A kinematics solution method for underactuated dexterous fingers

Abstract

This invention relates to a kinematics calculation method for an underactuated dexterous finger, comprising: Step 1, setting the line connecting the two centers of a rotational joint as a virtual link and describing the state of each joint; Step 2, establishing an improved D-H parameter table to obtain parameters including θ. ROLL θ MCP θ PIP The variable is the fingertip pose matrix; Step 3: Obtain the metacarpophalangeal joint angle θ. MCP With drive rope contraction l MCP Relationship and corresponding motor control position length P MCP Step 4: Obtain the lateral joint angle θ ROLL With drive rope contraction l ROLL Relationship and corresponding motor control position length P ROLL Step 5: According to P MCP and P ROLL Obtain the actual control position length P of the linear motor left and P right Step 6: Obtain the proximal interphalangeal joint angle θ PIP l with the amount of drive rope contraction PIP Relationship and corresponding motor control position length P PIP Step 7: According to P PIP Obtain the actual control position length P of the intermediate linear motor center Step 8: Controlling finger movement. This invention utilizes virtual linkages to perform kinematic modeling of the fingers, solving the joint rolling problem while achieving real-time and visualized control of the fingers.

Description

Technical Field

[0001] This invention relates to the field of robotics, and more specifically to a method for kinematic calculation of an underactuated dexterous finger. Background Technology

[0002] The hand is the most flexible movement structure in the human body. Humans cannot perform fine and flexible operations without the participation of the hand. Whether it is a complex object with an irregular shape or a small and light object, humans can achieve precise and reliable grasping and manipulation of objects through the coordinated movement of multiple fingers. Therefore, multi-fingered dexterous hands in robots have become one of the research hotspots in the field of robotics.

[0003] For the design of multi-fingered dexterous hands, a fully actuated approach—where the number of actuators equals the number of finger degrees of freedom—while achieving complete system control and stability, results in over 20 active degrees of freedom. This leads to poor overall system integration and requires numerous control joints and actuators. Especially with the drive motors placed directly at the finger joints, the fingers, often several times larger than normal human fingers, lack human-like characteristics. Furthermore, the motors at the joints reduce the fingers' flexibility against external impacts; a single significant impact can damage a joint motor. The large number of actuators also makes fully actuated dexterous finger control complex and prohibitively expensive. Therefore, current dexterous finger designs often employ underactuated approaches. Tendon Driven (wire drive) provides significant flexibility in the confined and precise space of a dexterous hand, allowing actuators to be moved back to reduce finger mass, decrease inertia, and increase resistance to impacts.

[0004] However, underactuated fingers, due to their fewer actuators than degrees of freedom, present significant challenges in kinematic calculation and complex motion control. These issues have long been bottlenecks restricting the application of dexterity. Kinematic modeling of underactuated fingers is a prerequisite for solving control problems, making accurate and appropriate kinematic modeling crucial for their control. Current research on dexterity often references the characteristics of human fingers. Except for the thumb, each human finger has four phalanges: metacarpal, proximal, intermediate, and distal. Therefore, if… Figure 1 As shown, the joints of a dexterous finger are generally named the metacarpophalangeal joint (MCP), proximal interphalangeal joint (PIP), and distal interphalangeal joint (DIP), with 2, 1, and 1 degrees of freedom, respectively. If the controlled finger adopts an underactuated design scheme with wire drive (left, middle, and right drive ropes, each drive rope corresponding to a linear motor) and the design is completely anthropomorphic, then the finger is generally connected by a non-fixed splicing method where four phalanges are connected together by wires. Figure 2As shown, when a single joint rotates, it does not rotate coaxially; it simultaneously exhibits both rotational and translational motions. Therefore, traditional hinge-based kinematics solutions cannot be used. Furthermore, due to the flexibility of the rope, this presents significant challenges for establishing the kinematic model and subsequent control. Summary of the Invention

[0005] The purpose of this invention is to provide a kinematic calculation method for underactuated dexterous fingers. This method uses virtual links to perform kinematic modeling of underactuated dexterous fingers, which solves the rolling problem that occurs when the non-fixed joints of the fingers rotate. This allows for a quantitative description of the mapping relationship between the drive rope length and the joint angle, and enables real-time and visualized control of the fingers.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A kinematics solution method for an underactuated dexterous finger includes the following steps:

[0008] Step 1: Use rotational joints to describe the motion states of the lateral joint, metacarpophalangeal joint (MCP), proximal interphalangeal joint (PIP), and distal interphalangeal joint (DIP), and set the line connecting the two centers of any pair of rotational joints as a virtual link.

