CN109760051A - A kind of rope drives the determining method of rope lengths variation of ultra-redundant degree of freedom robot - Google Patents

A kind of rope drives the determining method of rope lengths variation of ultra-redundant degree of freedom robot Download PDF

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CN109760051A
CN109760051A CN201910041486.6A CN201910041486A CN109760051A CN 109760051 A CN109760051 A CN 109760051A CN 201910041486 A CN201910041486 A CN 201910041486A CN 109760051 A CN109760051 A CN 109760051A
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rope
section
vertebra section
force
vertebra
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CN109760051B (en
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谷海宇
魏承
王萍萍
赵阳
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Harbin Institute of Technology
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Harbin Institute of Technology
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Abstract

The rope lengths that the present invention provides a kind of rope drive ultra-redundant degree of freedom robot change the method for determination, belong to technical field of robot control.The present invention drives in the rope that rope drives ultra-redundant degree of freedom robot establish coordinate system on serial parallel mechanism first;It defines rope section vector and the power that rope force acts on rope guide plate is acquired by rope section vector;Then the equivalent spinor of rope force is obtained using the power that rope force acts on rope guide plate;Jacobian matrix is obtained by mapping relations between rope force and equivalent moment;Long change of rope rate is obtained in conjunction with the angular speed and Jacobian matrix of rotational freedom, finally is integrated obtained long change of rope rate to obtain the variation of rope lengths.The control technology error that the present invention solves the problems, such as that existing rope drives ultra-redundant degree of freedom robot is larger.The present invention, which can be used for restricting, drives the control technology of ultra-redundant degree of freedom robot.

