three-degree-of-freedom robot arm; then take deviations of the actual values of the positions of the joints from a desired trajectory as a first-level tracking error, and use a backstepping method to start from the first-level tracking error, and construct Lyapunov functions and design control laws based on the estimated values of the speeds and the disturbances; then control the three-degree-of-freedom robot arm according to a target control signal output by a final-level control law to track the desired trajectory; wherein a time-dependent gain function is introduced in the nonlinear state observer, the construction of the Lyapunov functions, and the design of the control laws, the time-dependent gain function is determined by a predetermined convergence time, and the design purpose of each control law is to make a first-order time derivative of a corresponding Lyapunov function negative definite. Thus, fast and high-precision trajectory tracking can be achieved within the predetermined convergence time, overshoot is strictly avoided, and strong robustness is achieved against model uncertainties and external disturbances, thereby improving the safety and reliability of the robot arm in precision assembly tasks. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a flowchart of the control method of the three-degree-of-freedom robot arm in an embodiment of the present application;

[0021] Figure 2 is a structural schematic diagram of a three-degree-of-freedom robot arm in an embodiment of the present application;

[0022] Figure 3 is a structural schematic diagram of the control method of the three-degree-of-freedom robot arm in an embodiment of the present application;

[0023] Figure 4 is a flowchart of the backstepping control in an embodiment of the present application;

[0024] Figure 5is a result schematic diagram of three degrees of freedom mechanical arm control using the method of the present application according to an example of the present application;

[0025] Figure 6 is a result schematic diagram of three degrees of freedom mechanical arm control using the traditional PID method according to an example of the present application. DETAILED DESCRIPTION

[0026] In view of the technical problems that the existing PID or servo control has significant overshoot and oscillation in high-speed assembly, resulting in decreased precision and safety risks, the present application proposes a control method for a three degrees of freedom mechanical arm. The method is based on finite time non-overshoot control, including: estimating the state (including the speed of each joint of the three degrees of freedom mechanical arm and unmeasured dynamic disturbance) by using a nonlinear state observer; introducing a time-dependent gain function, such as , wherein is a predetermined convergence time; and realizing non-overshoot based on a backstepping method to design a multi-stage control law.

[0027] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference signs represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0028] The control method, system and controller for a three degrees of freedom mechanical arm of the embodiments of the present application are described below with reference to the accompanying drawings.

[0029] Figure 1 is a flowchart of the control method for a three degrees of freedom mechanical arm according to an embodiment of the present application.

[0030] As shown in Figure 1 , the control method for a three degrees of freedom mechanical arm includes the following steps:

[0031] S11, collecting the actual position values of each joint of the three degrees of freedom mechanical arm, and using a nonlinear state observer to obtain the speed estimation value and the disturbance estimation value of each joint according to the actual position values and the current control signal of the three degrees of freedom mechanical arm.

[0032] As shown in Figure 2 , the typical physical structure components of the 3-DOF (Degrees-of-Freedom) mechanical arm to which the present application is applied include:

[0033] Joint 1 (base): a rotary joint, moving around axis, used to control the horizontal orientation of the mechanical arm;

[0034] Joint 2 (large arm): a rotary joint, used to control the pitch movement of the large arm;

[0035] Joint 3 (Lower Arm): A revolute joint for controlling the pitch motion of the lower arm;

[0036] End Effector: Mounted at the end of the lower arm for performing specific tasks such as grasping, assembling, etc.

[0037] The parameters involved include: link parameters such as (vertical offset from the base to joint 2), (link length from joint 2 to joint 3), and (link length from joint 3 to the end effector). The X-Y-Z coordinate system is usually set at the base joint 1.

[0038] Optionally, the three-degree-of-freedom robot arm can include but is not limited to: a high-speed assembly robot arm (requiring fast positioning without overshoot), a medical rehabilitation robot arm (requiring safe and smooth motion), and a precision welding robot arm (requiring trajectory tracking without oscillation).

[0039] In an embodiment of the present application, a time-dependent gain function is introduced in the nonlinear state observer, which is determined by a predetermined convergence time.