[0009] Step 2: Establish an improved DH parameter table based on the finger parameters, including the link length a. i-1 α, connecting rod torsion angle i-1 Linkage offset d i and joint angle θ i Among them, the joint angles θ1 to θ8 and the lateral swing joint angle θ ROLL Metacarpophalangeal joint angle θ MCP θ, the angle of the proximal interphalangeal joint PIP and distal interphalangeal joint angle θ DIP The correspondence is as follows:

[0010] θ1+θ2=θ ROLL

[0011] θ3+θ4=θ MCP

[0012] θ5+θ6=θ PIP

[0013] θ7+θ8=θ DIP (2);

[0014] The pose of the fingertip is obtained through the transformation matrix. And the fingertip pose matrix For θ ROLL θ MCP θ PIP A function with three variables;

[0015] Step 3: Obtain the metacarpophalangeal joint angle θ MCP Corresponding to the contraction amount l of the drive rope MCP The relationship is then used to obtain the corresponding motor control position length P. MCP ;

[0016] Step 4: Obtain the lateral joint angle θ ROLL l corresponding to the contraction amount of the drive rope ROLL The relationship is then used to obtain the corresponding motor control position length P. ROLL ;

[0017] Step 5, Joint angle θ ROLL and joint angle θ MCP Driven by left and right drive ropes, according to P MCP and P ROLL Obtain the actual control position length P of the two linear motors (left and right). left and P right :

[0018] P left =P left (0)-P MCP -P ROLL

[0019] P right =P right (0)-P MCP +P ROLL (11);

[0020] Step 6: Obtain the proximal interphalangeal joint angle θ PIP l corresponding to the contraction amount of the drive rope PIP The relationship is then used to obtain the corresponding motor control position length P. PIP ;

[0021] Step 7, Joint Angle θ PIP Driven by the central drive rope, according to P PIP Obtain the actual control position length P of the intermediate linear motor drive center :

[0022] P center =P center (0)-P PIP (14);

[0023] Step 8: Determine the desired joint angle θ of the finger. MCP θ ROLL θ PIP The information is then input into the system, which calculates the fingertip target pose matrix according to steps one through seven. and the control position P of each linear motor left Pright P center Used to control finger movements.

[0024] In step two: Represented by the product of transformation matrices:

[0025]

[0026] The joint angles θ1~θ8 and the lateral joint angle θ ROLL Metacarpophalangeal joint angle θ MCP θ, the angle of the proximal interphalangeal joint PIP and distal interphalangeal joint angle θ DIP The correspondence is as follows:

[0027] θ1+θ2=θ ROLL

[0028] θ3+θ4=θ MCP

[0029] θ5+θ6=θ PIP

[0030] θ7+θ8=θ DIP (2);

[0031] In equation (2) above;

[0032]

[0033]

[0034]

[0035]

[0036] In equation (3) above, r i The radius of the circle corresponding to the revolute joint;

[0037] And θ DIP =α*θ PIP (4);

[0038] In equation (4) above, the proportionality coefficient α is always equal to 2 / 3;

[0039] Substituting equations (2) to (4) into the transformation matrix equation (1), we obtain the fingertip pose matrix. For θ ROLL θ MCP θ PIP A function with three variables:

[0040]

[0041] In equation (5) above:

[0042]

[0043]

[0044]

[0045] r 12 =-s(θ) ROLL ),

[0046] r 22 =c(θ) ROLL ),

[0047] r 32 =0,

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] In the above group of equations (6), s represents sin, c represents cos, and a i Obtained from the improved DH parameter table.

[0055] In step three, the rotation of the metacarpophalangeal joint is driven by the simultaneous contraction of two linear motors, pulling the left and right drive ropes. Both the left and right drive ropes are equipped with slings connected to the metacarpophalangeal bones. These slings remain taut and of constant length. Constrained by the slings, the angle θ between the drive ropes and the metacarpophalangeal bones remains constant during rotation. The position of the hole H on the metacarpophalangeal bones and the relative position of the centers O3 and O4 of the two circles at the joint end of the rotation joint are fixed. Therefore, the distance between H and the tangent point between the two circles of the rotation joint remains constant. Simultaneously, the angle α between the line connecting H and the tangent point between the two circles of the rotation joint and the drive rope also remains constant. The drive ropes contract by l... MCP After lengthening, the point of tangency between the two circles of the rotary joint is considered to have moved along the arc O3. MCP For length, we have:

[0056] l MCP =θ MCP *r3 (7);

[0057] In equation (7) above, r3 is the radius of circle O3;

[0058] The corresponding linear motor retraction position length P MCP for:

[0059]

[0060] In equation (8) above, m is the distance to a waypoint obtained by dividing the maximum working space of the linear motor by the total number of waypoints.

