Variable admittance control method based on visual features

Abstract

The invention belongs to the technical field of mechanical arm control, particularly relates to a variable admittance control method based on visual features, can solve the problems of environmental perception splitting, easy feature loss and parameter solidification of a collaborative robot in a visual servo task, and provides a self-adaptive admittance control method based on a visual feature space. Admittance control is introduced into a visual feature space, and a variable admittance law based on a barrier function is designed, so that deep fusion of vision and force perception, preset boundary constraint of feature errors and dynamic optimization of admittance parameters are realized, and therefore, in an unstructured man-machine interaction scene such as medical assistance and precision assembly, the visual sense and the force perception can be effectively improved. Target features are guaranteed to be always in the view of the camera, flexibility and tracking precision are balanced, and task safety and environmental adaptability are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of robotic arm control, and in particular relates to a variable admittance control method based on visual features. Background Art

[0002] In many robotic applications, the physical interaction between the robot and its environment is a key issue, and the robot's ability to manage this interaction often directly impacts task performance. To achieve effective interactive control, the robot not only needs to accurately acquire the environment's positional information and geometry to plan precise motion trajectories, but also needs to be able to sense external forces to cope with environmental uncertainty and avoid excessive contact forces in the directions of motion constraints. Existing technologies typically employ methods such as admittance control, impedance control, or equipping the robot with visual sensors to perceive unstructured task environments to design robust control systems. Admittance control precisely controls the robot's motion using only contact forces obtained from force sensors, offering a certain degree of stability and flexibility. Vision-based image servoing utilizes cameras to capture image information from the environment and uses this information to control and position the robot's motion. However, linear or nonlinear admittance control struggles to distinguish between applied forces, such as traction and impact, leading to a difficult balance between compliance and robustness. When vision sensors are used, uncertain visual servoing parameters can lead to model inaccuracies, compromising control performance. Therefore, in tasks in unstructured environments, it is often difficult to achieve a satisfactory balance between compliance and robustness by relying solely on the information provided by force sensors or visual sensors to control the robot. To this end, the present invention proposes a variable admittance control method based on visual features. Summary of the Invention

[0003] The purpose of this invention is to provide a variable admittance control method based on visual features, which can solve the problems of environmental perception fragmentation, easy feature loss, and parameter rigidity faced by collaborative robots in visual servoing tasks. This method proposes an adaptive admittance control method based on the visual feature space. By introducing admittance control into the visual feature space and designing a variable admittance law based on an obstacle function, this method achieves a deep fusion of vision and force perception, preset boundary constraints on feature errors, and dynamic optimization of admittance parameters. In unstructured human-machine interaction scenarios such as medical assistance and precision assembly, this method ensures that target features are always within the camera's field of view, while balancing compliance and tracking accuracy, significantly improving task safety and environmental adaptability.

[0004] The technical solutions adopted by the present invention are as follows:

[0005] A variable admittance control method based on visual features comprises the following steps:

[0006] Step 1: The robot's onboard visual sensor collects the target object's image in real time and extracts the current visual features;

[0007] Step 2: Collect the target object image in real time based on the sensor, extract the current visual features and establish visual servo kinematics;

[0008] Step 3: Construct an admittance control framework in the visual feature space. This framework takes the visual feature error, the rate of change of the feature error, and the external force projected into the feature space as input and outputs a compliant acceleration.

[0009] Step 4: Using variable impedance control with preset accuracy based on the barrier function, adjust the damping and stiffness parameters of the admittance control in real time according to the preset composite error safety boundary value, so that the composite error is always less than the safety boundary value;

[0010] Step 5: Generate a compliant visual feature trajectory through the admittance controller and input it into the visual servo controller to generate the robot end motion speed command;

[0011] Step 6: Convert the end motion velocity command into joint control commands to drive the robot to achieve target tracking and compliant interaction.

[0012] The technical effects achieved by the present invention are:

[0013] This invention addresses the control of constrained motion, using active compliance as an effective solution, which can be achieved through impedance or admittance control. This approach effectively adjusts the robot's dynamic response to external forces by establishing a mass-spring-damper dynamic model at the interface between the robot and its environment, such as the end effector.

[0014] This application proposes a compliant control framework that hybridizes visual servoing and force control. This framework achieves compliance in the visual feature space based on admittance control and ensures task accuracy through a variable impedance controller with preset performance. In visual servoing tasks, the camera must ensure that areas of interest, such as feature points and lines, remain within its field of view. By presetting task accuracy, these critical features can be effectively prevented from being lost within the camera's field of view, ensuring smooth task execution.

