Robot control method and system based on radial smoothing and control obstacle function

Abstract

The invention relates to the technical field of robot control, and discloses a robot control method and system based on radial smoothing and a control barrier function, the robot control method is applied to robot control equipment, and the robot control method specifically comprises the following steps: S101: obtaining position information and an original expected speed instruction of the tail end of a robot in a Cartesian space, and a virtual wall constraint area is defined as an annular working space with the designated center point as the reference, the virtual wall constraint area is jointly limited by the inner boundary radius and the outer boundary radius, and the allowable range of the tail end movement is output. Through an innovative radial-tangential speed decomposition strategy and in combination with a progressive speed regulation mechanism based on a cubic smoothing function, the problems of motion impact and sudden speed change caused by a traditional direct truncation method are thoroughly eliminated, and meanwhile, by introducing a control barrier function theory, the speed of the robot is improved. A complex geometric safety boundary is converted into a simple linear speed constraint, and it is guaranteed that an end effector strictly does not cross the boundary from the mathematical level.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and more specifically, to a robot control method and system based on radial smoothing and control obstacle functions. Background Technology

[0002] In the field of robot end effector motion control, virtual walls serve as an important safety constraint method. They limit the range of motion of the end effector by defining geometric boundaries in Cartesian space. Currently, the mainstream implementation methods include the direct truncation method and the virtual potential field method. The direct truncation method achieves constraint by directly setting the normal velocity component to zero when a risk of exceeding the boundary is detected. This method is computationally efficient and simple to implement, and is widely used in the basic safety protection of industrial robots. The virtual potential field method constructs a repulsive potential field in the boundary region and generates a corresponding repulsive velocity or torque based on the distance between the end effector and the boundary. This method can provide continuous velocity changes and is more advantageous in scenarios requiring compliant control.

[0003] In recent years, with the development of safety control theory, some methods based on control barrier functions (CBF) have begun to be applied to robot motion constraints. These methods ensure that the system state is always within the allowable range by constructing a mathematical description of the safety set. These traditional methods together constitute the main implementation scheme of current virtual wall technology.

[0004] However, existing virtual wall control methods face several prominent technical challenges in engineering practice. While the direct truncation method is simple to implement, its rigid truncation strategy can cause abrupt changes in end-effector velocity at the boundary. Such abrupt velocity changes can trigger mechanical shocks and motion jitter, affecting not only control accuracy and equipment lifespan but also potentially causing task failure in scenarios requiring precise operation. Although the virtual potential field method achieves continuous velocity adjustment, its position gradient-based control mechanism is prone to oscillations near the boundary, leading to continuous jitter at the end-effector. At the same time, the potential field method cannot theoretically guarantee that the end-effector will not cross the boundary, especially in cases of high-speed motion or high system inertia. The end-effector may break through the potential field barrier due to momentum effects, posing a safety hazard. While CBF-based methods can provide strict safety guarantees, they typically require solving complex optimization problems, resulting in a heavy computational burden and making it difficult to meet the stringent real-time requirements of robot motion control. These problems severely restrict the application of virtual wall technology in scenarios with extremely high motion quality requirements, such as high-end manufacturing, medical surgery, and human-robot collaboration. Summary of the Invention

[0005] The purpose of this invention is to provide a robot control method and system based on radial smoothing and control barrier functions. By using an innovative radial-tangential velocity decomposition strategy and combining it with a progressive velocity adjustment mechanism based on cubic smoothing functions, the invention completely eliminates the motion shock and velocity mutation problems caused by the traditional direct truncation method. At the same time, by introducing control barrier function theory, the complex geometric safety boundary is transformed into a simple linear velocity constraint, aiming to solve the problems in the prior art.

