A rigid graph-based multi-fingered hand precise manipulation control method

Abstract

The application discloses a kind of rigid graph theory-based multi-fingered hand accurate manipulation control method, first design a kind of coupled dynamics model of multi-fingered hand object manipulation, for accurately simulating the dynamic process of multi-fingered hand object manipulation.The core innovation of the application is to introduce rigid constraint to optimize the internal force distribution in the process of grabbing, so as to ensure that the contact point can maintain the initial configuration when the finger interacts with the object.Further, for the contact force distribution problem under the condition of friction constraint, an optimization framework is designed to achieve the optimal configuration of finger contact force.Finally, the control algorithm is designed in the Jacobian zero space of finger to prevent the finger joint from being in singular position.Through a series of innovative steps, the application significantly improves the performance of multi-fingered hand in precision manipulation task, especially in the breakthrough of maintaining operation precision and stability, which has important value for promoting the progress and application expansion of manipulator technology.

Description

Technical Field

[0001] This invention relates to the field of robotics, and particularly to a method for precise manipulation control of multi-fingered dexterous hands based on rigid graph theory. This method aims to improve the accuracy and stability of robotic hand grasping and manipulation, preventing damage to fragile objects during manipulation, while avoiding finger joints from falling into singular configurations, thus achieving more efficient and safer performance. Background Technology

[0002] In the development of multi-finger dexterity hand manipulation technology, achieving efficient and precise grasping and manipulation control has always been a key research focus. Especially in scenarios requiring dexterity hands to simulate the finer details of a human hand, ensuring grasping stability and operational safety has become a critical challenge for technological development. Existing technologies, in terms of grasping force planning and control strategies, often fail to effectively guarantee that the fingers maintain their initial configuration—that is, the initial grasping point position of the fingertips on the object—during grasping tasks. This can easily lead to the object slipping or being misaligned, especially when handling smooth or easily deformable objects.

[0003] For example, Chinese Patent Publication No. CN117428786A provides a method for optimizing the grasping force of a multi-finger dexterous hand based on quadratic programming. This invention focuses on optimizing the grasping force of a multi-finger dexterous hand, establishing the grasping force as a quadratic programming scheme for optimal control, then transforming it into a system of nonlinear equations, and finally solving it using a disturbance-resistant optimal grasping force solver based on neurodynamics. This allows the multi-finger dexterous hand to manipulate objects while minimizing the manipulation force to resist external disturbances and avoid damaging the object. However, this invention does not consider how to maintain the initial configuration of the finger's contact point on the object or how to prevent the finger from getting stuck in a strange configuration during manipulation.

[0004] To address the aforementioned issues, this proposal suggests an innovative approach: applying rigid graph theory to the fingertip grasping force planning of dexterous hands to optimize the distribution of grasping forces. This ensures that the fingers maintain their initial configuration throughout the grasping process, significantly reducing the risk of slippage. Furthermore, this approach constructs an optimization problem to adjust the internal grasping forces, effectively minimizing the applied force. This not only improves grasping efficiency but also reduces potential damage to the grasped object.

[0005] Meanwhile, addressing the problem in existing technologies where dexterous hands are prone to getting stuck in singular positions due to improper finger joint placement, this solution innovatively designs a control algorithm within the null space of the Jacobian matrix. This method not only prevents singular finger joint placement but also avoids control failures and inaccurate movements caused by finger joints getting stuck in singular positions, significantly improving the operational flexibility and reliability of dexterous hands.