[0061] In step four, the two linear motors drive the left and right drive ropes to move differentially, generating the lateral swing joint angle θ. ROLL The length of the perpendicular line between the input line hole on the lateral joint and the line connecting the centers O1 and O2 of the two circles of the corresponding rotary joint is r. R The intersection point is O. R , with O R Center r R Let a virtual circle be drawn with radius , and the arc length of the position change of the input wire hole on the virtual circle be approximately equal to the length of the drive rope contraction. Then:

[0062] l ROLL =θ ROLL *r R (9);

[0063] The corresponding length of the linear motor's contraction position is:

[0064]

[0065] In step six, the end of the drive rope is tied to the proximal interphalangeal joint to form a knot, and the initial tangent point between the two circles O5 and O6 of the joint end rotation joint is O. p The initial position of the joint to O p The distance between them is r P , with O p Center r P Draw an arc with radius l, and the arc length along which the knot travels is equivalent to the length l that drives the rope to contract. PIP Then we have:

[0066] l PIP =θ PIP *r P (12);

[0067] The corresponding length of the linear motor's contraction position is:

[0068]

[0069] In step eight, the control system includes a host computer for real-time calculation and a slave computer for controlling each linear motor. The host computer is equipped with a screen, and the slave computer is equipped with a controller.

[0070] First, input the desired joint angle θ into the host computer. MCPθ ROLL θ PIP The control positions P of the three linear motors are calculated based on steps one through seven. left P right P center and fingertip target pose matrix The data is sent to the lower-level controller, which controls each linear motor to reach the target position. Simultaneously, the controller sends the current status of the linear motors back to the upper-level computer, which calculates and obtains the real-time θ of the finger. MCP θ ROLL θ PIP Angle, thereby obtaining real-time finger position. Displayed on the screen.

[0071] The controller sends the target position to the linear motor at fixed time intervals and controls the linear motor to accurately reach the target position through PD feedback.

[0072] The advantages and positive effects of this invention are as follows:

[0073] 1. This invention utilizes virtual linkages to perform kinematic modeling of underactuated dexterous fingers, particularly for line-driven non-fixed fingers. It effectively solves the rolling problem that occurs during rotation of non-fixed joints and can quantitatively describe the mapping relationship between rope length and joint angles. Therefore, it can determine the fingertip pose at each joint angle by calculating the position of the fingertip at that joint angle. And to reach this state, the linear motor position information P needs to be sent to the controller. left P right P center This allows for real-time and visual control of the fingers.

[0074] 2. Considering that the rope, as the transmission medium, has strong flexibility and its trajectory is very complex during movement, this invention approximates the joint angle (arc length) of the finger movement and the rope length as a linear relationship. This not only does not affect the control effect, but also simplifies the model.

[0075] 3. This invention adopts a collaborative control method between upper and lower computers to give full play to the advantages of upper and lower computers. The upper computer performs a large amount of data calculation and provides a simple and user-friendly visual operation interface, which facilitates simple and intuitive control of the fingers. The lower computer is directly connected to the linear motor and realizes real-time motion control of the finger joints through closed-loop control. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the dexterous finger structure controlled by the present invention.

[0077] Figure 2 for Figure 1Schematic diagram of the coupling relationship between fixed joints in China and Africa.

[0078] Figure 3 for Figure 1 A schematic diagram of a finger model with virtual links added to a dexterous finger.

[0079] Figure 4 for Figure 3 A diagram illustrating the movement of the metacarpophalangeal joints.

[0080] Figure 5 for Figure 4 A simplified model diagram of the metacarpophalangeal joints.

[0081] Figure 6 for Figure 3 A schematic diagram of the lateral swing joint structure in the diagram.

[0082] Figure 7 for Figure 6 A simplified model diagram of the lateral swing joint in the diagram.

[0083] Figure 8 for Figure 3 A schematic diagram of the proximal interphalangeal joint structure.

[0084] Figure 9 for Figure 8 A simplified model diagram of the proximal interphalangeal joint.

[0085] Figure 10 This is a block diagram of the control system of the present invention.