[0006] This invention is implemented as follows: a robot control method based on radial smoothing and control barrier functions, applied to robot control equipment, specifically includes the following steps: S101: Obtain the position information and original desired velocity command of the robot end effector in Cartesian space, define the virtual wall constraint region as a ring-shaped workspace with a specified center point as the reference, the virtual wall constraint region is jointly defined by the inner boundary radius and the outer boundary radius, and output the allowable range of end effector motion; S102: Decompose the original desired speed command into radial speed components and tangential speed components, where the radial speed component represents the speed at which the end moves toward or away from the center of the constraint area, and the tangential speed component represents the speed at which the end moves along the boundary tangent direction, thus achieving a separation representation of the motion intention. S103: Based on the relative distance relationship between the allowable range of the end motion and the virtual wall boundary, a continuously differentiable mathematical function is used to obtain the node velocity command that separates the motion intention. The radial velocity component and the tangential velocity component are progressively scaled according to the node velocity command to generate a smoothed synthetic velocity command. S104: Based on the control barrier function theory, construct the velocity level linear constraint conditions corresponding to the inner and outer boundaries of the virtual wall, and transform the geometric boundary safety requirements into inequality constraint forms in the velocity space; S105: Based on the smoothed speed command, and under the premise of satisfying the linear constraint conditions, the corrected safe speed command is obtained by solving the convex optimization problem, and the safe speed command is output to the robot's actuator to realize the robot's safe and smooth end motion control.

[0007] Further, in S101, the virtual wall constraint region is jointly defined by the inner boundary radius and the outer boundary radius, and the allowable range of the output end motion includes: The mathematical definition of the virtual wall constraint region is: ; in It indicates the position of the robot's end effector. To the center of the virtual wall Euclidean distance, and The inner and outer boundary radii are respectively. The annular region can be expanded into a spherical region in three-dimensional space and into a circular region in two-dimensional space. The region parameters can be dynamically configured and updated in real time according to task requirements.

[0008] Furthermore, in S102, the original desired velocity command is decomposed into radial velocity components and tangential velocity components, including: The specific calculation formula for the velocity vector decomposition is as follows: ; in A radial unit vector. Represents the radial velocity component. Represents the tangential velocity component, when At that time, a singularity handling strategy is adopted to... Set to the zero vector or use the value from the previous control cycle.

[0009] Furthermore, in S103, based on the relative distance relationship between the allowable range of the end-effector motion and the virtual wall boundary, a continuously differentiable mathematical function is used to obtain the node velocity command representing the separation of motion intent, including: Using a cubic smoothing function: The normalized distance parameter η is calculated based on the direction of motion: When v r,cmd When η > 0, ou t=(r out－ r) / Δ out ; When v r,cmd When η < 0, in =(r-r in ) / Δ in ; Where Δ in and Δ out Given the widths of the inner and outer speed bumps, the smoothed radial velocity is calculated as follows: ; Before normalizing the distance parameter η, clamp η is applied: ; Ensure that the smoothing function s(η) only works within the effective normalized distance range, and keep the original speed command unchanged when the end is outside the speed bump.

[0010] Furthermore, in S104, based on the control barrier function theory, linear constraint conditions of velocity hierarchy corresponding to the inner and outer boundaries of the virtual wall are constructed, including: The control barrier function is constructed as follows: Outer boundary CBF function: ; Inner boundary CBF function: ; The corresponding linear velocity constraint is derived as follows: ; Where, γ in and γ out γ is the boundary relaxation coefficient. in and γ out It adaptively adjusts based on the robot's end effector motion state. When high-speed motion is detected, the coefficient value is automatically increased to strengthen safety constraints, and when low-speed motion is detected, the coefficient value is decreased to improve motion flexibility. The adjustment rule is as follows: ; Where γ0 is the basic relaxation coefficient and k is the adjustment gain coefficient.

[0011] Furthermore, in S105, based on the smoothed speed command, and under the premise of satisfying the linear constraint conditions, a corrected safe speed command is obtained by solving a convex optimization problem, including: The mathematical description of the convex optimization problem is as follows: ; in The optimization problem has an analytical solution for the smoothed velocity: ; The clamp function is defined as follows: .

[0012] Furthermore, the execution of the safe speed command includes a post-processing stage. This stage processes parameters including speed limiting protection, coordinate system transformation, and noise filtering to limit the speed and ensure that the command output by the algorithm can be safely and effectively executed by the physical system. ; Where v max The maximum permissible speed for the robot is then determined, and the Cartesian space velocity is subsequently converted into joint space velocity commands through an inverse Jacobian matrix transformation. ; J + (q) is the pseudo-inverse of the Jacobian matrix of the robot at joint position q.