[0006] In summary, compared with existing technologies, this solution has significant advantages in maintaining the stability of dexterous hand grasping, preventing operational errors, and improving grasping efficiency, providing a brand-new solution for dexterous hand grasping force planning and control technology. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the main objective of this invention is to provide a method for planning and controlling the grasping force of a multi-finger dexterous hand under rigid constraints. This method effectively solves the problems in the prior art: when a multi-finger dexterous hand manipulates an object, it ensures that the contact points of the fingers maintain their initial configuration during interaction with the object, while preventing finger joints from falling into unusual positions, thereby improving the accuracy and stability of the manipulation process, as shown in the flowchart. Figure 1 As shown, the specific technical solution of the present invention is as follows:

[0008] A precise manipulation control method for multi-finger dexterous hands based on rigid graph theory, the framework of which includes the following specific steps:

[0009] S1: Establish a coupled dynamics model for precise manipulation of a multi-fingered dexterous hand, comprehensively analyzing the mechanical structure and motion characteristics of each joint. First, the degrees of freedom and geometry of each finger are studied in detail to determine its possible range and direction of motion. Through theoretical calculations, a Jacobian matrix is ​​constructed to describe the transformation relationship between finger joint space and Cartesian space. Simultaneously, a grasping matrix is ​​constructed to accurately reflect the contact relationship between the finger and the object, including the location of the contact point, force distribution, and possible frictional forces. This entire process ensures that the coupled dynamics model can accurately describe the interaction between the multi-fingered dexterous hand and the object under different scenarios, enabling the dexterous hand to possess both stability and flexibility when manipulating objects.

[0010] S2: Planning the fingertip contact force. This step incorporates rigid constraints to ensure that the dexterous hand can stably grasp and maintain the initial configuration of the contact point when manipulating the target object. To achieve this, the manipulation force is first calculated based on the desired object motion, ensuring its magnitude and direction match the operational requirements. This can be done through modeling, simulation, and experimental data acquisition. Simultaneously, the manipulation force is optimized to ensure the object remains stable during movement and rotation. Second, under rigid and frictional constraints, internal forces are planned to maintain the initial configuration of the contact point. Through frictional analysis, the coefficient of friction between the finger and the object is calculated, and the distribution and magnitude of internal forces are planned according to different constraint conditions to ensure the finger remains balanced during manipulation. Finally, this planning process ensures that the multi-fingered dexterous hand can stably grasp and manipulate objects while maintaining the accurate configuration of the contact point.

[0011] S3: To ensure that the multi-fingered dexterous hand stays away from joint singularities when manipulating objects, the null space of the Jacobian matrix is ​​applied. The null space is the vector space in the Jacobian matrix that makes the output result zero. By utilizing this property, it can be ensured that the fingers avoid entering the singular positions of the joints during operation, thereby improving the operational stability of the dexterous hand. To achieve this goal, the Jacobian matrix must first be analyzed to determine its null space range. Then, a manipulation strategy is formulated to ensure that the movement path of the fingers remains within the null space of the Jacobian matrix when manipulating objects. This process includes adjusting joint angles and controlling finger movement trajectories to avoid the risk of joint singularities. In this way, the multi-fingered dexterous hand can operate more smoothly and flexibly, and reduce operational problems that may be caused by joint singularities.

[0012] S4: A PD (Proportional-Derivative) control algorithm is used to design the control law to ensure that the multi-fingered dexterous hand can accurately manipulate the position and orientation of the target object. First, the position error and orientation error of the target object are defined as inputs to the controller. Then, a PD controller is designed, in which the proportional term (P) is used to respond to the position error and the derivative term (D) is used to respond to the orientation error, thereby adjusting the relationship between the control quantity and the error. The design goal of the control law is to enable the multi-fingered dexterous hand to stably maintain the target position and orientation. Considering the dynamic characteristics of the fingers and environmental conditions, in practical applications, error is monitored by real-time acquisition of sensor data, and the parameters of the PD controller are adjusted in real time according to these errors to ensure that the system can respond quickly and accurately to external changes. Through this step, a PD controller that can accurately manipulate the position and orientation of the target object can be designed, thereby realizing the precise control of the multi-fingered dexterous hand.