Description

A kind of rope drives the determining method of rope lengths variation of ultra-redundant degree of freedom robot
Technical field
The rope lengths for driving ultra-redundant degree of freedom robot the present invention relates to a kind of rope change the method for determination, belong to robot Control technology field.
Background technique
Rope drives ultra-redundant degree of freedom robot:
It is to use rope as the serial parallel mechanism of driving medium that rope, which drives ultra-redundant degree of freedom robot,.Such robot by Intensive movable joint is connected in series, and uses rope parallel drive, and number of degrees of freedom is numerous, and movement flexibly, is limited narrow Environment in have extremely strong locomitivity.Since rope can only bear unidirectional force, one direction constraint energy can only be played to mechanism Power, therefore rope number is generally higher than number of degrees of freedom.Different from the joint motions control mode of traditional robot, such machine People needs to control rope lengths and speed.And the premise controlled this is rope when acquiring to complete desired motion Need to meet motion state (rope length and rope speed).Ultra-redundant degree of freedom robot described herein is by two-freedom universal joint string Robot made of connection.
Rope drives Robotic inverse kinematics:
It includes two parts that rope, which drives Robotic inverse kinematics: solving joint space by operating space motion state (end movement) Motion state and by joint motions state solve rope motion state.Wherein, joint space is solved by operating space motion state The method of motion state is identical as traditional inverse kinematics method of redundant robot, that is, passes through the Jacobean matrix of the velocity space Battle array mapping solves or seeks numerical solution by forward kinematics equation.
And the part of rope motion state is solved by joint motions state, traditional method for solving is rope multistage accumulation side Method establishes the mapping relations of the rope lengths and joint angles at simple joint, using Numerical Methods Solve, then to all rope sections It is overlapped, acquires the length of rope, the advantages of this method is that modeling is simple, and it is complicated to seek only solution.It is directed to solve non-thread Property equation group, there are the error accumulations in more Xie Xianxiang and multistage additive process.
Summary of the invention
The present invention is to solve the problems, such as that the control technology error of existing rope drive ultra-redundant degree of freedom robot is larger, is provided A kind of rope drives the determining method of rope lengths variation of ultra-redundant degree of freedom robot.
The rope lengths that a kind of rope of the present invention drives ultra-redundant degree of freedom robot change the method for determination, pass through following skill Art scheme is realized:
Coordinate system is established on serial parallel mechanism Step 1: driving in the rope that rope drives ultra-redundant degree of freedom robot;Define rope section Vector simultaneously acquires the power that rope force acts on rope guide plate by rope section vector;
Step 2: obtaining the equivalent spinor of rope force using the power that rope force acts on rope guide plate;
Step 3: obtaining Jacobian matrix by mapping relations between rope force and equivalent moment;
Step 4: the angular speed and Jacobian matrix in conjunction with rotational freedom obtain long change of rope rate;
Step 5: being integrated long change of rope rate obtained in step 4 to obtain the variation of rope lengths.
Present invention feature the most prominent and significant beneficial effect are:
The rope lengths that a kind of rope according to the present invention drives ultra-redundant degree of freedom robot change the method for determination, from speed Space carries out your kinematics solution, acquires rope lengths Jacobian matrix corresponding with rotational freedom (joint) speed, in turn Integral obtains the variable quantity of rope lengths, and then can drive ultra-redundant degree of freedom robot to the rope and control.The present invention Method operation is simple, and the changing values of the rope lengths acquired is unique and error very little, therefore it is also possible that rope drives super redundancy The control precision of degree of freedom robot improves, and compares conventional method, and the method for the present invention can effectively improve rope and drive super redundancy freedom Spend the control precision about 20% of robot.
Detailed description of the invention
Fig. 1 is the rope drive serial parallel mechanism structural schematic diagram that rope drives ultra-redundant degree of freedom robot;
Fig. 2 is each coordinate system schematic diagram that rope drives that the rope drive serial parallel mechanism of ultra-redundant degree of freedom robot is established;
Fig. 3 is vertebra section structure schematic diagram in the present invention;
Fig. 4 is flow chart of the present invention;
1. pedestal, 2, rope drive mechanical arm, 21. vertebra sections, 211. universal joints, 212. upper plates, 213. lower plates, 22. ropes.
Specific embodiment
Specific embodiment 1: being illustrated in conjunction with Fig. 1, Fig. 4 to present embodiment, a kind of rope that present embodiment provides The rope lengths for driving ultra-redundant degree of freedom robot change the method for determination, specifically includes the following steps:
Coordinate system is established on serial parallel mechanism Step 1: driving in the rope that rope drives ultra-redundant degree of freedom robot;Define rope section Vector simultaneously acquires the power that rope force acts on rope guide plate by rope section vector;
Step 2: obtaining the equivalent spinor of rope force using the power that rope force acts on rope guide plate;
Step 3: obtaining Jacobian matrix by mapping relations between rope force and equivalent moment;
Step 4: the angular speed and Jacobian matrix in conjunction with rotational freedom (joint) obtain long change of rope rate;
Step 5: being integrated long change of rope rate obtained in step 4 to obtain the variation of rope lengths.
Specific embodiment 2: the present embodiment is different from the first embodiment in that, the step 1 specifically includes Following procedure:
As shown in Figure 1 and Figure 2, the rope that rope drives ultra-redundant degree of freedom robot drive serial parallel mechanism and include: pedestal 1 and set The rope set on pedestal 1 drives mechanical arm 2;The rope is driven into any one universal joint 211 and universal joint 211 on mechanical arm 2 Part between to next universal joint 211 is defined as a vertebra section 21;In any vertebra section 21, the rope close to universal joint 211 is defined Rope guide plate is lower plate 213, and the rope guide plate far from universal joint 211 is upper plate 212;Upper plate 212 and the edge of lower plate 213 are equal Even to be provided with the cord hole equal with 22 quantity of rope, each rope sequentially passes through the lower plate 213 and upper plate of all vertebra sections 21 212。