[0013] Furthermore, the Cartesian space velocity is then converted into joint space velocity commands via an inverse Jacobian matrix transformation, including: Based on the robot's current configuration and joint angles, its kinematic Jacobian matrix is ​​calculated in real time. The safe velocity command v in Cartesian space is mapped to the joint angular velocity vector ˙q in joint space through the mathematical relationship ˙q = J†(q)v to deal with the possible singular configurations of the robot. The joint angular velocity command ˙q obtained from the solution is transmitted to the robot's underlying servo control system. The underlying servo control system operates at a high frequency, receives the command in real time, and drives each joint motor to accurately track the target speed. Through the motor driver and reduction mechanism and other execution components, the digital command is converted into the actual physical motion of the robot's end effector, realizing safe and precise control of the motion in Cartesian space.

[0014] Compared with the prior art, the robot control method and system based on radial smoothing and control obstacle function provided by the present invention have the following beneficial effects: 1. By adopting an innovative radial-tangential velocity decomposition strategy and combining it with a progressive velocity adjustment mechanism based on a cubic smooth function, the motion shock and velocity mutation problems caused by the traditional direct truncation method are completely eliminated. At the same time, by introducing the control barrier function theory, the complex geometric safety boundary is transformed into a simple linear velocity constraint, which mathematically ensures that the end effector does not exceed the boundary and overcomes the boundary oscillation and safety hazards of the potential field method. 2. The minimum correction algorithm based on convex optimization theory not only ensures the maximum consistency between control commands and original motion intentions, but also achieves millisecond-level real-time computing performance through analytical solution. It has good geometric versatility and can flexibly adapt to various virtual wall configurations such as rings and spheres. While ensuring strict safety, it gives the robot a natural interactive experience of smooth sliding along the virtual wall boundary, significantly improving the safety and compliance of human-machine collaboration.

[0015] A robot control system based on radial smoothing and a control barrier function is used to execute the above-described robot control method. The robot control system includes: The data acquisition and region definition module is used to acquire the position information of the robot end effector in Cartesian space and the original expected velocity command, and to define the virtual wall constraint region as a ring-shaped workspace with the specified center point as the reference. The velocity decomposition processing module is used to decompose the original desired velocity command into radial velocity components and tangential velocity components, so as to achieve the separation and representation of motion intention. The radial velocity smoothing module is used to progressively scale the radial velocity components based on the relative distance between the end point and the virtual wall boundary using a continuously differentiable mathematical function, thereby generating a smoothed synthetic velocity command. The safety constraint construction module is used to construct linear constraint conditions of velocity hierarchy corresponding to the inner and outer boundaries of the virtual wall based on the control obstacle function theory. The optimization solution and execution module is used to obtain a safe speed command by solving a convex optimization problem based on the smoothed speed command, under the premise of satisfying linear constraints, and then output it to the robot actuator.

[0016] Specifically, the optimization solution and execution module includes: The initial instruction processing unit is used to receive the smoothed speed instruction and prepare the parameters required for the optimization problem. The constraint processing unit is used to verify whether the current speed command satisfies the linear constraint conditions. The analytical solution calculation unit is used to calculate the corrected safe speed command using analytical solution formulas when the speed command violates the constraints. The command output unit is used to transmit the final safe speed command to the robot's underlying control system. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the robot control method based on radial smoothing and control obstacle function proposed in this invention. Figure 2 This is a schematic diagram of the robot arm velocity decomposition and virtual wall boundary in the robot control method based on radial smoothing and control obstacle function proposed in this invention. Figure 3 This is a schematic diagram of the robot control system based on radial smoothing and control barrier function proposed in this invention; Figure 4 This is a schematic diagram of the optimization solution and execution module in the robot control system based on radial smoothing and control obstacle function proposed in this invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] The implementation of the present invention will be described in detail below with reference to specific embodiments.