[0013] A further improvement of the present invention is that the specific steps in S1 are as follows:

[0014] S101: This step establishes a dynamic model of multiple fingers, the mathematical expression of which is as follows:

[0015]

[0016] Where m is the number of fingers, n is the number of joints in each finger, and n i Let q represent the number of joints in the i-th finger, and q be a joint variable. The first derivative of the joint variable. J is the second derivative of the joint variable. h For the Jacobian matrix of the hand, J h T Let M(q) be the transpose of the Jacobian matrix of the hand, and M(q) be the inertia matrix of the hand. Let g(q) be the Coriolis matrix of the hand, and g(q) = [g1… g m ] TLet f be the gravitational vector of the hand. c =[f c1 … f cm ] T Let be the vector of the contact force applied by the hand at the point of contact. This is for inputting joint torque.

[0017] S102: This step establishes the dynamic equations of the object's motion, and their mathematical expressions are as follows:

[0018] Where x = [p T ,η T ] T ∈R 6 Indicates the state of an object. The first derivative represents the state of an object. The second derivative represents the state of an object, p represents the object's position, η represents the object's Euler angles, and M represents the object's orientation. o (x) is the inertia matrix of the object. Let g be the Coriolis force matrix of the object. o (x) is the gravity vector of the object, G(x) is the grasping matrix, which is related to the contact method and the position of the contact point on the object, f c The contact force applied to the fingers;

[0019] S103: This step provides the velocity, force, and torque conversion relationships between the five objects, i.e.

[0020] in v is the velocity at the contact point. o Let ω be the linear velocity of the object. o Let G be the angular velocity of the object, and G be the grasping matrix. T To retrieve the transpose of a matrix, For the gripping force spiral, T is its second transformation matrix;

[0021] S104: This step is given, such as Figure 2 The coupling equations for multi-finger grasping and manipulating objects are shown.

[0022] in, J represents state variables, including object pose and joint angle variables. h + This is the pseudo-inverse of the Jacobian matrix. The inertia matrix, For the Coriolis matrix, f is the gravity vector. int In order to capture internal energy;

[0023] A further improvement of the present invention is that the specific steps in S2 are as follows:

[0024] S201: In this step, two inequality constraints for the contact forces are given, including the friction cone constraint. Force application range limitation constraint f min <f c <f max ;

[0025] Where f c Apply force to the finger, f x f is the component of the contact force along the x-axis. y Let f be the component of the contact force along the y-axis. z f is the component of the contact force along the z-axis. min f is the minimum contact force of the finger. max The maximum contact force applied by the finger;

[0026] S202: In this step, the contact forces are decoupled, and its mathematical expression is f. c =f ope +(IG + G)f int ;

[0027] Where f ope For control force, f int For internal forces, further decoupling of internal forces yields the mathematical expression: f int =f int,R +f int,μ , where f int,R For rigid internal forces, f int,μ Frictional internal force;

[0028] S203: In this step, the magnitude of the rigid internal forces is obtained through optimization. The objective function is to minimize the rigid internal forces, and the constraints are rigid constraints. Its mathematical expression is: Where R is a rigid matrix, The velocity at the point of contact;

[0029] S204: In this step, the magnitude of the internal friction force is obtained by solving the optimization method. The objective function is to minimize the internal friction force, and the constraints are friction cone constraint and force application range constraint.

[0030] A further improvement of the present invention is that the specific steps in S3 are as follows:

[0031] S301: During the manipulation of objects by a multi-finger robotic hand, there is a risk that the finger joints may become trapped in unusual configurations, directly affecting the flexibility and efficiency of the robotic hand during operation. Figure 3As shown, finger 1 has a normal configuration, and finger 2 has a singular configuration. This step establishes the relationship between finger joints falling into singular positions and the Jacobian matrix. When this phenomenon occurs, the Jacobian matrix J of the robotic arm will have at least one singular value approaching zero. Furthermore, a control algorithm is designed using the Jacobian matrix null space to keep the singular values ​​of the Jacobian matrix away from zero, thereby maintaining the robotic arm's operational flexibility and stability.

