A mechanical arm preset performance trajectory tracking control method with a singular configuration

Abstract

The application discloses a mechanical arm preset performance trajectory tracking control method and system with a singular configuration and a storage medium, and belongs to the technical field of robot control. The method comprises the following steps: establishing a first-order state space dynamics model of a mechanical arm; based on preset transient and steady-state performance indexes, time-varying funnel functions are respectively designed for position and speed tracking errors to construct normalized errors; and a double-edge barrier function with infinite boundary characteristics is used to directly design a virtual control signal and a final control torque. The application endogenously solves the problem that traditional methods fail due to input-output mapping degradation, control gain tending to zero or changing sign of the mechanical arm under the singular configuration from the structure level of the control law. The method does not need an accurate dynamics model and does not need to avoid singular regions, and can realize high-precision, strong-robust and safe trajectory tracking in the whole working space, effectively guaranteeing the transient and steady-state performance of the system.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and in particular relates to a method for tracking and controlling the preset performance trajectory of a robotic arm with a unique configuration. Background Technology

[0002] With the development of intelligent manufacturing and human-machine collaboration technologies, multi-degree-of-freedom robotic arms are widely used in complex scenarios such as assembly, operation, and contact work. In these applications, robotic arms typically need to move continuously within a large workspace. However, due to the inherent structural constraints of the robotic arm and the objective existence of task requirements, it inevitably enters or approaches singular configurations during operation, such as fully extended joints, collinear wrist axes, or degenerate input-output mapping. Near singular configurations, the input-output relationship of the robotic arm undergoes a fundamental change, manifesting as the equivalent control gain approaching zero, sign uncertainty, or a decrease in mapping rank, thus posing a fundamental challenge to the feasibility and stability of the control method.

[0003] For the problem of trajectory tracking and motion control of robotic arms, existing technologies mainly include control methods based on dynamic models and some weak model or model-free control methods. Model-based methods typically rely on Euler-Lagrange or Newton-Euler dynamic equations, compensating for system nonlinear terms through methods such as computational torque control, adaptive control, or robust control. While these methods can theoretically achieve good control performance, their control laws often implicitly assume that the dynamic mapping remains non-singular throughout the operation. Once the robotic arm approaches or enters a singular configuration, the inverse dynamics or the inverse of the equivalent gain involved in the control law becomes meaningless, easily leading to a sharp amplification of the control input or even system instability. Therefore, these methods usually rely on manually limiting the workspace or avoiding singular regions, making them difficult to adapt to complex real-world working conditions.

[0004] To reduce reliance on precise dynamic models, methods such as pre-defined performance control and funnel control have been proposed in recent years. These methods impose explicit constraints on system errors by constructing time-varying performance boundaries or barrier functions. However, existing pre-defined performance control and funnel control methods typically implicitly assume during the design process that the system's input-output link is continuous and non-degenerate, and that the control gain sign is known and does not change. When a multi-degree-of-freedom robotic arm enters a singular configuration, this assumption is broken. The control gain may approach zero or undergo sign crossover, causing the virtual control signal constructed based on backstepping or recursive structures to be unable to continuously map to the actual control input. This results in problems such as the inability to construct the control law or structural failure, which may lead to control failure or instability of the closed-loop system.

[0005] Against this backdrop, existing technologies typically avoid singular configurations by means of trajectory replanning, singularity avoidance, or artificially limiting the workspace of the robotic arm. However, such methods are essentially external modifications to the control problem, failing to address the degradation of the input-output mapping under singular configurations at the control law structure level, and significantly limiting the workspace and task flexibility of the robotic arm, making it difficult to meet the needs of complex application scenarios.

[0006] In summary, current technologies lack a control method that can address the control gain degradation, zero-crossing, and input-output link failure issues in singular configurations of robotic arms without relying on precise dynamic models or singularity avoidance, based on the control law structure. Therefore, a novel control strategy is urgently needed that can intrinsically address singular configurations and construct effective control inputs even under conditions of zero-crossing control coefficients or mapping degradation, in order to achieve stable and reliable operation of the robotic arm throughout its entire workspace. Summary of the Invention

[0007] This invention aims to solve the problem of control failure of robotic arms under singular configurations, and provides a preset performance trajectory tracking control method with inherent anti-singularity capability to ensure that the robotic arm can achieve high-precision, robust and safe trajectory tracking in the entire workspace.