[0086] Figure 11 This is a schematic diagram of the control flow of the present invention. Detailed Implementation

[0087] The invention will now be described in further detail with reference to the accompanying drawings.

[0088] like Figure 1 As shown, the finger of this invention includes a lateral pivot joint, a metacarpophalangeal joint (MCP), a proximal interphalangeal joint (PIP), and a distal interphalangeal joint (DIP). The finger is driven by lines, including left, middle, and right drive ropes, each drive rope corresponding to a linear motor. And as... Figure 2 As shown, based on the non-fixed structure of the finger, each joint of the finger can be considered as a pair of rotational joints. The above is a well-known technique in the art.

[0089] The present invention specifically includes the following steps:

[0090] Step 1: As Figures 1-3 As shown, this invention utilizes rotary joints to describe the motion state of corresponding joints, and adds virtual links at each joint of the finger. These virtual links are lines connecting the centers of two corresponding circles, such as... Figure 3As shown, the virtual link of the lateral swing joint is the line connecting the center O1 and O2, the virtual link of the metacarpophalangeal joint (MCP) is the line connecting the center O3 and O4, the virtual link of the proximal interphalangeal joint (PIP) is the line connecting the center O5 and O6, and the virtual link of the distal interphalangeal joint (DIP) is the line connecting the center O7 and O8.

[0091] like Figures 1-3 As shown, the finger can be approximated as a multi-degree-of-freedom robotic arm. The kinematic modeling method of the robotic arm is used to model the kinematics of the finger. Considering the special characteristics of the mechanical structure of the controlled finger, the present invention adds virtual links at the lateral swing, MCP, PIP and DIP joints. This can increase the degree of freedom of the finger and thus quantitatively describe the motion posture of the joint.

[0092] Step 2: Establish an improved DH parameter table based on the finger parameters, and obtain the fingertip pose through the transformation matrix. This completes the mapping relationship from joint space to Cartesian space (base coordinate system).

[0093] An improved DH parameter table was established based on the finger parameters. The established parameter table is shown in Table 1 below.

[0094] Table 1. Parameters of the Finger-Modified DH

[0095] i <![CDATA[α i-1 ]]> <![CDATA[a i-1 ]]> <![CDATA[d i ]]> <![CDATA[θ i-1 ]]> 1 0 0 0 <![CDATA[θ1]]> 2 0 <![CDATA[a1]]> 0 <![CDATA[θ2]]> 3 90° <![CDATA[a2]]> 0 <![CDATA[θ3]]> 4 0 <![CDATA[a3]]> 0 <![CDATA[θ4]]> 5 0 <![CDATA[a4]]> 0 <![CDATA[θ5]]> 6 0 <![CDATA[a5]]> 0 <![CDATA[θ6]]> 7 0 <![CDATA[a6]]> 0 <![CDATA[θ7]]> 8 0 <![CDATA[a7]]> 0 <![CDATA[θ8]]> 9 -90° <![CDATA[a8]]> 0 <![CDATA[θ9]]>

[0096] The improved DH parameter table based on finger parameters can be found in "Introduction to Robotics". For a multi-rigid-body serial robot, each link can be described by four kinematic parameters: two parameters describe the link itself, and the other two describe the connection between links. Adjacent links i-1 and i share a common joint axis. The length of the common perpendicular between joint axis i-1 and joint axis i is called the link length, denoted as a. i-1 The angle between joint axis i-1 and joint axis i is called the link torsion angle, denoted as α. i-1 The distance along the common axis of two adjacent links can be described by a parameter called the link offset, which is denoted as d on joint axis i. i Another parameter describes the angle between two adjacent links rotating about a common axis; this parameter is called the joint angle, denoted as θ. i .

[0097] For the purposes of this invention, in Table 1 above, links i = 2, 4, 6, and 8 are virtual links. Figure 3 The numbers (01O2, O3O4, O5O6, O7O8) are represented by dashed lines.