[0015] By analyzing and studying these background technologies, the authors introduced admittance control into visual servoing control, enabling the robot to exhibit compliant behavior during physical contact with humans, effectively achieving human-robot interaction. Furthermore, in the event of unexpected collisions or external forces, the robot can adapt to avoid damage to itself or the environment caused by excessive impact.

[0016] This invention addresses the issues of fragmented environmental perception, easy feature loss, and parameter rigidity faced by collaborative robots in visual servoing tasks. It proposes an adaptive admittance control method based on the visual feature space. By introducing admittance control into the visual feature space and designing a variable admittance law based on an obstacle function, this method achieves a deep fusion of visual and force perception, preset boundary constraints on feature errors, and dynamic optimization of admittance parameters. This approach ensures that target features remain within the camera's field of view in unstructured human-machine interaction scenarios such as medical assistance and precision assembly, while balancing compliance and tracking accuracy, significantly improving task safety and environmental adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram of the force projected onto the characteristic space in the constant admittance experiment provided by an embodiment of the present invention;

[0018] Figure 2 A schematic diagram of composite error in a constant admittance experiment provided by an embodiment of the present invention;

[0019] Figure 3 A schematic diagram of the force projected onto the characteristic space in the variable admittance experiment provided by an embodiment of the present invention;

[0020] Figure 4 A schematic diagram of composite error in a variable admittance experiment provided by an embodiment of the present invention;

[0021] Figure 5 A damping schematic diagram of a variable admittance control experiment provided by an embodiment of the present invention;

[0022] Figure 6 A schematic diagram of stiffness for a variable admittance control experiment provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0023] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is described in detail below with reference to the following examples. It should be understood that the following text is only used to describe one or more specific embodiments of the present invention and does not strictly limit the scope of protection of the present invention.

[0024] like Figures 1-6 As shown, a variable admittance control method based on visual features includes the following steps:

[0025] Step 1: The robot's onboard visual sensor collects the target object's image in real time and extracts the current visual features;

[0026] Step 2: Collect the target object image in real time based on the sensor, extract the current visual features and establish visual servo kinematics;

[0027] Step 3: Construct an admittance control framework in the visual feature space. This framework takes the visual feature error, the rate of change of the feature error, and the external force projected into the feature space as input and outputs a compliant acceleration.

[0028] Step 4: Using variable impedance control with preset accuracy based on the barrier function, adjust the damping and stiffness parameters of the admittance control in real time according to the preset composite error safety boundary value, so that the composite error is always less than the safety boundary value;

[0029] Step 5: Generate a compliant visual feature trajectory through the admittance controller and input it into the visual servo controller to generate the robot end motion speed command;

[0030] Step 6: Convert the end motion velocity command into joint control commands to drive the robot to achieve target tracking and compliant interaction.

[0031] Preferably, the visual servoing kinematics in step 2 specifically includes:

[0032] Image-based visual servoing (IBVS) directly controls the robot through visual features in the image plane. The control input is calculated based on the feature points in the image coordinate system. The control goal of visual servoing (IBVS) is to minimize the visual feature error e. s , is defined by the following formula:

[0033] e s =s d -s(m,a) (1)

[0034] The parameters in formula (1) are defined as follows: vector m is the set of image measurement points; these image measurements are used to calculate the vector of k visual features where a represents potential additional features related to the system (e.g., camera intrinsic parameters); the vector is the expected value of the visual feature; the change of the visual feature s(m,a) is related to the speed of the camera coordinate system c v c and the speed of the target feature c v o The kinematic relationship between the two coordinate systems (referenced to the camera coordinate system) is given by the following differential relationship:

[0035]

[0036] in is the interaction matrix. Different types of visual features have different explicit expressions of interaction matrices.