[0032] S302: In this step, the form of the entire control law is given, and its mathematical expression is as follows: τ u =τ u1 +(IJ + J)τ u2 ;

[0033] Where τ u1 For the position sub-control law, ensure that the position error and orientation error of the controlled object converge to zero, (IJ) + J) is the zero space of the Jacobian matrix, τ u2 This is a singular position control law that ensures that finger joints can be moved away from singular positions during object manipulation.

[0034] A further improvement of the present invention is that the specific steps in S4 are as follows:

[0035] S401: In this step, a PD (proportional-derivative) control strategy is used to design the position control law τ. u1 ;

[0036] S402: In this step, the singular position control law τ is designed using the gradient projection method. u2 .

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] First, this invention improves the stability of grasping. By optimizing the distribution of grasping force, it ensures that the fingers maintain their initial configuration throughout the grasping process, greatly reducing the risk of object slippage and thus improving the stability of grasping manipulation. Second, this invention reduces damage to the grasped object. By adjusting the internal grasping force, it minimizes the applied force, not only improving grasping efficiency but also reducing potential damage to the grasped object, making the method suitable for manipulating fragile or easily damaged objects. Furthermore, this invention avoids finger joints getting stuck in singular configurations. It innovatively designs the control algorithm within the null space of the Jacobian matrix, effectively preventing singular position phenomena of finger joints. This avoids control failures and inaccurate movements caused by finger joints getting stuck in singular positions, significantly improving the operational flexibility and reliability of dexterous hands, and has broad application prospects. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating a precise manipulation control method for a multi-finger dexterous hand based on rigid graph theory according to the present invention.

[0040] Figure 2 This is a schematic diagram of finger manipulation of an object in three-dimensional space.

[0041] Figure 3 This is a diagram showing a finger stuck in an unusual joint position.

[0042] Figure 4 The flowchart for step S1 is shown.

[0043] Figure 5 The flowchart for step S2 is shown.

[0044] Figure 6 The flowchart for the S3 step algorithm is shown below.

[0045] Figure 7 The flowchart for the S4 step algorithm is shown below. Detailed Implementation

[0046] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0047] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0048] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0049] Example

[0050] This embodiment describes a multi-fingered dexterous hand grasping force planning and control method applied in automobile manufacturing. In this scenario, the multi-fingered dexterous hand is used to grasp and position automotive parts, such as doors, hoods, or other large metal components. These parts require not only high positioning accuracy during assembly to ensure assembly quality, but also precise force control due to their weight and size to avoid damage or misoperation. On the automobile manufacturing assembly line, according to the method proposed in this invention, the multi-fingered dexterous hand, through the coordinated action of its multiple fingers, achieves stable grasping and precise manipulation of large automotive parts, such as… Figure 1As shown, a method for precise manipulation and control of a multi-finger dexterous hand based on rigid graph theory includes the following specific steps:

[0051] S1: Establish a coupled dynamics model for precise manipulation of multi-fingered dexterous hands, and comprehensively analyze the mechanical structure and motion characteristics of each joint of the dexterous hand. First, study the degrees of freedom and geometry of each finger in detail to determine its possible range of motion and direction. Through theoretical calculations, construct the Jacobian matrix to describe the transformation relationship between finger joint space and Cartesian space. At the same time, construct the grasping matrix to accurately reflect the contact relationship between the fingers and the object, including the position of the contact point, the distribution of force, and possible friction. The whole process ensures that the coupled dynamics model can accurately describe the interaction between the multi-fingered dexterous hand and the object under different scenarios, so that the dexterous hand has stability and flexibility when manipulating objects.