[0020] In the accompanying drawings of this embodiment, the same or similar reference numerals correspond to the same or similar components. In the description of this invention, it should be understood that if terms such as "upper," "lower," "left," and "right" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing this invention 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, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting this invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0021] Reference Figure 1-2 As shown, a robot control method based on radial smoothing and control barrier functions is applied to robot control equipment, specifically including the following steps: S101: Obtain the position information and original desired velocity command of the robot end effector in Cartesian space, define the virtual wall constraint region as a ring-shaped workspace with the specified center point as the reference, the virtual wall constraint region is jointly limited by the inner boundary radius and the outer boundary radius, and output the allowable range of end effector motion; The virtual wall constraint region is jointly defined by the inner and outer boundary radii, and the allowable range of the output end effector motion includes: The mathematical definition of a virtual wall-constrained region is: ; in It indicates the position of the robot's end effector. To the center of the virtual wall Euclidean distance, and These are the inner and outer boundary radii, respectively. The annular region can be expanded into a spherical region in three-dimensional space and into a circular region in two-dimensional space. The region parameters can be dynamically configured and updated in real time according to task requirements. S102: Decompose the original desired speed command into radial speed components and tangential speed components, where the radial speed component represents the speed at which the end moves toward or away from the center of the constraint area, and the tangential speed component represents the speed at which the end moves along the boundary tangent direction, thus achieving a separation representation of the motion intention. The original desired velocity command is decomposed into radial velocity components and tangential velocity components, including: The specific formula for calculating velocity vector decomposition is as follows: ; in A radial unit vector. Represents the radial velocity component. Represents the tangential velocity component, when At that time, a singularity handling strategy is adopted to... Set to the zero vector or use the value from the previous control cycle; S103: Based on the relative distance relationship between the allowable range of the end motion and the virtual wall boundary, a continuously differentiable mathematical function is used to obtain the node velocity command that separates the motion intention. The radial velocity component and the tangential velocity component are progressively scaled according to the node velocity command to generate a smoothed synthetic velocity command. Among them, based on the relative distance relationship between the allowable range of the end-effector motion and the virtual wall boundary, a continuously differentiable mathematical function is used to obtain the node velocity command, which is a separate representation of the motion intention, including: Using a cubic smoothing function: The normalized distance parameter η is calculated based on the direction of motion: When v r,cmd When η > 0, ou t=(r out－ r) / Δ out ; When v r,cmd When η < 0, in =(r-r in ) / Δ in ; Where Δ in and Δ out Given the widths of the inner and outer speed bumps, the smoothed radial velocity is calculated as follows: ; Before normalizing the distance parameter η, clamp η is applied: ; Ensure that the smoothing function s(η) only works within the effective normalized distance range, and keep the original speed command unchanged when the end is outside the speed bump; S104: Based on the control barrier function theory, construct the velocity level linear constraint conditions corresponding to the inner and outer boundaries of the virtual wall, and transform the geometric boundary safety requirements into inequality constraint forms in the velocity space; Based on the control barrier function theory, linear constraint conditions for velocity levels corresponding to the inner and outer boundaries of the virtual wall are constructed, including: The control barrier function is constructed as follows: Outer boundary CBF function: ; Inner boundary CBF function: ; The corresponding linear velocity constraint is derived as follows: ; Where, γ in and γ out γ is the boundary relaxation coefficient. in and γout It adaptively adjusts based on the robot's end effector motion state. When high-speed motion is detected, the coefficient value is automatically increased to strengthen safety constraints, and when low-speed motion is detected, the coefficient value is decreased to improve motion flexibility. The adjustment rule is as follows: ; Where γ0 is the basic relaxation coefficient and k is the adjustment gain coefficient; S105: Based on the smoothed speed command, and under the premise of satisfying linear constraints, a corrected safe speed command is obtained by solving a convex optimization problem. The safe speed command is then output to the robot's actuator, realizing safe and smooth end-effector motion control. Through an innovative radial-tangential velocity decomposition strategy, combined with a progressive speed adjustment mechanism based on a cubic smoothing function, the motion shock and speed mutation problems caused by the traditional direct truncation method are completely eliminated. At the same time, by introducing the control barrier function theory, the complex geometric safety boundary is transformed into a simple linear velocity constraint, which mathematically ensures that the end-effector strictly does not exceed the boundary, overcoming the boundary oscillation and safety hazards of the potential field method.