[0098] The pose of the fingertip relative to the finger base coordinate system. This can be represented by the product of transformation matrices:

[0099]

[0100] In equation (1) above, link 9 is added to describe the fingertip pose state, and it does not have an active degree of freedom, meaning the joint angle θ9 is always 0. However, as... Figure 3 and Figure 7 As shown, the remaining eight joint angles θ1 to θ8 are paired up to represent the lateral swing joint angles θ. ROLL Metacarpophalangeal joint angle θ MCP θ, the angle of the proximal interphalangeal joint PIP and distal interphalangeal joint angle θ DIP The corresponding relationship is as follows:

[0101] θ1+θ2=g ROLL

[0102] θ3+θ4=θ MCP

[0103] θ5+θ6=θ PIP

[0104] θ7+θ8=θ DIP (2);

[0105] In the above group of equations (2), each group of joint angles has a coupling relationship, such as Figure 2 As shown, when the joint rotates by an angle θ, it is constrained by the stiff and flexible rope in the diagram, and the joint only undergoes rolling motion. Therefore... Figure 2 The roll angle θ r The joint angle θ has the following relationship:

[0106]

[0107] Furthermore, due to the characteristics of finger structure, the pulley radius and the outline radius can be made equal, that is... Therefore:

[0108]

[0109]

[0110]

[0111]

[0112] In equation (3) above, r i The radius of the circle corresponding to the rotary joint.

[0113] And such Figure 1As shown, the finger PIP and DIP joints are underactuated, meaning that one actuator drives both joints, and the structural constraints ensure that the two joints satisfy the following relationship:

[0114] θ DIP =α*θ PIP (4);

[0115] In equation (4) above, the proportionality coefficient α is always equal to 2 / 3 under the constraints of the structure. This is a well-known technique in the field.

[0116] Substituting all the constraints in equations (2) to (4) into the transformation matrix equation (1), we can obtain the fingertip pose matrix. Only θ ROLL θ MCP θ PIP A function with three variables:

[0117]

[0118] In equation (5) above:

[0119]

[0120]

[0121]

[0122] r 12 =-s(θ) ROLL ),

[0123] r 22 =c(θ) ROLL ),

[0124] r 32 =0,

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] In the above group of equations (6), s represents sin, c represents cos, and a iAs shown in Table 1, the above equations constitute the kinematic equations of the finger, which explain how to calculate the position and orientation of the fingertip coordinate system {9} relative to the base coordinate system {0}.

[0132] Step 3: Obtain the metacarpophalangeal joint angle θ MCP Corresponding to the contraction amount l of the drive rope MCP The relationship is then used to obtain the corresponding motor control position length P. MCP That is, the relationship with the driving space.

[0133] like Figure 1 and Figures 4-5 As shown, based on the structural characteristics of the controlled finger, the rotation of the metacarpophalangeal joint (MCP) is driven by the simultaneous contraction of two linear motors, one on the left and one on the right, pulling the left and right drive ropes. Both the left and right drive ropes are equipped with suspension cables connected to the metacarpophalangeal bones. These suspension cables are designed to be pre-tensioned. Furthermore, the drive ropes are pre-tensioned before each system startup to ensure the finger is in its initial state while also ensuring the suspension cables remain taut. During subsequent movement, the traction ropes remain taut under the combined action of the motors and springs, thus ensuring the suspension cables also remain taut and their length remains constant. This is a well-known technique in the art. Therefore, as... Figure 4 As shown, when the left and right drive ropes contract, constrained by the sling, the angle θ between the drive rope and the metacarpophalangeal bones of the fingers remains constant during rotation. Furthermore, because the position of the metacarpophalangeal bone line hole H and the relative positions of the joint centers O3 and O4 at the joint ends are fixed, therefore... Figure 5 As shown, before and after rotation, the distance between H and the two tangent points of the rotary joint remains unchanged, i.e., HG = H'J. At the same time, H and the two tangent points of the rotary joint at the joint end form a line, and the angle α between this line and the drive rope also remains fixed.

[0134] like Figure 5 As shown, angle θ EHG This indicates the angle between the drive cord and the line EH connecting the metacarpal and phalangeal joint holes, as the drive cord contracts. MCP After lengthening, the joint rotates θ MCP Angle, or angle θ EHG Rotate to θ EH′J At this point, O3G = O3J, HG = H'J, angle α remains unchanged, O3E remains unchanged, and only the side EH shrinks. MCP The length changes to EH', and ∠EO3G changes to ∠EO3J. The arc length GJ corresponding to the apparent change in angle ∠GO3J is l. MCP That is, point G moves along the arc O3 by l MCP Length, and ∠GO3J is approximately equal to θ. MCP At this point, the length of the driving rope and the metacarpophalangeal joint angle θ can be determined. MCPThe mapping relationship between them can be determined, and then the relationship with the drive space can be determined based on the characteristics of the actuator.

[0135] Specifically:

[0136] Because point G moves along arc O3 MCP For length, we have:

[0137] l MCP =θ MCP *r3 (7);

[0138] In equation (7) above, r3 is the radius of the O3 arc.