[0040] Exemplarily, the nonlinear state observer adopts a sliding mode observer or an extended state observer. Thus, the velocity estimate and the disturbance estimate of each joint can be estimated within a finite time, realizing the compensation estimation of the unobservable state.

[0041] Taking the extended state observer as an example, the nonlinear state observer is expressed by the following formula:

[0042] (1)

[0043] wherein, respectively represent the position estimate, the velocity estimate and the disturbance estimate of each joint (including the above-mentioned joint 1, joint 2 and joint 3), 、 、 respectively represent the derivative of , represents the gain of the nonlinear state observer, represents the approximate matrix of , represents a time-dependent gain function, , represents the actual value of the position of each joint; , represents the inertia matrix, represents the current control signal.

[0044] Specifically, for the case that the part state of the three-degree-of-freedom robot arm cannot be directly measured (such as the speed of each joint, dynamic disturbance, etc.), a fast-converging nonlinear observer is designed to estimate the unmeasurable state, thereby ensuring the accuracy of the state information required for control feedback. The design process of the nonlinear observer includes:

[0045] First, system modeling

[0046] Let the joint angle (i.e., position) of the three-degree-of-freedom robot arm be The dynamics equation can be expressed as:

[0047] (2)

[0048] where represents the inertia matrix, represents the Coriolis force and centrifugal force term, represents the gravity term, represents the friction term, represents the joint driving torque (i.e., the current control signal).

[0049] Second, design of nonlinear state observer

[0050] For the joint speed of the three-degree-of-freedom robot arm It is usually difficult to directly and accurately measure, and there are uncertain terms (C, G, F, etc.) in the dynamics model, the nonlinear state observer is used to estimate the speed and lumped disturbance. The system dynamics equation can be rewritten as:

[0051] (3)

[0052] Let , , All uncertain terms and unmodeled dynamics are combined into a lumped disturbance defined as:

[0053] (4)

[0054] The system state equation is: where The nonlinear state observer shown in equation (1) is designed for this system.

[0055] The time-dependent gain function can be: is a function of time t, used to obtain the time gain, where T represents the predetermined convergence time, When t = 0, ; when , By properly choosing the gain, the nonlinear observer can quickly track the actual state, realize and , so as to provide accurate speed information and disturbance compensation for the subsequent control law.

[0056] It should be noted that the nonlinear state observer can be realized in a discrete form, and the Euler difference approximation can be used to realize the continuous form: where the observer gain is selected to ensure that the matrix is Hurwitz, that is, all eigenvalues of the matrix have negative real parts. This condition ensures that the observation error dynamics are exponentially stable without time-varying gain; when a suitable time-varying gain is further introduced, the observation error can converge to zero within a user-specified predetermined convergence time, thereby providing accurate and fast state and disturbance estimates for the subsequent control law.

[0057] S12, the deviation of the actual value of the position of each joint from the expected trajectory is taken as the first-level tracking error, and the backstepping method is used to start with the first-level tracking error, and based on the speed estimate and the disturbance estimate, a Lyapunov function is constructed and a control law is designed.

[0058] In the embodiments of the present application, a time-dependent gain function is introduced in the construction of each level of Lyapunov function and the design of each level of control law, and the time-dependent gain function is determined by the predetermined convergence time. The design purpose of each level of control law is to make the first-order time derivative of the corresponding Lyapunov function negative definite. By introducing the time-dependent gain function, when the time approaches the predetermined convergence time , the gain tends to infinity, so that the tracking error converges within the predetermined convergence time . This predetermined convergence time mechanism allows the control response to be specified in advance according to the task requirements, regardless of the size of the initial error (i.e. the first-level tracking error).

[0059] Exemplarily, the last-level control law is represented by the following formula:

[0060] (5)

[0061] wherein, denotes the target control signal output by the last-level control law, is a constant; , ; , , ; denotes the first-level control law; , , is a constant, denotes the expected trajectory The derivative; represents the adaptive gain (which can be "intelligently" varied to keep the entire function bounded to ensure the final system stability), and f represents the lumped disturbance value; This represents a positive constant, which is a preset value. express , express The first derivative, express of Second derivative.