[0022] In S105 of this embodiment, based on the smoothed speed command, and under the premise of satisfying linear constraints, the corrected safe speed command is obtained by solving a convex optimization problem, including: The mathematical description of a convex optimization problem is: ; in After smoothing the velocity, the optimization problem has an analytical solution: ; The clamp function is defined as follows: .

[0023] The execution of the safe speed command includes a post-processing stage. This stage processes parameters such as speed limiting protection, coordinate system transformation, and noise filtering to limit the speed and ensure that the command output by the algorithm can be executed safely and effectively by the physical system. ; Where v max The maximum permissible speed for the robot is then determined, and the Cartesian space velocity is subsequently converted into joint space velocity commands through an inverse Jacobian matrix transformation. ; J + (q) is the pseudo-inverse of the Jacobian matrix of the robot at joint position q.

[0024] In this embodiment, the Cartesian space velocity is then converted into a joint space velocity command via the inverse Jacobian matrix transformation, including: Based on the robot's current configuration and joint angles, its kinematic Jacobian matrix is ​​calculated in real time. The safe velocity command v in Cartesian space is mapped to the joint angular velocity vector ˙q in joint space through the mathematical relationship ˙q = J†(q)v to deal with the possible singular configurations of the robot. The joint angular velocity command ˙q obtained from the solution is transmitted to the robot's underlying servo control system. The underlying servo control system operates at a high frequency, receives the command in real time, and drives each joint motor to accurately track the target speed. Through the motor driver and reduction mechanism and other execution components, the digital command is converted into the actual physical motion of the robot's end effector, realizing safe and precise control of the motion in Cartesian space.

[0025] This technical solution, based on the minimum correction algorithm of convex optimization theory, not only ensures the maximum consistency between control commands and original motion intentions, but also achieves millisecond-level real-time computing performance through analytical solution. It has good geometric versatility and can flexibly adapt to various virtual wall configurations such as rings and spheres. While ensuring strict safety, it gives the robot a natural interactive experience of smooth sliding along the virtual wall boundary, significantly improving the safety and compliance of human-robot collaboration.

[0026] Reference Figure 3-4 As shown, a robot control system based on radial smoothing and a control barrier function is used to execute the above-mentioned robot control method. The robot control system includes: The data acquisition and region definition module acquires the position information of the robot's end effector in Cartesian space and the original desired velocity command, and defines the virtual wall constraint region as a ring-shaped workspace with a specified center point as the reference. The velocity decomposition processing module decomposes the original desired velocity command into radial and tangential velocity components to achieve a separate representation of motion intent. The radial velocity smoothing module uses a continuously differentiable mathematical function to progressively scale the radial velocity components based on the relative distance between the end effector and the virtual wall boundary to generate a smoothed synthetic velocity command. The safety constraint construction module constructs linear constraint conditions for the velocity hierarchy corresponding to the inner and outer boundaries of the virtual wall based on the control obstacle function theory. The optimization solution and execution module uses the smoothed velocity command as a reference to obtain a safe velocity command by solving a convex optimization problem under the premise of satisfying the linear constraint conditions, and outputs it to the robot actuator. Through an innovative radial-tangential velocity decomposition strategy combined with a progressive velocity adjustment mechanism based on a cubic smoothing function, the motion shock and velocity mutation problems caused by the traditional direct truncation method are completely eliminated.

[0027] In this city's example, the optimization solution and execution module includes: an initial instruction processing unit, used to receive the smoothed speed instruction and prepare the parameters required for the optimization problem; a constraint processing unit, used to verify whether the current speed instruction meets the linear constraint conditions; an analytical solution calculation unit, used to calculate the corrected safe speed instruction using the analytical solution formula when the speed instruction violates the constraints; and an instruction output unit, used to transmit the final safe speed instruction to the robot's underlying control system. By introducing the control obstacle function theory, the complex geometric safety boundary is transformed into a simple linear speed constraint, which mathematically ensures that the end effector strictly does not exceed the boundary, overcoming the boundary oscillations and safety hazards of the potential field method. This technical solution achieves millisecond-level real-time computing performance through analytical solutions, exhibits excellent geometric versatility, and can flexibly adapt to various virtual wall configurations such as rings and spheres. While ensuring strict safety, it endows robots with a natural interactive experience of smooth sliding along the boundaries of virtual walls, significantly improving the safety and compliance of human-machine collaboration.

