Robot inverse kinematics adaptive smooth constraint method and system

Abstract

The invention provides a robot inverse kinematics adaptive smooth constraint method and system, and relates to the technical field of robot motion control. The method aims at solving the problem that high-speed motion smoothness and low-speed positioning responsiveness cannot be considered at the same time through fixed parameter constraints. The method is executed in an iterative control loop and comprises the steps that the current state and the target state of the robot are obtained, and the pose error is calculated; calculating a theoretical joint update amount based on the pose error; according to real-time motion state parameters such as the die length of the pose error and / or the die length of the current joint angular velocity, a self-adaptive gain factor is dynamically calculated, and the value of the gain factor and the value of the parameter are in a monotone decreasing relation; a preset and continuously differentiable nonlinear saturation function is adopted, and the adaptive gain factor is used to constrain the theoretical joint update quantity to generate a final joint update quantity; and updating the state of the robot by using the final joint updating amount.

Description

Technical Field

[0001] This application relates to the field of robot motion control technology, and in particular to an adaptive smoothing constraint method for robot inverse kinematics. Background Technology

[0002] In multi-degree-of-freedom robot systems, inverse kinematics is a core component of motion control. Its goal is to calculate the joint variables that each joint should achieve based on the desired pose of the robot's end effector. Damped least squares based on the Jacobian matrix is ​​a commonly used technique for solving such problems. This method effectively mitigates the instability caused by ill-conditioned Jacobian matrices when the robot approaches singular configurations by introducing a damping term during the solution process.

[0003] To apply such methods to continuous trajectory tracking tasks, existing technologies typically place them within a closed-loop control framework. This involves iteratively calculating joint update amounts by real-time feedback of the error between the robot's actual end-effector pose and the target pose, thereby eliminating accumulated errors. However, when the target command changes abruptly, the calculated theoretical joint update amounts can be extremely large, causing severe shaking of the robot joints if executed directly. To address this, existing technologies have proposed strategies to constrain the theoretical joint update amounts. A common strategy is to use a "hard truncation" approach, where the theoretical update amount is directly set to a preset threshold. However, this approach introduces non-differentiable inflection points at the constraint boundary, leading to discontinuous output control commands and causing mechanical shaking of the robot, severely impacting motion smoothness. Another improvement is to use a smoothing saturation function with fixed parameters (such as a hyperbolic tangent function) to smoothly limit the theoretical update amounts. While this method ensures the continuity of control commands, it introduces new inherent drawbacks: to achieve sufficient smoothness during high-speed, wide-range movements, a smaller function gain is needed to flatten the constraint curve; conversely, to achieve rapid response and high positioning accuracy during low-speed, fine-tuning positioning, a larger function gain is required, making the constraint curve steeper near the origin. A fixed gain parameter is essentially a static trade-off between "smoothness" and "responsiveness," and cannot adaptively adjust according to the robot's real-time motion state, thus limiting the robot's overall performance across the entire operating range. Summary of the Invention

[0004] The purpose of this application is to provide an adaptive smoothing constraint method for robot inverse kinematics, which aims to solve the technical problem that the smoothness required for high-speed and large-range motion and the rapid response required for low-speed fine positioning cannot be simultaneously met by the smoothing constraint with fixed parameters in the prior art. This allows the robot to intelligently adjust the constraint characteristics according to the real-time motion state while ensuring the continuous smoothness of control commands.

[0005] To achieve the above objectives, this application provides a robot inverse kinematics adaptive smoothing constraint method, executed in an iterative control loop. The method includes: acquiring the robot's current state and target state, and calculating the pose error; calculating the theoretical joint update amount based on the pose error; dynamically calculating an adaptive gain factor according to at least one real-time motion state parameter of the robot, wherein the value of the adaptive gain factor is monotonically decreasing with the value of the at least one real-time motion state parameter; multiplying the theoretical joint update amount by the adaptive gain factor using a preset, continuously differentiable nonlinear saturation function, and using the product as the input of the nonlinear saturation function to generate the final joint update amount; and using the final joint update amount to update the robot's joint state to drive the robot's motion.

[0006] Furthermore, the calculation of the theoretical joint update includes: calculation using the damped least squares method.

[0007] Furthermore, the at least one real-time motion state parameter includes: the modulus of the pose error and / or the modulus of the robot's current joint angular velocity.

[0008] In a preferred embodiment of this application, the continuously differentiable nonlinear saturation function is a hyperbolic tangent function.