[0008] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows: In some embodiments of this application, a method for tracking and controlling a pre-defined performance trajectory of a robotic arm with a unique configuration is provided, comprising the following steps: Step 1: Based on the Newton-Euler equations, establish the dynamic model of the multi-degree-of-freedom robotic arm and rewrite it in a nonlinear form; Step 2: Collect information through the robotic arm's sensors and construct a time-varying funnel constraint boundary based on preset performance indicators; Step 3: Combining By constructing a potential energy wall using the limit definition and the two-sided barrier function, a singular intermediate virtual control signal is derived. Step 4: Based on the anti-singularity mechanism of the position loop and velocity loop, derive the system input control torque of the direct mapping; Step 5: Verify the global stability of the closed-loop system based on Lyapunov stability theory, and normalize the error to ensure the forward completeness of the system.

[0009] In some embodiments of this application, the dynamic equation in step 1 is described by a second-order nonlinear differential equation: ,in, The joint angle position vector, Let be the i-th component of the output vector, representing the angle of the i-th joint. and These are the joint angular velocity and angular acceleration vectors, respectively. The inertial matrix is ​​symmetric and positive definite. Represents the Coriolis force and centrifugal force terms; This is the term related to gravity. This represents the frictional torque of the joint; This is the control input torque for the system.

[0010] In some embodiments of this application, in step 2, the maximum permissible initial error, minimum convergence rate, and maximum steady-state error are set according to the requirements of the robotic arm's task.

[0011] In some embodiments of this application, a first-order continuously differentiable positive real-number funnel function is constructed based on the error setting required by the robotic arm's task. The positive real funnel function satisfies the reciprocal of the initial time. This corresponds to the maximum allowable initial error range, and the rate of increase of the function over time corresponds to the convergence rate of the error; finally, the asymptotic value of the function. Corresponding to the preset steady-state error accuracy, a preset performance funnel set is defined based on the positive real number funnel function. in, This constitutes an error The time-varying constraint boundary.

[0012] In some embodiments of this application, step 3 includes: Based on the funnel function defined in step 2 and position tracking error Construct normalized position error According to the preset performance requirements, the system must always meet the following conditions during operation. Introducing based on Limit-defined bilateral barrier function That is, it exists For any constant Both have constants. Make ; It can be expressed in limit form as: ; Design virtual control signals The desired joint velocity command is designed directly as a negative feedback form of a bilateral obstacle function: .

[0013] In some embodiments of this application, the robotic arm is a multi-degree-of-freedom serial robotic arm, comprising at least one rotary joint or translational joint.

[0014] In some embodiments of this application, the control method can still generate continuous and bounded control torques under singular configurations without the need for singularity avoidance or trajectory replanning.

[0015] In some embodiments of this application, a robotic arm control system is characterized by comprising: The sensor module is used to collect the position and speed signals of the robotic arm joints; The control module is used to execute the control method as described in any one of the above statements; The drive module is used to drive the robotic arm to move according to the torque commands output by the control module.

[0016] In some embodiments of this application, a computer-readable storage medium is provided having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the method described in any of the preceding claims.

[0017] In some embodiments of this application, an electronic device is disclosed, including a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the program to implement the method as described in any of the preceding claims.