[0028] In this embodiment, the entire operation process can be controlled by a computer, and the PLC can be used to achieve automated operation control. In each operation stage, sensors can be set to provide signal feedback and ensure that the steps are performed in sequence. These are all conventional knowledge of current automation control, and will not be elaborated on in this embodiment.

[0029] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robot control method based on radial smoothing and control obstacle function, characterized in that, Applied to robot control equipment, it specifically includes the following steps: S101: Obtain the position information and original desired velocity command of the robot end effector in Cartesian space, define the virtual wall constraint region as a ring-shaped workspace with a specified center point as the reference, the virtual wall constraint region is jointly defined by the inner boundary radius and the outer boundary radius, and output the allowable range of end effector motion; S102: Decompose the original desired speed command into radial speed components and tangential speed components, where the radial speed component represents the speed at which the end moves toward or away from the center of the constraint area, and the tangential speed component represents the speed at which the end moves along the boundary tangent direction, thus achieving a separation representation of the motion intention. S103: Based on the relative distance relationship between the allowable range of the end motion and the virtual wall boundary, a continuously differentiable mathematical function is used to obtain the node velocity command that separates the motion intention. The radial velocity component and the tangential velocity component are progressively scaled according to the node velocity command to generate a smoothed synthetic velocity command. S104: Based on the control barrier function theory, construct the velocity level linear constraint conditions corresponding to the inner and outer boundaries of the virtual wall, and transform the geometric boundary safety requirements into inequality constraint forms in the velocity space; S105: Based on the smoothed speed command, and under the premise of satisfying the linear constraint conditions, the corrected safe speed command is obtained by solving the convex optimization problem, and the safe speed command is output to the robot's actuator to realize the robot's safe and smooth end motion control.

2. The robot control method based on radial smoothing and control obstacle function as described in claim 1, characterized in that, In S101, the virtual wall constraint region is jointly defined by the inner boundary radius and the outer boundary radius, and the allowable range of the output end motion includes: The mathematical definition of the virtual wall constraint region is: ; in It indicates the position of the robot's end effector. To the center of the virtual wall Euclidean distance, and The inner and outer boundary radii are respectively. The annular region can be expanded into a spherical region in three-dimensional space and into a circular region in two-dimensional space. The region parameters can be dynamically configured and updated in real time according to task requirements.

3. The robot control method based on radial smoothing and control obstacle function as described in claim 2, characterized in that, In S102, the original desired velocity command is decomposed into radial velocity components and tangential velocity components, including: The specific calculation formula for the velocity vector decomposition is as follows: ； in A radial unit vector. Represents the radial velocity component. Represents the tangential velocity component, when At that time, a singularity handling strategy is adopted to... Set to the zero vector or use the value from the previous control cycle.

4. The robot control method based on radial smoothing and control obstacle function as described in claim 3, characterized in that, In S103, based on the relative distance relationship between the allowable range of the end-effector motion and the virtual wall boundary, a continuously differentiable mathematical function is used to obtain the node velocity command representing the separation of motion intent, including: Using a cubic smoothing function: The normalized distance parameter η is calculated based on the direction of motion: When v r,cmd When η > 0, ou t=(r out－ r) / Δ out ; When v r,cmd < 0, η in = (r − r in ) / Δ in ; Where Δ in and Δ out Given the widths of the inner and outer speed bumps, the smoothed radial velocity is calculated as follows: ; Before normalizing the distance parameter η, clamp η is applied: ； Ensure that the smoothing function s(η) only works within the effective normalized distance range, and keep the original speed command unchanged when the end is outside the speed bump.