[0009] In a preferred embodiment of this application, the continuously differentiable nonlinear saturation function is an arctangent function.

[0010] Furthermore, the calculation of the adaptive gain factor includes multiplying a reference gain by at least one exponentially decaying modulation function, wherein the exponentially decaying modulation function is calculated based on the magnitude of the pose error and / or the magnitude of the joint angular velocity.

[0011] Furthermore, the calculation of the adaptive gain factor includes dividing a reference gain by a rational function, which is calculated based on the magnitude of the pose error and / or the magnitude of the joint angular velocity.

[0012] Furthermore, the method further includes: dynamically adjusting a damping factor used in the damped least squares method based on the evaluation results of the robot singularity.

[0013] Furthermore, the evaluation results of robot singularity include operability measures.

[0014] This application also provides a robot system including a robot body and a robot controller, characterized in that the robot controller is configured to perform the method described in any embodiment.

[0015] Compared with existing technologies, the technical solution provided in this application has the following beneficial effects: By introducing a continuously differentiable saturation function dynamically adjusted by an adaptive gain factor, the inherent contradiction between smoothness and responsiveness in existing technologies is resolved, achieving adaptive motion quality. This ensures smooth, shock-free motion at high speeds and rapid response and high precision in fine positioning. This method enables the robot to intelligently adjust its control strategy according to its own motion state and task objectives, adapting to changing working conditions without manual parameter retuning, thus enhancing the system's intelligence, robustness, and versatility. Simultaneously, the inherited closed-loop feedback mechanism effectively compensates for various errors, ensuring high accuracy in trajectory tracking. Furthermore, smooth and adaptive control commands avoid impacting the hardware, helping to extend the service life of the robot's core components. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating an adaptive smoothing constraint method for robot inverse kinematics provided in this application embodiment;

[0018] Figure 2 A schematic diagram of the architecture of a robot control system provided in an embodiment of this application;

[0019] Figure 3 This is a schematic diagram illustrating the relationship between the adaptive gain factor and the system state in an embodiment of this application;

[0020] Figure 4 This is a comparative schematic diagram showing the saturation function morphology under different gains in the embodiments of this application.

[0021] Explanation of reference numerals in the attached figures:

[0022] 10-The robot body;

[0023] 20-Joint sensor;

[0024] 30 - Controller;

[0025] 31-Inverse Kinematics Optimization Module;

[0026] 40 - Target pose input terminal;

[0027] S101 - Status Acquisition and Error Calculation Steps;

[0028] S102 - Steps for solving theoretical joint update quantities;

[0029] S103 - Adaptive gain factor calculation steps;

[0030] S104 - Smoothing saturation constraint application step;

[0031] S105 - Joint Status Update and Closed-Loop Feedback Steps. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining this application and are not intended to limit this application.

[0033] Example 1

[0034] This embodiment provides a basic implementation scheme for an adaptive smooth constraint method for robot inverse kinematics. This scheme aims to solve the trade-off between smoothness and responsiveness in robot motion control in existing technologies, and to achieve performance optimization across the entire operating range by dynamically adjusting the characteristics of the constraint function.

[0035] Please see Figure 2 This document illustrates a robot control system architecture according to an embodiment of this application. The system may include a robot body 10, such as a multi-degree-of-freedom industrial robot or collaborative robot with multiple rotary joints. Each joint of the robot body 10 is equipped with a joint sensor 20 to measure the physical state of each joint in real time, such as joint angles and joint angular velocities. The core of the system is a controller 30, which may be implemented by hardware devices such as an industrial computer, embedded system, or digital signal processor. The controller 30 receives instructions from a target pose input terminal 40, which may be a teach pendant, offline programming software, a teleoperating master hand, or an advanced task planner. The controller 30 internally runs an inverse kinematics optimization module 31, which is configured to execute the adaptive smooth constraint method described in this embodiment. During the system's workflow, the target pose input terminal 40 sends the desired robot end effector pose to the controller 30; simultaneously, the joint sensors 20 continuously feed back the real-time joint states detected from the robot body 10 to the inverse kinematics optimization module 31 within the controller 30. Based on these inputs, the inverse kinematics optimization module 31 calculates optimized smooth joint commands and sends them to the joint actuators of the robot body 10, thereby driving the robot to move and forming a complete high-precision closed-loop control system.