[0018] Compared with existing technologies, the advantages of this invention are that it not only enables the robotic arm to maintain continuous and bounded control torque when traversing unusual configurations, achieving high-precision trajectory tracking throughout the entire workspace, but also employs a model-free preset performance funnel design, which has strong robustness to unmodeled dynamics, load changes, and external disturbances. At the same time, this method applies strong constraints to the tracking error through time-varying funnel boundaries, mathematically guaranteeing the transient overshoot and steady-state accuracy of the system. This effectively avoids motion overshoot and collision risks in safety-sensitive scenarios such as human-machine collaboration, significantly improving the reliability and engineering practical value of the system. Attached Figure Description

[0019] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A schematic diagram of the time-varying evolution trajectory of the output position tracking error e1 of the first joint of the robotic arm provided in an embodiment of the present invention; Figure 2 A schematic diagram of the state tracking error (i.e., virtual velocity error) e2 provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the time response curve of the actual control torque u provided in an embodiment of the present invention; Figure 4A flowchart illustrating the technical solution provided in the embodiments of the present invention; Figure 5 The flowchart is provided for an embodiment of the present invention. Detailed Implementation

[0020] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0021] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0022] See appendix Figure 1-5 As shown, according to some embodiments of this application, Step 1: Based on the Newton-Euler equations, establish the dynamic model of the multi-degree-of-freedom robotic arm and rewrite it in a nonlinear form; According to the Euler-Lagrange equations, its dynamic equations can be described by second-order nonlinear differential equations: ,in, The joint angle position vector, Let be the i-th component of the output vector, representing the angle of the i-th joint. and These are the joint angular velocity and angular acceleration vectors, respectively. The inertial matrix is ​​symmetric and positive definite. Represents the Coriolis force and centrifugal force terms; This is the term related to gravity. This represents the frictional torque of the joint; This is the control input torque for the system.

[0023] To facilitate the application of the preset performance funnel control strategy, the above second-order dynamic equations need to be converted into a first-order state-space form. Define the system state position variables. and velocity variables The system can then be rewritten in the following form: ; in In this model, the nonlinear function Includes the inverse of the inertia matrix and control input torque The coupling terms.

[0024] Step 2: Collect information through the robotic arm's sensors and construct a time-varying funnel constraint boundary based on preset performance indicators; Sensors mounted at the joints of the robotic arm collect joint position signals in real time. and joint velocity signals The initial state variables of the robotic arm obtained from the multi-source sensors are: Based on the actual joint position collected by sensors With the preset expected trajectory Define position tracking error .

[0025] Based on the requirements of the robotic arm's operation tasks, set the maximum permissible initial error. Minimum convergence rate and maximum steady-state error. Based on these indices, a first-order continuously differentiable positive real funnel function is constructed. The function must satisfy the reciprocal of the initial time. This corresponds to the maximum allowable initial error range, and the rate of increase of the function over time corresponds to the convergence rate of the error; finally, the asymptotic value of the function. This corresponds to the preset steady-state error accuracy. Based on this funnel function, a preset performance funnel set is defined. in, This constitutes an error The time-varying constraint boundary. Similarly, for the joint velocity state of the robotic arm, the velocity error is set according to the requirements of the velocity tracking task. Based on the performance metrics, construct the corresponding velocity funnel function. This forms a set of preset performance funnels representing the velocity state.

[0026] Step 3: Combining By constructing a potential energy wall using the limit definition and the two-sided barrier function, a singular intermediate virtual control signal is derived. Based on the funnel function defined in step 2 and position tracking error Construct normalized position error According to the preset performance requirements, the system must always meet the following conditions during operation. Introducing based on Limit-defined bilateral barrier function That is, it exists For any constant Both have constants. Make ; It can be expressed in limit form as: ; Design virtual control signals The desired joint velocity command is designed directly as a negative feedback form of a bilateral obstacle function: .

[0027] Step 4: Based on the anti-singularity mechanism of the position loop and velocity loop, derive the system input control torque of the direct mapping; Unlike traditional backstepping methods that require repeated differentiation of the virtual control law, this application directly utilizes the algebraic form of the bilateral barrier function for mapping, without relying on the model-defined control law, and directly designs the final control torque input. A bilateral barrier function is used. Constructing the control law: ,in It can also be expressed in the limit form: To represent this, stability analysis of the control system is conducted as follows: To prove that the control method proposed in this application can guarantee the global stability of the closed-loop system and that the error does not exceed the limit, a proof by contradiction combined with Lyapunov stability theory is used for analysis.