[0052] The specific steps in S1 are as follows:

[0053] S101: This step establishes a dynamic model of multiple fingers, the mathematical expression of which is as follows:

[0054] Where m is the number of fingers, n is the number of joints in each finger, and n i Let q represent the number of joints in the i-th finger, and q be a joint variable. The first derivative of the joint variable. J is the second derivative of the joint variable. h For the Jacobian matrix of the hand, J h T Let M(q) be the transpose of the Jacobian matrix of the hand, and M(q) be the inertia matrix of the hand. Let g(q) be the Coriolis matrix of the hand, and g(q) = [g1… g m ] T Let f be the gravitational vector of the hand. c =[f c1 … f cm ] T Let be the vector of the contact force applied by the hand at the point of contact. This is for inputting joint torque.

[0055] S102: This step establishes the dynamic equations of the object's motion, and their mathematical expressions are as follows:

[0056] Where x = [p T ,η T ] T ∈R 6 Indicates the state of an object. The first derivative represents the state of an object. The second derivative represents the state of an object, p represents the object's position, η represents the object's Euler angles, and M represents the object's orientation. o (x) is the inertia matrix of the object. Let g be the Coriolis force matrix of the object. o (x) is the gravity vector of the object, G(x) is the grasping matrix, which is related to the contact method and the position of the contact point on the object, f c The contact force applied to the fingers.

[0057] S103: This step provides the velocity, force, and torque conversion relationships between the five objects, i.e.

[0058] in v is the velocity at the contact point. o Let ω be the linear velocity of the object. o Let G be the angular velocity of the object, and G be the grasping matrix. T To retrieve the transpose of a matrix, For the gripping force spiral, T is the second transformation matrix.

[0059] S104: This step provides the coupling equations for the manipulated object.

[0060] in, J represents state variables, including object pose and joint angle variables. h + This is the pseudo-inverse of the Jacobian matrix. The inertia matrix, For the Coriolis matrix, f is the gravity vector. int In order to capture internal energy.

[0061] The specific implementation flowchart is as follows: Figure 4 As shown, firstly, the mass, length, and initial position of the contact point of the target object and finger are defined. Then, the parameters in the dynamic equation are calculated according to steps S101 and S102. Next, the desired trajectory of the object is given, and the trajectory of the contact point is solved according to the contact method given in step S103. The trajectory in the joint space is solved by the inverse kinematics of the linkage system, and it is analyzed whether the joint trajectory conforms to the finger posture. If it does, the joint trajectory information is saved and the process ends. If it does not, a new set of inverse kinematic trajectories is used and analyzed.

[0062] S2: Planning fingertip contact forces. The goal of planning fingertip contact forces is to ensure that the dexterous hand can stably grasp and maintain the initial configuration of the contact point when manipulating the target object. To achieve this goal, the manipulation force must first be calculated based on the desired object motion, ensuring that its magnitude and direction match the operational requirements. This can be done through modeling, simulation, and experimental data acquisition. At the same time, the manipulation force is optimized to ensure that the object remains stable during movement and rotation. Second, under rigid and frictional constraints, internal forces are planned to maintain the initial configuration of the contact point. Through frictional analysis, the coefficient of friction between the finger and the object is calculated, and the distribution and magnitude of internal forces are planned according to different constraint conditions to ensure that the finger remains balanced during manipulation. Finally, this planning process ensures that the multi-fingered dexterous hand can stably grasp and manipulate objects while maintaining the accurate configuration of the contact point.

[0063] The specific steps in S2 are as follows:

[0064] S201: In this step, two inequality constraints for the contact forces are given, including the friction cone constraint. Force application range limitation constraint f min <f c <f max ;

[0065] S202: In this step, the contact forces are decoupled, and its mathematical expression is f. c =f ope +(IG + G)f int ;

[0066] Where f ope For control force, f int For internal forces, further decoupling of internal forces yields the mathematical expression: f int =f int,R +f int,μ , where f int,R For rigid internal forces, f int,μ Frictional internal force;

[0067] S203: In this step, the magnitude of the rigid internal forces is obtained through optimization. The objective function is to minimize the rigid internal forces, and the constraints are rigid constraints. Its mathematical expression is: Where R is a rigid matrix;

[0068] S204: In this step, the magnitude of the internal friction force is obtained by solving the optimization method. The objective function is to minimize the internal friction force, and the constraints are friction cone constraint and force application range constraint.