[0036] Please refer to the following: Figure 1This is a detailed flowchart of the method provided in this embodiment. The method is executed in a high-frequency iterative control loop; for example, the control frequency can be set to 200 Hz, i.e., each control cycle is 5 milliseconds. In the k-th control cycle, the inverse kinematics optimization module 31 within the controller 30 performs the following steps:

[0037] In step S101, state acquisition and error calculation are performed. Specifically, the controller 30 obtains the current joint angle vectors of all joints of the robot by communicating with the joint sensor 20. and the current joint angular velocity vector Subsequently, the inverse kinematics optimization module 31 calls a pre-established robot forward kinematics model, which is a function that maps joint space variables to Cartesian space pose. This is achieved by mapping the current joint angle vector... As input, i.e., execution The calculation yields the actual pose of the robot's end effector at the current moment. Wherein, the pose Typically, it is a six-dimensional vector containing three position components (such as coordinates along the X, Y, and Z axes) and three attitude components (such as Euler angles or quaternion representations around the X, Y, and Z axes). Simultaneously, the controller 30 obtains the target end-effector pose for the current cycle from the target pose input terminal 40. Then, the current actual pose is calculated. With the target end pose pose error vector between The calculation method is as follows Accordingly, this error vector This is also a six-dimensional vector, whose components represent deviations in position and attitude, respectively. To quantify the overall error, the Euclidean magnitude of this error vector also needs to be calculated, denoted as . The length of the module It intuitively reflects the distance between the robot's end effector and the target.

[0038] Subsequently, in step S102, the theoretical joint update amount is solved. This step aims to calculate a theoretical joint angle increment to drive the robot end effector toward eliminating pose errors. The direction of movement. In one embodiment of this application, damped least squares method is used. First, it is necessary to determine the direction of movement based on the current joint angle. Calculate the Jacobian matrix of the robot. This matrix describes the linear relationship between joint velocity and end effector velocity. Then, based on the Jacobian matrix... and the pose error vector calculated in the previous step The theoretical joint update volume is calculated using the following formula. :

[0039]

[0040] in, It is the transpose of the Jacobian matrix. It is the identity matrix. It is a pre-defined, small positive number called the damping factor. The damping term is introduced. The aim is to address the issue of robots approaching singular configurations (i.e.) When the matrix is ​​close to singular (and its determinant is close to zero), the numerical stability of matrix inversion is guaranteed, thus avoiding the calculated joint update amount from becoming infinite. In this embodiment, It can be set to a fixed experience value.

[0041] Next, in step S103, the adaptive gain factor is calculated. It is understood that this step is one of the core components of this application, and its purpose is to dynamically generate an adaptive gain factor for adjusting the strength of subsequent smoothing constraints based on the robot's real-time motion state. In this embodiment, two parameters are selected for evaluating the robot's real-time motion state: the pose error modulus calculated in the previous step. and the magnitude of the current joint angular velocity vector. . It reflects the progress of the task execution, and This reflects the current intensity of the robot's movement. Adaptive gain factor The calculation rule can be designed as follows: when the robot is in a high-speed, large-range motion state (usually corresponding to a large... and ), The value is reduced to apply a smoother constraint; this is especially important when the robot is in a low-speed, fine-positioning state (which typically corresponds to a smaller value). and ), Increasing the value of will result in a faster response.

[0042] Please see Figure 3 The figure schematically illustrates this monotonically decreasing relationship between the adaptive gain factor and the system state. In this embodiment, this relationship is realized through the following specific mathematical formula: First, two modulation functions based on exponential decay are defined, one for error... Another one is used for speed. :

[0043]

[0044]

[0045] in, and These are two positive constants, referred to as the error attenuation coefficient and the velocity attenuation coefficient, respectively. For example, they can be set to... , As can be seen from the formula, when or As the gain increases, the corresponding modulation function value decays rapidly in an exponential manner and approaches zero; as they decrease, the function value approaches 1. Subsequently, these two modulation functions are compared with a preset reference gain. Multiplying them yields the final adaptive gain factor. :

[0046]

[0047] Among them, the reference gain This represents the expected response gain of the system under ideal static, zero-error conditions, and can be set as follows: In this way, when the robot moves away from the target or at high speed, It will be significantly smaller than When the robot approaches the target and slows down, It will gradually increase and approach .