[0062] Specifically, given the desired trajectory Define the actual value of the position. Deviation from the expected trajectory This serves as the first-level tracking error. Based on the predetermined convergence time control concept, a step-by-step backstepping method is used to design the control law. The system order is... And perform the following coordinate transformation:

[0063] (6)

[0064] in, The proportional gain function represents the scaling factor (constant) between virtual controllers (i.e., control laws) used for scaling of hierarchical variables. , This is the estimator for the nonlinear observer. Based on this, the control law is designed step-by-step as follows:

[0065] First-level control law: The derivative of the desired trajectory A time gain-based The feedback term of the error sign function is designed to make the position error... Approaching zero.

[0066] Second-level control law: ;

[0067] in, , , , , The known function is related to the partial derivatives of the control law; It is a constant, which affects the convergence speed and the conservatism of the no-overshoot condition.

[0068] The final control law is obtained, as shown in equation (5) above. Nonlinear observer gain. The matrix should be made For Hurwitz matrices, Thus, the error convergence can be guaranteed, and the real negative and mutually unequal eigenvalues can be selected to suppress oscillation; is given by formula (1) using a nonlinear observer, which can realize the preset time estimation convergence, is a known joint angle, is an estimated state quantity. The nonlinear observer can be realized by Euler difference approximation: . After selecting a suitable , the observation error satisfies .

[0069] For each Lyapunov function (denoted as a composite function) of each level, the Lyapunov function of the nonlinear observer error and the combined Lyapunov function of the virtual quantity can be expressed as: composite function . Wherein E satisfies , is a preset coefficient, and , denotes a unit matrix. By strictly estimating V, a structured inequality of the form can be obtained, which is a positive number used to ensure that the derivative of V is less than 0. When , there is , thereby ensuring and (that is, the error converges in a predetermined time), and giving a boundedness conclusion.

[0070] Based on this, the implementation process of the final control law can be as follows:

[0071] 1) Set the predetermined convergence time T and the sampling period (such as 1 ms), and initialize .

[0072] 2) In each control period: read the actual value of the joint position , calculate (if t is close to T, saturation processing is performed on to avoid numerical divergence).

[0073] 3) Update according to the nonlinear observer equation, calculate and .

[0074] 4) Calculate , and then calculate the final control law (the partial derivative terms containing , etc. can be pre-calculated by an analytical expression or evaluated by a difference approximation).

[0075] As above, based on the state information provided by the observer, the control law is designed step by step using the backstepping method, and the nonlinear coupling of the system is gradually eliminated and the time-dependent feedback term is introduced. In each step of backstepping design, the time-dependent gain function and the observed state are integrated to construct the corresponding Lyapunov function, so as to ensure that each level of error can converge to zero within a predetermined time.

[0076] By introducing the time-dependent gain function, the stable convergence of the closed-loop system within a predetermined convergence time is realized, and the overshoot phenomenon is completely avoided. Compared with the traditional finite time control, the convergence time of the predetermined time control described in the present application only depends on the parameter T, and is independent of the initial error size, thus having good engineering predictability and realizability.

[0077] Even in the presence of modeling errors and external disturbances, the tracking error can still maintain the monotonic convergence property, thereby strictly guaranteeing the no-overshoot performance. Specifically, when designing the control law step by step, the "monotonic convergence" strategy is adopted, and by constraining the sign of the control quantity or introducing boundary conditions, the tracking error is always approaching from the same side of the target: when the error is positive, the control action continuously pushes it to monotonically decrease to zero; the same is true when the error is negative. This design can ensure that the trajectory converges from one side of the target, and even in the presence of random disturbances, the mean value of the system output can still achieve no-overshoot control within a predetermined time.

[0078] S13, controlling the three-degree-of-freedom robot arm according to the target control signal output by the last-stage control law to track the desired trajectory.