[0028] Establish the hypothesis of contradiction: To demonstrate the control system described in this application in the full time domain To determine the stability of the closed-loop system, we first use proof by contradiction. Assume the state solution of the closed-loop system... The maximum interval of existence is And assume .

[0029] Introducing the continuation theorem for differential equations: According to the continuation theorem of solutions in the theory of ordinary differential equations: for equations defined on an open set... For a system of differential equations on a given surface, if its maximum existence interval is... It is finite, so as time goes on... Approaching The solution of the system It must exhibit that the modulus of the solution tends to infinity and the solution approaches an open set. The boundary, that is, if Then the solution They will inevitably escape from the opening set. Any compact subset within.

[0030] Constructing Lyapunov functions: Regarding the first One control loop Construct the energy function: ; right Differentiate, we have Substitute the position error dynamic and virtual control laws ,get: ; Consider the nonlinear terms in the robotic arm's dynamics equations, friction, and external disturbances. Due to the funnel function... Both the reference trajectory and the uncertainty term are bounded, and the aforementioned uncertainty term has an upper bound within a finite time period, denoted as . The derivative can be scaled to: As can be seen from the bilateral barrier function defined in step 3, for arbitrarily large upper bound perturbations... Both have constants. , making when When the error approaches the funnel boundary, the bilateral barrier function The generated control potential energy is sufficient to overcome the disturbance. That is, it satisfies: Substitution inequalities yield: .

[0031] For the second control loop (speed loop), Differentiate and substitute into the dynamic equation and actual control law have: ; Here It includes unknown nonlinear dynamics and singular input-output link characteristics. Based on the anti-singularity mechanism proposed in this paper, although... There may be unknowns, but by utilizing... Limit-defined bilateral barrier function It exhibits infinite growth characteristics at the boundaries. Even if the system has singularities or control coefficients that cross zero, as long as... Approaching Control input It will increase rapidly, generating a sufficiently large dominant force. Similar to the derivation of position loops, there exists... , making when hour: .

[0032] Demonstrate the boundedness of the system state within the assumed interval: In summary, the energy decreases as the error approaches the boundary, which means that the normalization error... Never able to touch the boundary Therefore, throughout the entire interval There exists a constant above. Make: Based on the above derivation, the system state vector In the interval The interior remains in a compact state. In, that is: System state vector There was never an escape.

[0033] Derive the contradiction and establish the conclusion: On the one hand, based on the proof by contradiction assumption and the continuation theorem, the solution... Must Approaching Escape from the tight cluster On the other hand, based on the control law design and Lyapunov analysis of the robotic arm system, the solution... It was confirmed that the cluster remained in a state of tight concentration. Inside, there is no escape. This contradiction shows that the initial statement about " The assumption that "the solution is a finite value" is incorrect. Therefore, the maximum interval of existence of the solution to the closed-loop system must not be finite, i.e. This proves that the control system is... The above is forward complete, achieving a globally stable and singular control objective.

[0034] Example 1 In this embodiment, the experiment uses the first joint of a seven-DOF Franka Panda collaborative robot for verification, while the angles of other joints remain unchanged using traditional impedance control. The corresponding nonlinear system model of the robot's first joint can be expressed as follows: ; To verify the advantages of the control strategy proposed in this application, no specific restrictions are imposed on the system's nonlinear model. The experiment was conducted on an Ubuntu 20.04 operating system based on the ROS real-time control architecture, with the control frequency set to 1kHz. The desired tracking trajectory was set. This is a time-varying combination of sine and cosine signals used to simulate complex dynamic tracking tasks, where... The regulations specify that the maximum permissible overshoot for the transient performance of the robotic arm system, namely the joint position overshoot, is 3 rad, and the maximum permissible overshoot for the speed is 5 rad; and the position tracking error of the robotic arm must be no slower than... The speed decays, and the virtual speed tracking error must be no slower than... The velocity decay rate; the steady-state performance, i.e., the final position control accuracy, is 0.03 rad, and the final virtual velocity control accuracy is 0.3 rad. At the initial moment of the experiment, the robotic arm is in a stationary state, and there is a large, artificially set deviation between the initial position and the desired trajectory to verify the controller's convergence ability to large initial errors.