[0048] In step S104, a smooth saturation constraint is applied. This step utilizes the adaptive gain factor calculated in the previous step. Theoretical joint update quantity Apply a continuous, smooth, and variable-strength constraint to generate the final executable joint update amount. In this embodiment, the hyperbolic tangent function tanh can be selected as a preset, continuously differentiable nonlinear saturation function. This constraint process is performed element-wise (i.e., for each joint) independently. The theoretical joint update vector... The first in Each component The corresponding final joint update component Calculated using the following formula:

[0049]

[0050] in, This is the first The maximum allowable update amount per step for each joint is a constant preset based on the physical limits of the joint and safety considerations.

[0051] Please see Figure 4 This figure visually explains the adaptive gain. How does this affect the constraint effect? ​​The hyperbolic tangent function is an S-shaped saturating function whose output value is constrained to... Between. When its independent variable is multiplied by a gain factor. When, the shape of the function changes. When When the value is relatively small (corresponding to high-speed, large-scale motion scenarios), the tanh function curve becomes very flat near the origin, which means that even with the theoretical update amount... It is very large, and its output is large. It will also be gently and smoothly limited to The proximity of the robot ensures smooth movement and effectively suppresses impacts and vibrations. Conversely, when... When the value is large (corresponding to low-speed fine-precision positioning scenarios), the tanh function curve becomes very steep near the origin, and its shape is close to a slope of The linear function implies that the system has a high amplification capability for small theoretical updates (i.e., small errors), thus ensuring fast response and high-precision convergence. In this way, the method of this embodiment dynamically adjusts the "hardness" of the constraints, thereby effectively balancing the relationship between smoothness and responsiveness.

[0052] Finally, in step S105, joint state updates and closed-loop feedback are performed. In this step, the final update values ​​of all joints calculated in the previous step are combined. Combined into the final joint update vector Then, through integration, the command joint angle for the next control cycle is calculated. This new joint angle vector The command is sent to the underlying servo controller of the robot body 10 for execution. At this point, the k-th control cycle is complete. In the next cycle (k+1-th cycle), the system returns to step S101, using the new actual joint state and target pose (which can be the same or new), and repeats the entire process. Through this iterative closed-loop feedback, the robot is ensured to continuously track the target pose and effectively compensate for errors caused by inaccurate models, external disturbances, and other factors.

[0053] In summary, this embodiment introduces an adaptive gain factor that is negatively correlated with the robot's real-time motion state (pose error and joint velocity), and uses it to dynamically adjust the constraint characteristics of the hyperbolic tangent saturation function. This enables the robot to exhibit good smoothness when rapid movement is required and fast responsiveness when precise positioning is required, thereby improving the robot's overall motion performance under various working conditions.

[0054] Example 2

[0055] As an optional implementation, this embodiment proposes an enhanced technical solution based on embodiment 1. This solution further integrates adaptive damping technology, which aims to synergistically address the stability problem near the robot's singular configuration and the dynamic performance optimization problem across the entire working range.

[0056] The overall system architecture of this embodiment is the same as that of Embodiment 1, and can be referred to as follows. Figure 2 Its methodology and process are also similar to... Figure 1 The process shown is basically the same, also including the state acquisition and error calculation step S101, the adaptive gain factor calculation step S103, the smooth saturation constraint application step S104, and the joint state update and closed-loop feedback step S105, and the specific implementation of these steps is the same as that described in Example 1. The core difference and improvement of this embodiment lies in the theoretical joint update amount solution step S102.

[0057] It should be noted that, in Example 1, the damping factor in the least squares damping formula... It is set to a fixed, small constant. This setting works in most cases, but becomes less effective when the robot is very close to a singular configuration. It may not be sufficient to completely suppress the sudden increase in joint velocity; or, when far from the singularity, the fixation... This will unnecessarily reduce tracking performance.

[0058] To address this issue, this embodiment improves the theoretical joint update calculation step S102. Based on the current joint angle... Calculate the Jacobian matrix Subsequently, a sub-step for real-time evaluation of robot singularity was added. Various methods exist for evaluating singularity; in this embodiment, a computational operability metric can be used. The method. Operability measure is one of the indicators for evaluating a robot's ability to move in a given configuration. A common formula for its calculation is:

[0059]

[0060] in, This represents the determinant of the matrix. As the robot moves away from the singular configuration, It is full rank, and its determinant value is relatively large. It is also relatively large; when the robot approaches a singular configuration, As the rank decreases, its determinant value approaches zero. It also decreases accordingly. Therefore, The value can be used as an effective indicator to determine the distance between the robot and the singular interval.