[0079] After obtaining the target control signal, the target control signal can be processed by channel limiting (such as driver current, torque limiting, etc.) according to the physical limiting parameters of each joint driver of the three-degree-of-freedom robot arm to obtain a safe control signal. Specifically, if the theoretical torque limit value corresponding to the target control signal is less than the minimum output torque limit value, the minimum output torque limit value is taken as the safe control signal; if the theoretical torque limit value corresponding to the target control signal is greater than the maximum output torque limit value, the maximum output torque limit value is taken as the safe control signal; if the theoretical torque limit value corresponding to the target control signal is greater than or equal to the minimum output torque limit value and less than or equal to the maximum output torque limit value, the target control signal is taken as the safe control signal.

[0080] For example, the target control signal can be sent to the servo driver of the three-degree-of-freedom robot arm through current loop limiting ( ), and the motor torque output by the driver acts on each joint of the robot arm to realize the tracking of the predetermined trajectory. In this way, the instantaneous overload or impact of the actuator can be avoided.

[0081] In some embodiments of the present application, the method further comprises: updating a time variable t = t + Ts at the end of each control cycle, where Ts represents a sampling period; and determining the output of the target control signal as , where represents a proportional feedback gain matrix, represents a desired trajectory, represents a position actual value, represents a preset threshold value, which is close to 0, such as 0.05.

[0082] Specifically, a time update is performed at the end of each control cycle If , a steady-state holding law or a differential back-off strategy can be switched to avoid high-frequency jitter caused by divergence. In actual implementation, the term can be saturated or smoothly truncated when close to T, and the stable control law can be switched to avoid digital overflow or driver mutation when . That is, when is small, t tends to T, all terms with η(t) will become extremely large, and the final control signal will also become extremely large, and is switched to to avoid instability caused by η(t) to the system and improve safety.

[0083] The following describes a control method for a three-degree-of-freedom mechanical arm according to an embodiment of the present application in combination with Figure 3 , Figure 4 , Figure 5 , Figure 6 .

[0084] Figure 3 The overall architecture and signal flow of the closed-loop control system involved in the method of the present application are shown. As shown in the figure, the control cycle starts with the mechanical arm body as the controlled object. The position / speed sensors (such as encoders) installed on each joint of the mechanical arm measure the actual angles (position actual values) of each joint in real time. The measurement signals are transmitted to the nonlinear state observer. Since the speed of each joint is usually difficult to measure directly and accurately or is easily disturbed by noise, the nonlinear observer uses the measurable position signals and the current control input to estimate the state quantities that are difficult to obtain directly, including the speed of each joint and unmodeled dynamic disturbances, online. Figure 3

[0085] ​​​The actual position value, the estimated state of the nonlinear observer output (including the estimated value of the speed, the estimated value of the disturbance, etc.) and the externally given desired trajectory (not directly shown in the figure) are fed into the backstepping controller. The backstepping controller calculates the tracking error e(t) of the system, and according to the tracking error, in combination with the time gain generation module and the non-overshoot strategy, the joint control torque required to achieve the preset time without overshoot is calculated through multi-stage backstepping recursion, that is, the target control signal.

[0086] The target control signal is sent to the actuator to drive the movement of the robot arm. The new position information generated by the movement of the robot arm is captured by the sensor again and fed back to the nonlinear observer, thereby forming a continuously running closed-loop feedback control system to achieve accurate, stable and non-overshoot tracking of the desired trajectory. By considering the influence of model error and external disturbance in the design of the closed-loop control, a compensation or robust term is introduced to improve the fault tolerance of the system, which can ensure that the preset time convergence is achieved under a certain range of model uncertainty.

[0087] Figure 4 The algorithm logic and data processing flow inside the backstepping controller in Figure 3 are shown, including:

[0088] 1) Obtain the actual position value and obtain the estimated value of the system state at the current time estimated by the nonlinear state observer;

[0089] 2) Error calculation: compare the actual position value with the desired trajectory (not directly shown in the figure) , and calculate multi-stage error variables (such as the error of joint 1 ) in combination with the state estimation value;

[0090] 3) Time gain generation: according to the predetermined convergence time and the current time , calculate the "time gain" . The time gain will tend to infinity as approaches ;

[0091] 4) Signal merging: the result of "error calculation" (error signal) is sent to the next step together with the "time gain";

[0092] 5) Cascade control law design: use the error signal with time gain to design the control law step by step, and embed the "non-overshoot" strategy (such as limiting the control sign or constraining the error range) in this step, wherein the control law discretization can be realized by using a first-order forward difference;

[0093] 6) Control output generation: after the last step of backstepping design is completed, the final and actual control output signal (i.e. the target control signal) is generated, which is then sent to the actuator.