[0035] To tolerate large initial errors and ensure steady-state accuracy, the controller's detailed design parameters utilize a funnel function of the following form, with the position error set accordingly. funnel function for: ; Velocity loop funnel function design: To ensure rapid convergence of intermediate virtual control quantities, a funnel function with faster convergence speed is selected, and a velocity error is set. funnel function for: ; A singularity-resistant controller is designed by utilizing the algebraic mapping properties of a two-sided barrier function. A singularity-free intermediate virtual control signal is designed using a logarithmic two-sided barrier function, and a virtual control law is constructed from this non-singular intermediate virtual control signal. : ; Calculate the velocity loop error and normalization error The system input for direct mapping is designed using a fractional bilateral barrier function: ; The control law That is, the final torque command issued to the robot. .

[0036] Simulation results are as follows Figures 1 to 3 As shown. First, Figure 1 The tracking error of the first joint output of the robotic arm is displayed intuitively. The time-varying evolution trajectory is shown in the figure. As can be seen from the figure, the initial position of the system is not zero, but rather a very significant positional deviation. However, under the action of the funnel controller, the error converges rapidly, reflecting the system's fast convergence characteristics. (Tracking error) Always strictly limited to the preset performance funnel boundary The time-varying safety envelope formed by this.

[0037] Secondly Figure 2 This further reveals the stability of the system's internal dynamics. State tracking error (i.e., virtual velocity error) They are also constrained within the corresponding funnel. Within the specified range, it exhibits rapid convergence characteristics. This verifies that the recursive design strategy based on the backstepping method can guarantee the global uniformity and boundedness of all signals in the closed-loop system, and the system does not exhibit local divergence due to internal coupling.

[0038] at last, Figure 3 Demonstrates actual control torque The time response curve is shown. Simulation results address the unknown nonlinear coupling terms, potential singular configuration motion poses, and singular input-output links present in the robotic arm. The results demonstrate that the control input signal remains continuous and smooth, with its amplitude maintained at [value missing]. to Within a reasonable engineering range, no surge or singular divergence in control quantity, which is common in traditional control methods when dealing with the problem of control coefficients crossing zero, was observed.

[0039] The technical effects achieved by the above technical solution in the embodiments of this application are as follows: This application no longer treats the singular configuration of the robotic arm as an abnormal operating condition that needs to be avoided, but rather as an operating state that the control system must inherently cope with. Starting from the control law structure level, to address the problems of input-output mapping degradation, control gain approaching zero, or sign change under singular configurations, a control strategy that maintains definability under singular conditions is designed. This avoids the structural failure caused by irreversible mapping in the vicinity of singular configurations in traditional control methods. Moreover, unlike the complex differentiation and parameter identification of traditional backstepping methods, this application constructs a series of static bilateral barrier functions as virtual control laws, utilizing their infinite characteristics at the boundaries to forcibly constrain the system state, achieving low-complexity model-free control. Among these, existing technologies usually deal with unknown but non-zero gains, while the method of this application theoretically and practically supports the control coefficients crossing zero (changing sign) during operation, filling the technical gap of existing preset performance control. This application achieves independent transient performance constraints on the position, velocity, and other state variables of the robotic arm by designing independent funnel functions for each state variable, ensuring high-precision trajectory tracking. Furthermore, experimental results on the Franka robotic arm demonstrate that even under complex conditions such as friction from actual hardware, sensor noise, and unmodeled dynamics, the control strategy of this application still ensures extremely high tracking accuracy. Data shows that when the robotic arm performs complex trajectory tracking tasks, the final position tracking error converges to 0.03, and the virtual velocity tracking error is stably controlled within 0.3.