[0061] Next, based on the assessed operability measures The damping factor used in the damping least squares method is dynamically adjusted. The adjustment rule can be designed as follows: when the robot moves away from the singularity region, reduce the damping to ensure tracking performance; when the robot approaches the singularity region, increase the damping to ensure stability. A specific implementation is as follows: First, preset a singularity threshold. and a maximum damping coefficient Then, in each control cycle, based on the currently calculated... Determine Value: If ,but like ,but ;

[0062] This rule shows that when operability is measured... Greater than or equal to the threshold When the system considers the robot to be in a non-singular safe zone, the damping term is set to zero, and the damped least squares method degenerates into an undamped pseudo-inverse method to obtain a faster tracking response. Starting less than the threshold As the value gradually decreases, it indicates that the robot is approaching a singular configuration. The value will increase smoothly from 0, and... It reaches its maximum value when it approaches 0. In this way, the strength of the damping effect is adaptively correlated with the degree of singularity.

[0063] After calculating the dynamic Then, the same damped least squares formula as in Example 1 is used to calculate the theoretical joint update amount. :

[0064]

[0065] Because of this It is dynamic, so even when approaching singular configurations, the formula can calculate stable, finite theoretical joint update amounts.

[0066] It should be noted that the two adaptive mechanisms in this embodiment work synergistically. The adaptive damping mechanism (step S102) is mainly responsible for handling the theoretical solutions caused by the kinematic structure (singularity). The ill-conditioned problem is addressed by ensuring that the condition remains bounded; the subsequent adaptive smoothing constraint mechanism (steps S103 and S104) handles the issues caused by task instructions (large errors) or dynamic processes (high speed). Excessive size issues, ensuring the final output It meets the dynamic requirements of smoothness and responsiveness. For example, when the robot rapidly passes near a singularity, adaptive damping will intervene first to prevent... The calculation diverges; simultaneously, due to the large speed and error at this point, the adaptive gain... It will become very small, further compared to what may still be large. By applying smooth amplitude limiting, a stable and smooth joint movement command is ultimately generated.

[0067] By combining adaptive damping with adaptive smoothing constraints, this embodiment provides a more comprehensive and robust robot inverse kinematics optimization scheme. While solving the trade-off between smoothness and responsiveness, it also enhances the robot's motion stability near singular configurations, thereby exhibiting stable performance in a wider range of more challenging task scenarios.

[0068] Example 3

[0069] This embodiment provides another optional implementation of the adaptive gain factor calculation step S103, to illustrate that the core idea of ​​this application is not limited to a specific function form, but has scalability.

[0070] The overall process of this embodiment is completely the same as that of Embodiment 1, the only difference being the calculation of the adaptive gain factor in step S103. The specific formula is as follows. In Example 1, the method of multiplying the reference gain by an exponential decay function was used. In this example, a rational function is used to construct the modulation effect of error and speed.

[0071] Specifically, in the adaptive gain factor calculation step S103, the pose error magnitude is also obtained. and joint angular velocity modulus Set a reference gain. And two normal numbers used to adjust the weights of error and speed influence, respectively. and Adaptive gain Calculated using the following formula:

[0072]

[0073] As can be seen from this formula, it also satisfies the core design principle that "the larger the error / speed, the smaller the gain." When the pose error... or joint angular velocity When it increases, the denominator in Item or The term will increase linearly, causing the entire denominator to increase, thus affecting the final gain. Decrease. As the robot approaches the target and its velocity approaches zero, and When both terms approach zero, the denominator approaches 1, and the gain... It then approaches the reference gain. .

[0074] This rational function-based calculation method, compared to the exponential decay function-based method, has a relatively slower decay rate, potentially offering different adjustment characteristics and applicable ranges for parameter tuning. For example, in some applications, it may be desirable to prevent the gain from decaying too quickly in order to maintain a high response speed over a large error range; in such cases, the rational function form may be more suitable.

[0075] The adaptive gain calculated in this embodiment Substituting step S104 of Example 1, and using it in conjunction with the hyperbolic tangent saturation function, adaptive smooth constraint on the theoretical joint update amount can also be achieved. Its working process and the beneficial effects it can achieve—namely, ensuring smoothness during high-speed motion and ensuring rapid response during fine positioning—are basically the same as in Example 1.