[0094] Figure 5 、 Figure 6 The control and result of the control of the three-degree-of-freedom robot arm by the method of the application and the traditional PID method are respectively shown. In the example, T=3s, the initial position angle of each joint is , and the expected trajectory is a continuous time-varying signal (as shown by the dashed line in Figure 5 、 Figure 6 . In Figure 5 、 Figure 6 , q1, q2, q3 respectively represent the actual position angle of joint 1, joint 2, and joint 3, qd1, qd2, qd3 respectively represent the expected position angle of joint 1, joint 2, and joint 3, and e1, e2, e3 respectively represent the difference between the actual position angle and the expected position angle of joint 1, joint 2, and joint 3. As can be seen from Figure 5 、 Figure 6 , compared with the traditional PID method, the tracking speed of the method of the application is faster, the tracking accuracy is higher, and there is no overshoot phenomenon.

[0095] In summary, the three-degree-of-freedom robot arm control method of the embodiment of the application combines nonlinear state observation, time-varying gain design, and backstepping control, effectively solves the contradiction between overshoot and response speed in high-speed and high-precision control of the three-degree-of-freedom robot arm, and strictly realizes non-overshoot, fast, and high-precision trajectory tracking by introducing a “monotonic convergence” strategy, constraining the sign of the virtual control quantity or setting the corresponding boundary condition in the controller design, so that the system tracking error always approaches from one side of the target direction. And it has strong robustness to model uncertainty and external disturbance. Even if the system model has errors or is disturbed by a bounded disturbance, the controller can still guarantee convergence to the target neighborhood within a predetermined time, significantly improving the operation reliability and operation safety of the robot arm in precision assembly operations. Compared with the traditional PID control method, the application simultaneously realizes the control performance of preset time convergence and strict non-overshoot, can quickly and smoothly reach the target position within a specified time, and can better meet the comprehensive requirements of response speed, positioning accuracy, and operation safety in industrial assembly scenes.

[0096] The application further provides a three-degree-of-freedom robot arm control system.

[0097] In the embodiment of the present application, the control system of the three-degree-of-freedom robot arm comprises a signal acquisition module, a state observation module, a backstepping control module and an execution module. The signal acquisition module is configured to acquire actual values of positions of joints of the three-degree-of-freedom robot arm; the state observation module is configured to obtain estimated values of velocities and estimated values of disturbances of the joints according to the actual values of the positions and a current control signal of the three-degree-of-freedom robot arm by using a nonlinear state observer; the backstepping control module is configured to take deviations of the actual values of the positions of the joints from a desired trajectory as a first-level tracking error, and to construct Lyapunov functions and design control laws based on the estimated values of the velocities and the estimated values of the disturbances by using a backstepping method with the first-level tracking error as a starting point; and the execution module is configured to control the three-degree-of-freedom robot arm according to a target control signal output by a final-level control law, so as to track the desired trajectory.

[0098] In the nonlinear state observer, the construction of the Lyapunov functions at different levels and the design of the control laws at different levels, a time-dependent gain function is introduced, the time-dependent gain function is determined by a predetermined convergence time, and the design of the control laws at different levels aims to make a first-order time derivative of a corresponding Lyapunov function negative definite.

[0099] It should be noted that other specific embodiments of the control system of the three-degree-of-freedom robot arm in the embodiment of the present application can refer to the specific embodiments of the control method of the three-degree-of-freedom robot arm in the above-described embodiment.

[0100] The present application also provides a controller, which comprises a memory, a processor and a computer program stored in the memory, and is characterized in that the computer program is executed by the processor to implement the control method of the three-degree-of-freedom robot arm in the above-described embodiment.

[0101] Exemplarily, the controller is a digital signal processor or a microcontroller.

[0102] Specifically, in the digital signal processor or the microcontroller, the backstepping control and the observation algorithm can be implemented by a software algorithm, so as to ensure actual implementability and flexibility of the algorithm.