[0037] When the relative motion between the camera and the object is caused only by the motion of the robot, i.e. c v o = 0, we get:

[0038]

[0039] Desired visual features * It is constant under certain circumstances. According to equations (1) and (3), the relationship between camera speed and error over time is obtained:

[0040]

[0041] Consider c v c As input to the robot controller the following velocity controller is used:

[0042]

[0043] Make the error e s The exponential decreases, i.e. where λ is a constant, is the interaction matrix L s Moore-Penrose pseudoinverse; when L s When the rank is not full, the controller (5) makes and || c v c ||minimize;

[0044] According to formula (3), the Jacobian matrix is ​​used to link the visual feature velocity with the robot joint velocity, that is:

[0045]

[0046] in e J e Represents the robot reference end coordinate system Σ e The Jacobian matrix of ; is the adjoint transformation matrix, which is used to convert the six-dimensional velocity or six-dimensional force spinor of different reference coordinate systems; the six-dimensional velocity includes translational velocity and angular velocity; the six-dimensional force spinor includes force and torque, that is e v e represents the terminal velocity in the terminal reference coordinate system; accompanied by the transformation matrix The expression is:

[0047]

[0048] in, c p e and c R erepresents the position of the camera coordinate system in the end coordinate system in the "eye-in-hand" configuration. These quantities are obtained by hand-eye calibration. By differentiating Equation (6) with respect to time, the acceleration of the visual feature can be obtained:

[0049]

[0050] Formula (8) can be rewritten as:

[0051]

[0052] in, The characteristic Jacobian matrix representing the visual servoing, and:

[0053]

[0054] Preferably, the admittance control framework of the visual feature space in step 3 specifically includes:

[0055] Let Σ c is the pose of the current camera coordinate system in the base coordinate system, Σ d is the desired camera coordinate system pose; represents the error vector between the desired visual features and the current visual features; the impedance control in the feature space aims to achieve the following dynamic behavior:

[0056]

[0057] Among them, M s ,D s and K s is a diagonally positive definite k × k matrix representing the relative virtual mass, damper, and stiffness in the feature space; It is a virtual force projected into the feature space and acting on the visual features;

[0058] The dynamics of a serial robot is a coupled nonlinear second-order differential equation written as:

[0059]

[0060] in are the gravity term and the Coriolis force term, e F ext is the six-dimensional external force spinor acting on the end of the robot with reference to the end coordinate system; according to (12) and (9), we can get:

[0061]

[0062] Considering the characteristic Jacobian matrix and six-dimensional force spinor e F extThe adjoint transformation from the end coordinate system to the camera coordinate system is in c F ext is the external force in the reference camera coordinate system, and we get:

[0063]

[0064] in, is the inverse of the robot inertia matrix projected in the camera coordinate system; Equation (14) shows how the force acting on the camera coordinate system is projected into the feature space as a virtual force acting on the image features; by rewriting some terms in Equation (13):

[0065] f s =J s M(q) -1 τ, (15)

[0066] b s =J s M(q) -1 b, (16)

[0067]

[0068] Get the dynamic model in the feature space:

[0069]

[0070] The system in the feature space has no inertia; it behaves as a mechanical system with unit mass or inertia; the new control input for the robot model in the feature space is a virtual force u = f s When the external force F ext When it cannot be measured

[0071] Define the following controller:

[0072] u=wh q +b s (19)

[0073] Substituting equation (19) into equation (18) yields the dynamics after compensation:

[0074]

[0075] in, represents the command acceleration in the feature space, and the following values ​​are selected:

[0076]

[0077] Combining equations (18), (19) and (21), we can obtain the closed-loop dynamics of the feature space:

[0078]

[0079] The closed-loop dynamics (22) are similar to the target dynamics (11), except that M s is replaced by the identity matrix; however, since the external force projected in the feature space includes the inertia matrix of the robot, the closed-loop system will exhibit compliant behavior that is dependent on the joint angle; To overcome this problem and achieve isotropic compliant behavior, a simple approach is to measure the external force applied to the robot and fully compensate for it; in the external force e F ext When it can be measured, the feature space controller u is defined as:

[0080] u=wh q +b s +L s M c c F ext (twenty three)

[0081] The controller (23) fully compensates for the external force. Substituting (23) into (18) yields:

[0082]

[0083] The command acceleration w is defined as:

[0084]

[0085] in and are the desired representation mass and inertia respectively; combining (18), (23) and (25) we can get the closed-loop dynamics of the feature space:

[0086]

[0087] in Compared with Equation (26), the projected external force in the feature space is No longer dependent on robot joint angles.