[0069] The specific implementation flowchart is as follows: Figure 5As shown, the trajectory of the contact point is first obtained from S1. Then, the kinematic equation of the object is substituted to obtain the desired motion force spiral of the object, and the control force is calculated. Based on the trajectory of the contact point, the stiffness matrix is ​​calculated. The rigid internal forces are optimized by solving the rigid internal forces, and the magnitude of the contact force is calculated by the resultant force of the control force. It is then determined whether the contact force satisfies the friction cone constraint. If it does, the internal force data is saved and the process ends. If it does not, the friction internal forces are optimized to ensure that the total resultant force satisfies the friction cone constraint.

[0070] S3: To ensure that the multi-fingered dexterous hand stays away from joint singularities when manipulating objects, the null space of the Jacobian matrix is ​​applied. The null space is the vector space in the Jacobian matrix that makes the output result zero. By utilizing this property, it can be ensured that the fingers avoid entering the singular positions of the joints during operation, thereby improving the operational stability of the dexterous hand. To achieve this goal, the Jacobian matrix must first be analyzed to determine its null space range. Then, a manipulation strategy is formulated to ensure that the movement path of the fingers remains within the null space of the Jacobian matrix when manipulating objects. This process includes adjusting joint angles and controlling finger movement trajectories to avoid the risk of joint singularities. In this way, the multi-fingered dexterous hand can operate more smoothly and flexibly, and reduce operational problems that may be caused by joint singularities.

[0071] The specific steps in S3 are as follows:

[0072] S301: In this step, the relationship between the finger joint falling into a singular position and the Jacobian matrix is ​​given, and the Jacobian matrix null space design control algorithm is used to move away from the singular position of the joint, so as to keep the singular value of the Jacobian matrix away from the zero point, thereby maintaining the operational flexibility and stability of the robot hand.

[0073] S302: In this step, the form of the entire control law is given, and its mathematical expression is as follows: τ u =τ u1 +(IJ + J)τ u2 ;

[0074] Where τ u1 For the position sub-control law, ensure that the position error and orientation error of the controlled object converge to zero, (IJ) + J) is the zero space of the Jacobian matrix, τ u2 This is a singular position control law that ensures that finger joints can move away from singular positions during object manipulation.

[0075] The specific implementation flowchart is as follows: Figure 6 As shown, the Jacobian matrix is ​​calculated based on the result of step S1, then the null space of the Jacobian matrix is ​​calculated, the data is saved, and sent to step S4.

[0076] S4: A PD (Proportional-Derivative) control algorithm is used to design the control law to ensure that the multi-finger dexterity hand can accurately manipulate the position and orientation of the target object. First, the position error and orientation error of the target object are defined as inputs to the controller. Then, a PD controller is designed, in which the proportional term (P) is used to respond to the position error and the derivative term (D) is used to respond to the orientation error, thereby adjusting the relationship between the control quantity and the error. The design goal of the control law is to enable the multi-finger dexterity hand to stably maintain the target position and orientation. Considering the dynamic characteristics of the fingers and environmental conditions, in practical applications, error is monitored by real-time acquisition of sensor data, and the parameters of the PD controller are adjusted in real time according to these errors to ensure that the system can respond quickly and accurately to external changes. Through this step, a PD controller that can accurately manipulate the position and orientation of the target object can be designed, thereby realizing the precise control of the multi-finger dexterity hand.

[0077] The specific steps in S4 are as follows:

[0078] S401: In this step, a PD (proportional-derivative) control strategy is used to design the position control law τ. u1 ;

[0079] S402: In this step, the singular position control law τ is designed using the gradient projection method. u2 .