[0103] The present application also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the control method of the three-degree-of-freedom robot arm in the above-described embodiment.

[0104] Although the embodiments of the present application have been shown and described above, it should be understood that the above-described embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-described embodiments within the scope of the present application.

Claims

1. A control method of a three-degree-of-freedom robot arm, characterized by, The method comprises the following steps: collecting actual values of positions of joints of a three-degree-of-freedom robot arm, and obtaining estimated values of velocities and estimated values of disturbances of the joints according to the actual values of the positions and current control signals of the three-degree-of-freedom robot arm by using a nonlinear state observer; taking deviations of the actual values of the positions of the joints from a desired trajectory as first-level tracking errors, and constructing Lyapunov functions and designing control laws based on the estimated values of the velocities and the estimated values of the disturbances by using a backstepping method starting from the first-level tracking errors; controlling the three-degree-of-freedom robot arm according to target control signals output by a final-level control law to track the desired trajectory; The nonlinear state observer, the construction of each level Lyapunov function and the design of each level control law all introduce a time-dependent gain function, the time-dependent gain function is determined by a predetermined convergence time, the design of each level control law aims to make the first order time derivative of the corresponding Lyapunov function negative definite, and the time-dependent gain function is determined by represents, represents the predetermined convergence time, .

2. The control method of a three-degree-of-freedom robot arm according to claim 1, characterized by, the nonlinear state observer is a sliding mode observer or an extended state observer.

3. The control method of a three-degree-of-freedom robot arm according to claim 1, wherein The nonlinear state observer is represented by the following formula: ； wherein respectively represent a position estimation value, a velocity estimation value, and a disturbance estimation value of each joint, respectively represent a derivative of represents a gain of the nonlinear state observer, represents an approximate matrix of represents the time-dependent gain function, represents an actual value of a position of each joint, , represents an inertia matrix, represents the current control signal.

4. The control method of a three-degree-of-freedom robot arm according to claim 3, wherein The final-level control law is represented by the following formula: ； wherein represents a target control signal of the final control law output, is a constant; , , ; , , ; represents a first control law; , , is a constant, represents a derivative of a desired trajectory ; represents an adaptive gain, represents a positive constant, and f represents a lumped disturbance value, represents , represents a first derivative of represents a second derivative of 5. The control method of a three-degree-of-freedom robot arm according to claim 1, wherein The method further comprises: updating a time variable t = t + Ts at the end of each control period, wherein Ts represents a sampling period; When the output of the target control signal is determined as wherein, represents a proportional feedback gain matrix, represents the desired trajectory, represents the position actual value, represents a preset threshold value.

6. A control system for a three degree of freedom robotic arm, characterized by, comprising: a signal collecting module configured to collect actual values of positions of joints of a three-degree-of-freedom robot arm; a state observing module configured to obtain estimated values of velocities and estimated values of disturbances of the joints according to the actual values of the positions and current control signals of the three-degree-of-freedom robot arm by using a nonlinear state observer; a backstepping control module configured to take deviations of the actual values of the positions of the joints from a desired trajectory as first-level tracking errors, and to construct Lyapunov functions and design control laws based on the estimated values of the velocities and the estimated values of the disturbances by using a backstepping method starting from the first-level tracking errors; an executing module configured to control the three-degree-of-freedom robot arm according to target control signals output by a final-level control law to track the desired trajectory; The nonlinear state observer, the construction of each level Lyapunov function and the design of each level control law all introduce a time-dependent gain function, the time-dependent gain function is determined by a predetermined convergence time, the design of each level control law aims to make the first order time derivative of the corresponding Lyapunov function negative definite, and the time-dependent gain function is determined by represents, represents the predetermined convergence time, .

7. A controller comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program is configured to cause the processor to perform the method of any one of claims 1-6. the computer program is executed by a processor to implement the control method of the three-degree-of-freedom robot arm according to any one of claims 1-5.

8. The controller of claim 7, wherein, The controller is a digital signal processor or a microcontroller.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, the computer program is executed by a processor to implement the control method of the three-degree-of-freedom robot arm according to any one of claims 1-5.

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