[0088] Preferably, the preset precision variable impedance control based on the barrier function in step 4 specifically includes:

[0089] To effectively balance contact compliance and tracking accuracy and ensure that the tracking error always remains within a predefined range, a composite tracking error is introduced here that combines position and velocity errors to accurately characterize the tracking performance of the system. In joint space, the composite tracking error is defined as:

[0090]

[0091] When Λ=diag(λ1,...,λ n ),λ i > 0, i = 1, ..., n, the joint space error boundary vector is ζ = diag (ζ1, ..., ζ n ),λ i >0,i=1,...,n; The goal of joint space preset precision variable impedance control is to design the following joint space variable impedance model:

[0092]

[0093] in and Represent the time-varying stiffness and damping respectively, ensuring the error |e during the interaction process i |<ζ i ,i=1,...,n,i=1,...,m, where e i is the tracking error vector e i The i-th element of ;

[0094] In Cartesian space, the composite tracking error is similarly defined as:

[0095]

[0096] where Γ=diag(γ1,...,γ n ),γ i >0,i=1,...,n, the Cartesian space error boundary vector is ξ=[ξ1,...,ξ n ],ξ i >0, i=1,...,n; The goal of Cartesian space preset precision variable impedance control is to design the following Cartesian space variable impedance model:

[0097]

[0098] in and Represent the time-varying stiffness and damping respectively, ensuring the error |e during the interaction process task,i |<ξ i ,i=1,...,m, where e task,i is the Cartesian error vector e task The i-th element of ;

[0099] The following joint space is used as an example to analyze the variable impedance control of the obstacle function. The Cartesian space method is similar to the joint space method. Consider the following joint space impedance model:

[0100]

[0101] Where B=diag(b1,...,b n )and where b i >0,ζ i >0,i=1,...,n; This new impedance model \ref{eq3.3_1} is interpreted as a variable stiffness and damping model, expressed as:

[0102]

[0103] in Both are time-varying; based on the variable impedance model (32), the following joint space variable impedance control law is proposed:

[0104]

[0105] For IBVS, the variable admittance law of the barrier function is extended to the feature space and the variable admittance model is defined as:

[0106]

[0107] And variable admittance law and composite error:

[0108]

[0109] where X = diag(χ1,...,χ k ),χ i >0,i=1,...,k, the visual feature space error boundary vector η=[η1,...,η k ],η i >0,i=1,...,k,P=diag(p1,...,p k )and b i >0,ζ i >0,i=1,...,k;s * represents the compliant coordinates. In classical admittance control, the compliant coordinates serve as the input of the position controller; in visual admittance control, the compliant coordinates serve as the input of the visual control loop; separated from (34) And integrate it twice to get and s * As the compliant coordinates; change the controller (5) to:

[0110]

[0111] That is, achieving the desired compliant behavior in the feature space (34);

[0112] The control system modifies the reference visual features based on the visual feature space and admittance control to achieve compliance along the direction of the visual features. Different compliance behaviors are achieved according to the type of selected visual features and different variable impedance parameters. When the robot is not subjected to external forces, s * =s d , at this time the visual servo controller (38) is consistent with (5).

[0113] In this invention, to verify the effectiveness and practicality of this algorithm, a Franka Panda collaborative robot was used in the experiment. A Hyberson HPS-FT025 six-axis force / torque sensor and a RealSense D455 camera with a resolution of 1280×800 and a maximum frame rate of 90fps were installed on its end. The experiment was based on the Visual Servoing Platform (Visp) library for hand-eye calibration, and the "AprilTag" icon attached to the board was selected as the target. The visual features are the coordinates of the four corners of the icon, i.e. After selecting features, the relevant interaction matrix can be calculated expression.

[0114] The experiment also compared constant admittance control and variable admittance control and demonstrated the changes in visual features under external forces. In this experiment, the tracking goal is to ensure that the expected feature points coincide with the actual feature points. First, a fixed admittance model is used, that is, P in (34) is a zero matrix. Then, the robot end is pushed to simulate external interaction. The parameters of the admittance model are shown in the table. In the controller (38), λ = 1.

[0115] To prevent force sensor noise from causing unexpected robot motion, a dead zone was used for the sensor data: when the force measurement was less than 0.2N, the admittance model was not used.

[0116] Figure 1 Demonstrates the projection of external forces into the eigenspace in a constant admittance control experiment Figure 2 Demonstrates the composite error during the constant admittance control experiment Under the action of external force, the composite error becomes larger. The maximum value of the error reaches 0.58, which exceeds 175% of the preset limit.