[0139] In this embodiment, the maximum working space of the linear motor is 50mm. After dividing it into 2000 path points, each path point corresponds to 0.025mm. Therefore, for rotation θ... MCP (Angle system), the length P of the position where the linear motor needs to retract. MCP for:

[0140]

[0141] Step 4: Obtain the lateral joint angle θ ROLL l corresponding to the contraction amount of the drive rope ROLL The relationship is then used to obtain the corresponding motor control position length P. ROLL That is, the relationship with the driving space.

[0142] like Figures 6-7 As shown, the lateral joint angle θ ROLL This describes the left-right rolling motion of the metacarpophalangeal joint (MCP) of the fingers, generated by the differential motion of the left and right driving ropes. Compared to the change in the linear path, its range of motion is very small and can be considered a linear motion. Figure 1 and Figures 6-7 As shown, the length of the perpendicular line between the input line hole on the lateral joint and the line connecting the centers O1 and O2 of the two circles of the corresponding rotary joint is r. R The intersection point is O. R , with O R Center r R Create a virtual circle with radius , so that... Figure 7 In the simplified model, the arc length PK of the input wire hole on the virtual circle is approximately equal to the contraction length PI of the drive rope. Therefore, the length l of the drive rope can be determined. ROLL and the lateral joint angle θ ROLL The mapping relationships between them are:

[0143] l ROLL =θ ROLL *r R (9);

[0144] Similarly, if the maximum working space of a linear motor is 50mm, and this is divided into 2000 path points, with each path point corresponding to 0.025mm, then for rotation θ... MCP (Angle system), the length R of the position where the linear motor needs to retract. ROLL for:

[0145]

[0146] Step 5, because of the joint angle θ ROLL and joint angle θ MCP Both are driven by left and right drive ropes, according to R MCP and P ROLL Finally, the actual control position length P of the two linear motors on the left and right sides is obtained. left and P right :

[0147] P left =P left (0)-P MCP -P ROLL

[0148] P right =P right (0)-P MCP +P ROLL (11);

[0149] In equation (11) above, P left (0) and P right (0) represents the initial position.

[0150] Step 6: Obtain the proximal joint angle θ PIP l corresponding to the contraction amount of the drive rope PIP The relationship is then used to obtain the corresponding motor control position length P. PIP That is, the relationship with the driving space.

[0151] like Figures 8-9 As shown, for the simplification of the proximal interphalangeal joint (PIP), based on the simplification of the first two joints, it was found that the joint angle and the cord contraction distance have a good linear relationship. Therefore, it was determined that the cord contraction length of the PIP is also the arc length corresponding to the central angle subtended by rotation around a certain center. Figure 1 As shown, the end of the driving rope that drives the proximal interphalangeal joint is tied to a coil to form a knot, as shown. Figure 8 As shown, the knot rotates θ at the proximal interphalangeal joint. PIP The positional change after the angle means that the radius of rotation of this knot changes continuously during the contraction process (first increasing and then decreasing). To correspond with the rotation angle, it can be approximated as the initial tangent point O between the initial position of the knot and the two circles O5 and O6 of the joint. p The distance between them is radius r PTangent point O p An arc centered at a circle, such as Figure 9 As shown, the arc length LF traveled by the knot on this arc can be calculated as the equivalent length l of the intermediate driving rope contraction. PIP At this point, the rope length l can be determined. PIP and proximal interphalangeal joint angle θ PIP The mapping relationships between them are:

[0152] l PIP =θ PIP *r P (12);

[0153] Similarly, if the maximum working space of a linear motor is 50mm, and this is divided into 2000 path points, with each path point corresponding to 0.025mm, then for rotation θ... MCP (Angle system), corresponding to the length P of the position where the linear motor needs to retract. PIP for:

[0154]

[0155] Step 7: According to P PIP Obtain the actual control position length P of the intermediate linear motor drive center :

[0156] P center =P center (0)-P PIP (14).

[0157] Step 8: Based on the desired joint angle θ MCP θ ROLL θ PIP Obtain the control position P of each linear motor left P right P center and fingertip target pose matrix Control finger movements.