5. The robot control method based on radial smoothing and control obstacle function as described in claim 4, characterized in that, In S104, based on the control barrier function theory, linear constraint conditions of velocity hierarchy corresponding to the inner and outer boundaries of the virtual wall are constructed, including: The control barrier function is constructed as follows: Outer boundary CBF function: ; Inner boundary CBF function: ; The corresponding linear velocity constraint is derived as follows: ； Where, γ in and γ out γ is the boundary relaxation coefficient. in and γ out It adaptively adjusts based on the robot's end effector motion state. When high-speed motion is detected, the coefficient value is automatically increased to strengthen safety constraints, and when low-speed motion is detected, the coefficient value is decreased to improve motion flexibility. The adjustment rule is as follows: ； Where γ0 is the basic relaxation coefficient and k is the adjustment gain coefficient.

6. The robot control method based on radial smoothing and control obstacle function as described in claim 5, characterized in that, In S105, based on the smoothed speed command, and under the premise of satisfying the linear constraint conditions, the corrected safe speed command is obtained by solving a convex optimization problem, including: The mathematical description of the convex optimization problem is as follows: ； in The optimization problem has an analytical solution for the smoothed velocity: ； The clamp function is defined as follows: 。 7. The robot control method based on radial smoothing and control obstacle function as described in claim 6, characterized in that, The execution of the safe speed command includes a post-processing stage. This stage processes parameters such as speed limiting protection, coordinate system transformation, and noise filtering to limit the speed and ensure that the command output by the algorithm can be safely and effectively executed by the physical system. ； Where v max The maximum permissible speed for the robot is then determined, and the Cartesian space velocity is subsequently converted into joint space velocity commands through an inverse Jacobian matrix transformation. ； J + (q) is the pseudo-inverse of the Jacobian matrix of the robot at joint position q.

8. The robot control method based on radial smoothing and control obstacle function as described in claim 7, characterized in that, Subsequently, the Cartesian space velocity is converted into joint space velocity commands through the inverse Jacobian matrix transformation, including: Based on the robot's current configuration and joint angles, its kinematic Jacobian matrix is ​​calculated in real time. The safe velocity command v in Cartesian space is mapped to the joint angular velocity vector ˙q in joint space through the mathematical relationship ˙q = J†(q)v to deal with the possible singular configurations of the robot. The joint angular velocity command ˙q obtained from the solution is transmitted to the robot's underlying servo control system. The underlying servo control system operates at a high frequency, receives the command in real time, and drives each joint motor to accurately track the target speed. Through the motor driver and reduction mechanism and other execution components, the digital command is converted into the actual physical motion of the robot's end effector, realizing safe and precise control of the motion in Cartesian space.

9. A robot control system based on radial smoothing and control barrier function, characterized in that, For performing the robot control method according to any one of claims 1-8, the robot control system comprises: The data acquisition and region definition module is used to acquire the position information of the robot end effector in Cartesian space and the original expected velocity command, and to define the virtual wall constraint region as a ring-shaped workspace with the specified center point as the reference. The velocity decomposition processing module is used to decompose the original desired velocity command into radial velocity components and tangential velocity components, so as to achieve the separation and representation of motion intention. The radial velocity smoothing module is used to progressively scale the radial velocity components based on the relative distance between the end point and the virtual wall boundary using a continuously differentiable mathematical function, thereby generating a smoothed synthetic velocity command. The safety constraint construction module is used to construct linear constraint conditions of velocity hierarchy corresponding to the inner and outer boundaries of the virtual wall based on the control obstacle function theory. The optimization solution and execution module is used to obtain a safe speed command by solving a convex optimization problem based on the smoothed speed command, under the premise of satisfying linear constraints, and then output it to the robot actuator.

10. The robot control system based on radial smoothing and control obstacle function as described in claim 9, characterized in that, The optimization solution and execution module includes: The initial instruction processing unit is used to receive the smoothed speed instruction and prepare the parameters required for the optimization problem. The constraint processing unit is used to verify whether the current speed command satisfies the linear constraint conditions. The analytical solution calculation unit is used to calculate the corrected safe speed command using analytical solution formulas when the speed command violates the constraints. The command output unit is used to transmit the final safe speed command to the robot's underlying control system.

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