[0040] This application utilizes The "potential energy wall" mechanism, constructed using limit definitions and bilateral obstacle functions, eliminates the need for manual planning to avoid dynamic singularities or regions where control coefficients cross zero. The controller automatically generates the driving torque required to traverse singularities, ensuring system controllability and smoothness throughout the entire workspace and solving the problem of traditional control methods failing at singularities.

[0041] This solution employs a model-free design, eliminating the need for complex parameter identification experiments to obtain the precise inertia matrix or friction coefficient of the Franka robotic arm. Relying on a pre-defined performance funnel feedback mechanism, the system exhibits exceptional robustness to load variations and external disturbances. As long as the initial error remains within the funnel range, the controller can force the system state to evolve within a pre-defined error envelope, significantly reducing the barrier to algorithm deployment and debugging costs.

[0042] By employing a pre-set performance funnel control technology, this application mathematically guarantees the transient performance (such as maximum overshoot) and steady-state error boundaries of the robotic arm. In scenarios with high safety requirements, such as human-robot collaboration or precision assembly, this means that regardless of the disturbance, the robotic arm's motion deviation will never exceed the pre-set safety range, i.e., the funnel boundary. This effectively avoids the risk of collision and improves the operational safety of the system.

[0043] In the description of this application, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0044] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0045] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0046] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0047] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for tracking and controlling the preset performance trajectory of a robotic arm with a unique configuration, characterized in that, Includes the following steps: Step 1: Based on the Newton-Euler equations, establish the dynamic model of the multi-degree-of-freedom robotic arm and rewrite it in a nonlinear form; Step 2: Collect information through the robotic arm's sensors and construct a time-varying funnel constraint boundary based on preset performance indicators; In step 2, the maximum permissible initial error, minimum convergence rate, and maximum steady-state error are set according to the requirements of the robotic arm's operation task. Based on the error setting required by the robotic arm's task, a first-order continuously differentiable positive real funnel function is constructed. The positive real funnel function satisfies the reciprocal of the initial time. This corresponds to the maximum allowable initial error range, and the rate of increase of the function over time corresponds to the convergence rate of the error; finally, the asymptotic value of the function. Corresponding to the preset steady-state error accuracy, a preset performance funnel set is defined based on the positive real number funnel function. in, This constitutes an error Time-varying constraint boundary; Step 3: Combining By constructing a potential energy wall using the limit definition and the two-sided barrier function, a singular intermediate virtual control signal is derived. Among them, the funnel function defined in step 2 and position tracking error Construct normalized position error According to the preset performance requirements, the system must always meet the following conditions during operation. Introducing based on Limit-defined bilateral barrier function That is, it exists For any constant Both have constants. , making ； It can be expressed in limit form as: ； Design virtual control signals The desired joint velocity command is designed directly as a negative feedback form of a bilateral obstacle function: ; Step 4: Based on the anti-singularity mechanism of the position loop and velocity loop, derive the system input control torque of the direct mapping; Step 5: Verify the global stability of the closed-loop system based on Lyapunov stability theory.

2. The method for tracking and controlling the preset performance trajectory of a robotic arm with a unique configuration according to claim 1, characterized in that, The dynamic equations in step 1 are described by second-order nonlinear differential equations: ,in, The joint angle position vector, Let be the i-th component of the output vector, representing the angle of the i-th joint. and These are the joint angular velocity and angular acceleration vectors, respectively. The inertial matrix is ​​symmetric and positive definite. Represents the Coriolis force and centrifugal force terms; This is the term related to gravity. This represents the frictional torque of the joint; This is the control input torque for the system.

3. The method according to claim 1, characterized in that, The robotic arm is a multi-degree-of-freedom serial robotic arm, which includes at least one rotary joint or translational joint.

4. The method according to claim 1, characterized in that, The control method can still generate continuous and bounded control torques under singular configurations without the need for singularity avoidance or trajectory replanning.

5. A robotic arm control system, characterized in that, include: The sensor module is used to collect the position and speed signals of the robotic arm joints; A control module is configured to execute the control method as described in any one of claims 1 to 4; The drive module is used to drive the robotic arm to move according to the torque commands output by the control module.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 4.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 4.

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