[0158] Building such Figure 10 The system shown first requires inputting the desired joint angles θ on the host computer PC during operation. MCP θ ROLL θ PIP Based on the real-time kinematic model calculations in steps one through seven above, the control positions P of the three linear motors are calculated. left P right P center and fingertip target pose matrix (As can be seen from step one, it is θ) ROLL θ MCP θ PIPA function of three variables sends the position of the linear motor to the lower-level controller. The controller uses servo mode to control the linear motor, sending the target position to the linear motor at fixed time intervals and controlling the linear motor to accurately reach the target position through PD feedback. At the same time, the controller sends the current status of the linear motor back to the upper-level computer. The upper-level computer can calculate and obtain the real-time θ of the finger. MCP θ ROLL θ PIP Angle, thereby obtaining real-time finger position. This means that the position and posture of the fingers can be observed in real time.

[0159] The specific control process is as follows: Figure 11 As shown, this system first initializes the peripherals of the upper and lower computer, establishes a communication connection between the upper and lower computer, and determines the data transmission rate and data volume between the upper and lower computer. After a stable and reliable connection is established between the upper and lower computer, the finger pose is initialized, allowing the finger to return to the "zero position". Then, the upper computer continuously queries, reads and calculates the current pose of the finger, while waiting for the user to send joint angle commands. When a new angle command is received, it first checks whether the angle exceeds the joint limit. If it exceeds the joint limit, a warning is issued and the joint angle command is discarded. If it does not exceed the joint limit, kinematic calculation is performed to obtain the position of the linear motor at the current angle and the result is sent to the lower computer. The lower computer sends the target position of the motor at a fixed time interval of 2ms through the motor position servo mode, and ensures that the motor accurately reaches the target position through PD feedback control. Then, closed-loop control is used to realize the motion control of each joint, ultimately controlling the fingertip to reach the desired position and posture, and returning the fingertip pose in the current state to the screen of the upper computer for display.

[0160] This invention determines the fingertip position at each finger joint angle by calculating the position of the fingertip at that joint angle. And to reach this state, the linear motor position information P needs to be sent to the controller. left P right P center This completes the mapping relationship from the drive space to the joint space and finally to the Cartesian space. The control system of this invention can achieve real-time and visual control of the fingers.

Claims

1. A method for kinematic calculation of an underactuated dexterous finger, characterized in that: Includes the following steps: Step 1: Use rotational joints to describe the motion states of the lateral joint, metacarpophalangeal joint (MCP), proximal interphalangeal joint (PIP), and distal interphalangeal joint (DIP), and set the line connecting the two centers of any pair of rotational joints as a virtual link. Step 2: Establish an improved DH parameter table based on the finger parameters, including the link length a. i-1 α, connecting rod torsion angle i-1 Linkage offset d i and joint angle θ i Among them, the joint angles θ1 to θ8 and the lateral swing joint angle θ ROLL Metacarpophalangeal joint angle θ MCP θ, the angle of the proximal interphalangeal joint PIP and distal interphalangeal joint angle θ DIP The correspondence is as follows: θ1+θ2=θ ROLL θ3+θ4=θ MCP θ5+θ6=θ PIP θ7+θ8=θ DIP (2); The pose of the fingertip is obtained through the transformation matrix. And the fingertip pose matrix For θ ROLL θ MCP θ PIP A function with three variables; Step 3: Obtain the metacarpophalangeal joint angle θ MCP Corresponding to the contraction amount l of the drive rope MCP The relationship is then used to obtain the corresponding motor control position length P. MCP ; Step 4: Obtain the lateral joint angle θ ROLL l corresponding to the contraction amount of the drive rope ROLL The relationship is then used to obtain the corresponding motor control position length P. ROLL ; Step 5, Joint angle θ ROLL and joint angle θ MCP Driven by left and right drive ropes, according to P MCP and P ROLL Obtain the actual control position length P of the two linear motors (left and right). left and P right : P left =P left (0)-P MCP -P ROLL P right =P right (0)-P MCP +P ROLL (11); Step 6: Obtain the proximal interphalangeal joint angle θ PIP l corresponding to the contraction amount of the drive rope PIP The relationship is then used to obtain the corresponding motor control position length P. PIP ; Step 7, Joint Angle θ PIP Driven by the central drive rope, according to P PIP Obtain the actual control position length P of the intermediate linear motor drive center : P center =P center (0)-P PIP (14); Step 8: Determine the desired joint angle θ of the finger. MCP θ ROLL θ PIP The information is then input into the system, which calculates the fingertip target pose matrix according to steps one through seven. and the control position P of each linear motor left P right P center Used to control finger movements.