[0080] The specific implementation flowchart is as follows: Figure 7 As shown, according to steps S2 and S3, the desired trajectory and internal forces are introduced. The error is defined and calculated based on the current trajectory and the desired trajectory. The control input joint torque is calculated to update the object position. It is determined whether the object has reached the desired pose. If yes, the process ends; otherwise, it returns to the error calculation step. This process is repeated until the object's position error and orientation error converge to zero.

[0081] Could you combine simulation or relevant experimental data for comparison, and illustrate the technical advantages of this invention with the data, such as its good robustness, good control precision, and good flexibility?

[0082] Through the implementation of this invention, the application of multi-fingered dexterous hands in the automotive manufacturing industry has significantly improved assembly efficiency and quality. In particular, when handling the assembly of large or heavy automotive parts, it has demonstrated excellent operational precision and stability, which is of great practical significance for promoting the development of automotive manufacturing technology.

[0083] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for precise manipulation and control of a multi-finger dexterous hand based on rigid graph theory, characterized in that, Includes the following steps: S1: Establish a coupled dynamic model for precise manipulation of multi-finger dexterity hand, and comprehensively analyze the mechanical structure of dexterity hand and the motion characteristics of each joint; Based on the degrees of freedom and geometry of each finger, its possible range of motion and direction are determined. Through theoretical calculations, a Jacobian matrix is ​​constructed to describe the transformation relationship between finger joint space and Cartesian space. Construct a grasping matrix to accurately reflect the contact relationship between the fingers and the object, including the location of the contact point, the distribution of force and possible friction, to ensure that the coupled dynamics model can accurately describe the interaction between the multi-finger dexterity hand and the object in different scenarios, so that the dexterity hand has stability and flexibility when manipulating the object. S2: Planning fingertip contact force. The goal of planning fingertip contact force is to ensure that the dexterous hand can stably grasp and maintain the initial configuration of the contact point when manipulating the target object. The manipulation force is calculated based on the desired object motion to ensure that its magnitude and direction match the operation requirements. This is done through modeling, simulation, and experimental data acquisition. At the same time, the manipulation force is optimized to ensure that the object remains stable during movement and rotation. Under rigid and frictional constraints, internal forces are planned to maintain the initial configuration of the contact point. Through frictional analysis, the friction coefficient between the finger and the object is calculated, and the distribution and magnitude of internal forces are planned according to different constraint conditions to ensure that the finger remains in balance during manipulation. During the planning process, ensure that the multi-fingered dexterous hand can stably grasp and manipulate objects while maintaining the accurate configuration of the contact point; S3: To ensure that multi-finger dexterity hands stay away from joint singularities when manipulating objects, the null space of the Jacobian matrix is ​​applied. The null space is the vector space in the Jacobian matrix that makes the output result zero, ensuring that the fingers avoid entering the singular positions of the joints during operation; first, the Jacobian matrix is ​​analyzed to determine its null space range. Then, a manipulation strategy is developed to ensure that the movement path of the fingers remains within the null space of the Jacobian matrix when manipulating objects, including adjusting joint angles and controlling the movement trajectory of the fingers to avoid the risk of singular joint positions. S4: The control law is designed using the PD proportional-derivative control algorithm to ensure that the multi-finger dexterity hand can accurately manipulate the position and orientation of the target object; First, define the position error and orientation error of the target object as inputs to the controller; Subsequently, a PD controller was designed, in which the proportional term P is used to respond to position error and the derivative term D is used to respond to orientation error, thereby adjusting the relationship between the control quantity and the error. The design goal of the control law is to enable the multi-finger dexterity hand to stably maintain the target position and orientation. Considering the dynamic characteristics of the fingers and environmental conditions, the error is monitored by real-time acquisition of sensor data, and the parameters of the PD controller are adjusted in real time according to the monitored error to ensure that the system can respond quickly and accurately to external changes. A PD controller capable of precisely manipulating the position and orientation of the target object is designed, thereby realizing the precise control of the multi-finger dexterity hand. The specific steps in S1 are as follows: S101: First, establish the dynamic model of the multiple fingers, the expression of which is as follows: ; in, The number of fingers. The number of joints for each finger. Indicates the first The number of joints in each finger. For joint variables, The first derivative of the joint variable. The second derivative of the joint variable. The Jacobian matrix for the hand, Let be the transpose of the Jacobian matrix of the hand. The inertia matrix of the hand, The Coriolis matrix for the hand, Let be the gravitational vector of the hand. Let be the vector of the contact force applied by the hand at the point of contact. Input joint torque; S102: Establish the dynamic equations of the object's motion, the expression of which is as follows: ; Among them, Indicates the state of an object. The first derivative represents the state of an object. The second derivative represents the state of an object. This refers to the object's position information. This provides the Euler angle orientation information of the object. Let be the object's inertia matrix. Let be the Coriolis force matrix of the object. Let be the object's gravitational vector. The method of capturing the matrix depends on the contact method and the position of the contact point on the object. The contact force applied to the fingers; S103: Give the velocity, force, and torque conversion relationships between the five objects, i.e. , ; in For the contact point velocity, Let be the linear velocity of the object. Let be the angular velocity of the object. To capture the matrix, To retrieve the transpose of a matrix, For gripping force spiral, This is the next transformation matrix; S104: Give the coupling equations for the manipulated object. ; in, These are state variables, including object pose and joint angle variables. This is the pseudo-inverse of the Jacobian matrix. The inertia matrix, For the Coriolis matrix, The gravity vector In order to capture internal energy.