[0117] The variable admittance experiment selection model (34), the variable admittance parameter M s =I,D s =11I,K s =2I,P=1.2I,X=IError boundary vector η=[0.33,...,0.33]. Figure 3 Demonstrates the external forces projected into the feature space during the variable admittance control experiment Figure 4 Demonstrates the composite error during the variable admittance control experiment As can be seen from the figure, the variable admittance control experiment is subjected to a greater external force during the interaction process, but its maximum composite error reaches 0.31, which does not exceed the preset limit η. Figure 5 and Figure 6 The dynamic adjustment of the stiffness and damping of the variable admittance control during the entire interaction process is demonstrated.

[0118] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained herein shall, unless otherwise specified or limited, be implemented in accordance with conventional means in the art.

Claims

1. A variable admittance control method based on visual features, characterized by: The following steps are involved: Step 1: The robot's onboard visual sensor collects the target object's image in real time and extracts the current visual features; Step 2: Collect the target object image in real time based on the sensor, extract the current visual features and establish visual servo kinematics; Step 3: Construct an admittance control framework in the visual feature space. This framework takes the visual feature error, the rate of change of the feature error, and the external force projected into the feature space as input and outputs a compliant acceleration. Step 4: Using variable impedance control with preset accuracy based on the barrier function, adjust the damping and stiffness parameters of the admittance control in real time according to the preset composite error safety boundary value, so that the composite error is always less than the safety boundary value; Step 5: Generate a compliant visual feature trajectory through the admittance controller and input it into the visual servo controller to generate the robot end motion speed command; Step 6: Convert the end motion velocity command into joint control commands to drive the robot to achieve target tracking and compliant interaction.

2. The variable admittance control method based on visual features according to claim 1, characterized in that: The visual servo kinematics in step 2 specifically includes: Image-based visual servoing (IBVS) directly controls the robot through visual features in the image plane. The control input is calculated based on the feature points in the image coordinate system. The control goal of visual servoing (IBVS) is to minimize the visual feature error e. s , is defined by the following formula: e s =s d -s(m,a) (1) The parameters in formula (1) are defined as follows: vector m is the set of image measurement points; these image measurements are used to calculate the vector of k visual features Where a represents the potential additional features related to the system; vector is the expected value of the visual feature; the change of the visual feature s(m,a) is related to the speed of the camera coordinate system c v c and the speed of the target feature c v o The kinematic relationship between the two coordinate systems (referenced to the camera coordinate system) is given by the following differential relationship: in is the interaction matrix. Different types of visual features have different explicit expressions of interaction matrices. When the relative motion between the camera and the object is caused only by the motion of the robot, i.e. c v o = 0, we get: Desired visual features * It is constant under certain circumstances. According to equations (1) and (3), the relationship between camera speed and error over time is obtained: Consider c v c As input to the robot controller the following velocity controller is used: Make the error e s The exponential decreases, i.e. where λ is a constant, is the interaction matrix L s Moore-Penrose pseudoinverse; when L s When the rank is not full, the controller (5) makes and || c v c ||minimize; According to formula (3), the Jacobian matrix is ​​used to link the visual feature velocity with the robot joint velocity, that is: in e J e Represents the robot reference end coordinate system Σ e The Jacobian matrix of ; is the adjoint transformation matrix, which is used to convert the six-dimensional velocity or six-dimensional force spinor of different reference coordinate systems; the six-dimensional velocity includes translational velocity and angular velocity; the six-dimensional force spinor includes force and torque, that is e v e represents the terminal velocity in the terminal reference coordinate system; accompanied by the transformation matrix The expression is: in, c p e and c R e The position of the camera coordinate system in the terminal coordinate system is in the "eye-on-hand" configuration, and its value is obtained by hand-eye calibration. The acceleration of the visual feature is obtained by derivatizing Equation (6) with respect to time: Formula (8) can be rewritten as: in, The characteristic Jacobian matrix representing the visual servoing, and:

3. The variable admittance control method based on visual features according to claim 2, characterized in that: The admittance control framework of the visual feature space in step 3 specifically includes: Let Σ c is the pose of the current camera coordinate system in the base coordinate system, Σ d is the desired camera coordinate system pose; represents the error vector between the desired visual features and the current visual features; the impedance control in the feature space aims to achieve the following dynamic behavior: Among them, M s ,D s and K s is a diagonally positive definite k × k matrix representing the relative virtual mass, damper, and stiffness in the feature space; It is a virtual force projected into the feature space and acting on the visual features; The dynamics of a serial robot is a coupled nonlinear second-order differential equation written as: in are the gravity term and the Coriolis force term, e F ext is the six-dimensional external force spinor acting on the end of the robot with reference to the end coordinate system; according to (12) and (9), we can get: Considering the characteristic Jacobian matrix and six-dimensional force spinor e F ext The adjoint transformation from the end coordinate system to the camera coordinate system is in c F ext is the external force in the reference camera coordinate system, and we get: in, is the inverse of the robot inertia matrix projected in the camera coordinate system; Equation (14) shows how the force acting on the camera coordinate system is projected into the feature space as a virtual force acting on the image features; by rewriting some terms in Equation (13): f s =J s M(q) -1 τ, (15) b s =J s M(q) -1 b, (16) Get the dynamic model in the feature space: The system in the feature space has no inertia; it behaves as a mechanical system with unit mass or inertia; the control input of the robot model in the feature space is a virtual force u = f s When the external force F ext When it cannot be measured Define the following controller: u=w-h q +b s (19) Substituting equation (19) into equation (18) yields the dynamics after compensation: in, represents the command acceleration in the feature space, and the following values ​​are selected: Combining equations (18), (19) and (21), we can obtain the closed-loop dynamics of the feature space: The closed-loop dynamics (22) are similar to the target dynamics (11), except that M s is replaced by the identity matrix; the external forces applied to the robot are measured and fully compensated for; in the case of external forces e F ext When it can be measured, the feature space controller u is defined as: u=w-h q +b s +L s M c c F ext (23) The controller (23) fully compensates for the external force. Substituting (23) into (18) yields: The command acceleration w is defined as: in and are the desired representation mass and inertia respectively; combining (18), (23) and (25) we get the closed-loop dynamics of the feature space: in Compared with Equation (26), the projected external force in the feature space is No longer dependent on robot joint angles.

4. The variable admittance control method based on visual features according to claim 3, characterized in that: The preset precision variable impedance control based on the barrier function in step 4 specifically includes: The composite tracking error is introduced to combine the position and velocity errors to accurately characterize the tracking performance of the system. In the joint space, the composite tracking error is defined as: When Λ=diag(λ1,...,λ n ),λ i > 0, i = 1, ..., n, the joint space error boundary vector is ζ = diag (ζ1, ..., ζ n ),λ i >0,i=1,...,n; The goal of joint space preset precision variable impedance control is to design the following joint space variable impedance model: in and Represent the time-varying stiffness and damping respectively, ensuring the error |e during the interaction process i |<ζ i ,i=1,...,n,i=1,...,m, where e i is the tracking error vector e i The i-th element of ; In Cartesian space, the composite tracking error is similarly defined as: where Γ=diag(γ1,...,γ n ),γ i >0,i=1,...,n, the Cartesian space error boundary vector is ξ=[ξ1,...,ξ n ],ξ i >0, i=1,...,n; The goal of Cartesian space preset precision variable impedance control is to design the following Cartesian space variable impedance model: in and Represent the time-varying stiffness and damping respectively, ensuring the error |e during the interaction process task,i |<ξ i ,i=1,...,m, where e task,i is the Cartesian error vector e task The i-th element of ; Consider the following joint space impedance model: Where B=diag(b1,...,b n )and where b i >0,ζ i >0,i=1,...,n; This impedance model \ref{eq3.3_1} is interpreted as a variable stiffness and damping model, expressed as: in Both are time-varying; based on the variable impedance model (32), the following joint space variable impedance control law is proposed: For IBVS, the variable admittance law of the barrier function is extended to the feature space and the variable admittance model is defined as: And variable admittance law and composite error: where X = diag(χ1,...,χ k ),χ i >0,i=1,...,k, the visual feature space error boundary vector η=[η1,...,η k ],η i >0,i=1,...,k,P=diag(p1,v,p k )and b i >0,ζ i >0,i=1,...,k;s * represents the compliant coordinates; in visual admittance control, the compliant coordinates serve as the input of the visual control loop; separated from (34) And integrate it twice to get and s * As the compliant coordinates; change the controller (5) to: That is, achieving the desired compliant behavior in the feature space (34); The control system modifies the reference visual features based on the visual feature space and admittance control to achieve compliance along the direction of the visual features. Different compliance behaviors are achieved according to the type of selected visual features and different variable impedance parameters. When the robot is not subjected to external forces, s * =s d , at this time the visual servo controller (38) is consistent with (5).

Images