[0076] This embodiment demonstrates that the core of achieving adaptive gain lies in constructing a function relationship that monotonically decreases with respect to the robot's real-time motion state parameters (such as error and velocity). The specific mathematical form of this relationship can be diverse, including exponential functions, rational functions, or any other function that satisfies this monotonically decreasing characteristic. This increases the flexibility and versatility of the proposed solution.

[0077] Example 4

[0078] This embodiment provides another optional implementation of the smooth saturation constraint application step S104, namely, using a different continuously differentiable nonlinear saturation function, to prove that the core idea of ​​this application is not limited to a specific type of saturation function.

[0079] The overall process of this embodiment is basically the same as that of Embodiment 1, and its adaptive gain factor... The calculation can be performed in any of the ways described in Example 1 or Example 3. The only difference in this example is the saturation function used in step S104 and its application formula.

[0080] In Example 1, the hyperbolic tangent function tanh was selected. As an alternative, this example uses the arctangent function atan as a pre-defined, continuously differentiable, nonlinear saturating function. The arctangent function is also an S-shaped function, approximately linear near the origin, and tends to saturate far from the origin, with a range of... To align its output range with the scheme using the hyperbolic tangent function, i.e., to saturate it... It needs to be scaled appropriately.

[0081] Specifically, in the smooth saturation constraint application step S104, the theoretical joint update vector is... The Each component The corresponding final joint update component Calculated using the following formula:

[0082]

[0083] In this formula, It is the adaptive gain factor calculated in step S103. When When the value is large, the derivative of the arctangent function near the origin is large, and the function shape is steep, making the system sensitive to small theoretical updates. When When the input is small, it's equivalent to compressing the input, lengthening the effective input segment of the arctangent function, and flattening the overall curve, thus smoothing and limiting large theoretical updates. Its working principle is similar to the scheme using the hyperbolic tangent function, and it can also be referenced... Figure 4 The logic shown is based on The size of the constraint dynamically changes its "hardness" or "softness".

[0084] The implementation of this embodiment demonstrates that the adaptive smoothing constraint framework proposed in this application has universality. Any continuously differentiable sigmoid function with saturation characteristics, such as the Gaussian error function erf, can be used as the nonlinear saturation function in the scheme of this application, along with the adaptive gain factor, after appropriate parameterization and scaling. By combining these methods, the same technical effect can be achieved. This further broadens the scope of protection of this application and the range of choices in practical applications.

[0085] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. An adaptive smoothing constraint method for robot inverse kinematics, characterized in that, The method, executed within an iterative control loop, includes: Obtain the robot's current state and target state, and calculate the pose error; Based on the pose error, the theoretical joint update amount is calculated; An adaptive gain factor is dynamically calculated based on at least one real-time motion state parameter of the robot, wherein the value of the adaptive gain factor is monotonically decreasing with the value of the at least one real-time motion state parameter. The theoretical joint update amount is multiplied by the adaptive gain factor using a preset, continuously differentiable nonlinear saturation function, and the product is used as the input of the nonlinear saturation function to generate the final joint update amount. The robot's joint states are updated using the final joint update values ​​to drive robot movement.

2. The method according to claim 1, characterized in that, The calculation of the theoretical joint update includes calculation using the damped least squares method.

3. The method according to claim 1, characterized in that, The at least one real-time motion state parameter includes: The magnitude of the pose error and / or the magnitude of the robot's current joint angular velocity.

4. The method according to claim 1, characterized in that, The continuously differentiable nonlinear saturation function is a hyperbolic tangent function.

5. The method according to claim 1, characterized in that, The continuously differentiable nonlinear saturation function is the arctangent function.

6. The method according to claim 3, characterized in that, The calculation of the adaptive gain factor includes multiplying a reference gain by at least one exponentially decaying modulation function, wherein the exponentially decaying modulation function is calculated based on the magnitude of the pose error and / or the magnitude of the joint angular velocity.

7. The method according to claim 3, characterized in that, The calculation of the adaptive gain factor includes dividing a reference gain by a rational function, which is calculated based on the magnitude of the pose error and / or the magnitude of the joint angular velocity.

8. The method according to claim 2, characterized in that, The method further includes: dynamically adjusting a damping factor used in the damped least squares method based on the evaluation results of the robot singularity.

9. The method according to claim 8, characterized in that, The evaluation results of robot singularity include operability measures.

10. A robot system, comprising a robot body and a robot controller, characterized in that, The robot controller is configured to perform the method as described in claim 1.

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