2. The method for precise manipulation and control of a multi-finger dexterous hand based on rigid graph theory according to claim 1, characterized in that: The specific steps in S2 are as follows: S201: Provides two inequality constraints for contact forces, friction cone constraint. Force application range limitation constraints ; in Apply force to the fingers, The contact force is the component along the x-axis. Let the contact force be the component along the y-axis. Let the contact force be the component along the z-axis. This represents the minimum contact force of the fingers. The maximum contact force applied by the finger; S202: Decoupling of contact forces, its mathematical expression is as follows: ; in For control force, For internal forces, further decoupling of internal forces yields the following mathematical expression: ,in For rigid internal forces, Frictional internal force; S203: The magnitude of the rigid internal force is obtained through optimization. The objective function is to minimize the rigid internal force, and the constraints are rigid constraints. Its expression is: ,in, It is a rigid matrix. The velocity at the point of contact; S204: In this step, the magnitude of the frictional internal force is obtained by solving the optimization method. The objective function is to minimize the frictional internal force, and the constraints are friction cone constraint and force application range constraint.

3. The method for precise manipulation and control of a multi-finger dexterous hand based on rigid graph theory according to claim 2, characterized in that: The specific steps in S3 are as follows: S301: The relationship between finger joints falling into singular positions and the Jacobian matrix is ​​given, and the control algorithm is designed using the Jacobian matrix null space to keep the singular values ​​of the Jacobian matrix away from the singular positions of the joints, thereby maintaining the operational flexibility and stability of the robot. S302: The form of the entire control law is given, and its expression is as follows: ; in This is a position control law that ensures the position and orientation errors of the controlled object converge to zero. Let the zero space be the Jacobian matrix. This is a singular position control law that ensures that finger joints are kept away from singular positions during object manipulation.

4. The method for precise manipulation and control of a multi-finger dexterous hand based on rigid graph theory according to claim 3, characterized in that: The specific steps in S4 are as follows: S401: Position control law is designed using a PD proportional-derivative control strategy. ; S402: Design of Singular Position Control Laws Using Gradient Projection Method .

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