2. The kinematics calculation method for underactuated dexterous fingers according to claim 1, characterized in that: In step two: Represented by the product of transformation matrices: The joint angles θ1~θ8 and the lateral joint angle θ ROLL Metacarpophalangeal joint angle θ MCP θ, the angle of the proximal interphalangeal joint PIP and distal interphalangeal joint angle θ DIP The correspondence is as follows: θ1+θ2=θ ROLL θ3+θ4=θ MCP θ5+θ6=θ PIP θ7+θ8=θ DIP (2); In equation (2) above; In equation (3) above, r i The radius of the circle corresponding to the revolute joint; And th DIP =α*θ PIP (4); In equation (4) above, the proportionality coefficient α is always equal to 2 / 3; Substituting equations (2) to (4) into the transformation matrix equation (1), we obtain the fingertip pose matrix. For θ ROLL θ MCP θ PIP A function with three variables: In equation (5) above: r 12 =-s(θ ROLL ), r 22 =c(θ ROLL ), r 32 ＝0， In the above equation (6), s represents sin, c represents cos, and ai is obtained from the improved DH parameter table.

3. The kinematics calculation method for underactuated dexterous fingers according to claim 1, characterized in that: In step three, the rotation of the metacarpophalangeal joint is driven by the simultaneous contraction of two linear motors, pulling the left and right drive ropes. Both the left and right drive ropes are equipped with slings connected to the metacarpophalangeal bones. These slings remain taut and of constant length. Constrained by the slings, the angle θ between the drive ropes and the metacarpophalangeal bones remains constant during rotation. The position of the hole H on the metacarpophalangeal bones and the relative position of the centers O3 and O4 of the two circles at the joint end of the rotation joint are fixed. Therefore, the distance between H and the tangent point between the two circles of the rotation joint remains constant. Simultaneously, the angle α between the line connecting H and the tangent point between the two circles of the rotation joint and the drive rope also remains constant. The drive ropes contract by l... MCP After lengthening, the point of tangency between the two circles of the rotary joint is considered to have moved along the arc O3. MCP For length, we have: l MCP =θ MCP *r3 (7); In equation (7) above, r3 is the radius of circle O3; The corresponding linear motor retraction position length P MCP for: In equation (8) above, m is the distance to a waypoint obtained by dividing the maximum working space of the linear motor by the total number of waypoints.

4. The kinematics calculation method for underactuated dexterous fingers according to claim 3, characterized in that: In step four, the two linear motors drive the left and right drive ropes to move differentially, generating the lateral swing joint angle θ. ROLL The length of the perpendicular line between the input line hole on the lateral joint and the line connecting the centers O1 and O2 of the two circles of the corresponding rotary joint is r. R The intersection point is O. R , with O R Center r R Let a virtual circle be drawn with radius , and the arc length of the position change of the input wire hole on the virtual circle be approximately equal to the length of the drive rope contraction. Then: l ROLL =θ ROLL *r R (9); The corresponding length of the linear motor's contraction position is:

5. The kinematics calculation method for underactuated dexterous fingers according to claim 1, characterized in that: In step six, the end of the drive rope is tied to the proximal interphalangeal joint to form a knot, and the initial tangent point between the two circles O5 and O6 of the joint end rotation joint is O. p The initial position of the joint to O p The distance between them is r P , with O p Center r P Draw an arc with radius l, and the arc length along which the knot travels is equivalent to the length l that drives the rope to contract. PIP Then we have: l PIP =θ PIP *r P (12); The corresponding length of the linear motor's contraction position is:

6. The kinematics calculation method for underactuated dexterous fingers according to claim 1, characterized in that: In step eight, the control system includes a host computer for real-time calculation and a slave computer for controlling each linear motor. The host computer is equipped with a screen, and the slave computer is equipped with a controller.

7. The kinematics calculation method for underactuated dexterous fingers according to claim 6, characterized in that: First, input the desired joint angle θ into the host computer. MCP θ ROLL θ PIP The control positions P of the three linear motors are calculated based on steps one through seven. left P right P center and fingertip target pose matrix The data is sent to the lower-level controller, which controls each linear motor to reach the target position. Simultaneously, the controller sends the current status of the linear motors back to the upper-level computer, which calculates and obtains the real-time θ of the finger. MCP θ ROLL θ PIP Angle, thereby obtaining real-time finger position. Displayed on the screen.

8. The kinematics calculation method for underactuated dexterous fingers according to claim 7, characterized in that: The controller sends the target position to the linear motor at fixed time intervals and controls the linear motor to accurately reach the target position through PD feedback.

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