As shown in Figure 2 and Figure 3, with the lower plate center C of vertebra sectioniVertebra section coordinate system { C is established for origini-xiyizi, i indicates vertebra The serial number of section, i=1,2 ..., I;The total number of I expression vertebra section;Definition is by lower plate center CiIt is directed toward the 1st cord hole in lower plate Direction is xiAxis direction, perpendicular to lower plate direction be ziAxis direction, yiAxis is both perpendicular to xiAxis and ziAxis;In universal center Place establishes a kind of D-H (Denavit moral receive peacekeeping Hartenberg Hardenbergh in nineteen fifty-five propose general method) coordinate system {On-xnynzn, n indicates the serial number of rotational freedom, n=1,2 ..., N;N indicates the total number of rotational freedom, N=2I;? That is all having the rotational freedom of both direction in each universal center;Cord hole on the upper plate of vertebra section i exists Vector in inertial coodinate system { O-XYZ } is denoted asIt is in vertebra section coordinate system { Ci-xiyiziIn vector beJ indicates rope The serial number of the serial number of rope, the cord hole that j rope passes through on vertebra section is also j, j=1,2 ..., M;M is the sum of rope, N=3I;Position It is denoted as in vector of the cord hole in the lower plate of vertebra section i in inertial coodinate system { O-XYZ }It is in vertebra section coordinate system { Ci- xiyiziIn vector be
Vector from the upper plate cord hole j of the lower plate cord hole j to vertebra section i of vertebra section i+1 is rope section vectorIts calculation formula Are as follows:
Vector from the upper plate cord hole j of the lower plate cord hole j to vertebra section i-1 of vertebra section i is rope section vectorIts calculation formula Are as follows:
Then act on the rope active force in the lower plate and upper plate of vertebra section i are as follows:
Wherein,The active force in the lower plate of vertebra section i is acted on for rope j;The upper plate of vertebra section i is acted on for rope j On active force;For rope section vectorUnit vector;For rope section vectorUnit vector;fjIndicate rope j's Pulling force size.
Other steps and parameter are same as the specific embodiment one.
Specific embodiment 3: present embodiment is unlike specific embodiment two, rope section vectorUnit Vector AmountRope section vectorUnit vector
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: present embodiment is unlike specific embodiment two, rope force described in step 2 Equivalent spinor specifically:
Wherein, SiFor on vertebra section i rope generate rope force equivalent spinor,The power on vertebra section i is acted on for rope j The force screw generated at the vertebra section coordinate origin of vertebra section i;F=[f1 f2 … fM]TIt indicates from rope force to i-th The Jacobian matrix that force screw maps on vertebra section.
Other steps and parameter are identical with embodiment two.
Specific embodiment 5: present embodiment is unlike specific embodiment four, it is describedSpecifically calculated Journey includes:
Rope force suffered by vertebra section is divided into two classes:
A, the rope of driving vertebra section i movement, number are as follows: j=i, I+i, 2I+i;
B, vertebra section i+1, i+2 are interfered ..., the rope number of I movement is j=i+1, i+2 ... I, I+i+1, I+i+2 ... 2I,2I+i+1,2I+i+2,…3I;
When rope j is the driving rope of vertebra section i, the power acted on vertebra section i only has it to act on the lower plate of vertebra section i On active force, i.e., are as follows:
At this point,The force screw generated at the vertebra section coordinate origin of vertebra section i are as follows:
When rope j is the perturbed force of vertebra section i, the power acted on vertebra section i acts on the lower plate of vertebra section i under for it Active force on plate vector sum:
At this point,The force screw generated at the vertebra section coordinate origin of vertebra section i are as follows:
Other steps and parameter are identical as specific embodiment one, two or three.
Specific embodiment 6: present embodiment is unlike specific embodiment five, Jacobi described in step 3 Matrix are as follows:
It is obtained by formula (7), (9)Are as follows:
SiIt is converted into the calculation method of τ are as follows:
Wherein, τiFor SiThe equivalent driving moment of caused joint space;JiIt is equivalent to joint for the force vector on vertebra section i The Jacobian matrix of torque mapping, consisting of:
Wherein, z0,z1,…z2i-1For unit vector of the Z axis in inertial space of D-H coordinate system, p0,p1,…p2iFor D- Phasor coordinate of the origin of H coordinate system in inertial coodinate system;
Force screw suffered by whole vertebra sections is converted into the equivalent moment of joint space are as follows:
Convolution (14):
τ=Jtf (14)
Obtain JtAre as follows:
Wherein, JtThe force Jacobian matrix mapped for rope force to joint equivalent moment.
Other steps and parameter and specific embodiment one, two, three, four or five are identical.
Specific embodiment 7: present embodiment is unlike specific embodiment two, three, four, five or six, step 4 Described in obtain the detailed process of long change of rope rate and include:
Rope is firmly replaced, can be obtained using the principle of virtual work:
It is obtained by formula (4)And it is brought into formula (16) with formula (3) and obtained:
δ is variation operator, τnIndicate the big of the equivalent moment of n-th of rotational freedom (joint) as caused by rope It is small;qnIndicate the angular speed of n-th of rotational freedom;
By formula (2) andIt obtainsThen formula (17) can rewrite are as follows:
Due toljFor the length of rope j, then formula (18) can convert are as follows:
fTδ l=τTδq (19)
Wherein, δ l=[δ l1 δl2 … δlM]T;τ=[τ1 τ2 … τN]T;δq=[δ q1 δq2 … δqN]T
Formula (14) is brought into (19) and is obtained:
fTδ l=fTJt Tδq (20)
It is obtained by formula (20):
δ l=Jt Tδq (21)
Since all constraints are scleronomic constraint, steady constraint, long change of rope rateBetween the angular speed of rotational freedom Relationship are as follows:
Wherein,Subscript " " is indicated to time derivation.
The key of (22) is Method of Obtaining Jacobian Matrix J when solving inverse kinematics relationshipt, the J known to formula (14)tIt can pass through Mapping relations obtain between rope force and equivalent moment.
Other steps and parameter are identical as specific embodiment one to six.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to The protection scope of the appended claims of the present invention.

Claims (7)

1. the rope lengths that a kind of rope drives ultra-redundant degree of freedom robot change the method for determination, which is characterized in that the rope drives super The control method of redundant degree of freedom robot specifically includes the following steps:
Coordinate system is established on serial parallel mechanism Step 1: driving in the rope that rope drives ultra-redundant degree of freedom robot;Define rope section vector And the power that rope force acts on rope guide plate is acquired by rope section vector;
Step 2: obtaining the equivalent spinor of rope force using the power that rope force acts on rope guide plate;
Step 3: obtaining Jacobian matrix by mapping relations between rope force and equivalent moment;
Step 4: the angular speed and Jacobian matrix in conjunction with rotational freedom obtain long change of rope rate;
Step 5: being integrated long change of rope rate obtained in step 4 to obtain the variation of rope lengths.
2. the rope lengths that a kind of rope drives ultra-redundant degree of freedom robot according to claim 1 change the method for determination, special Sign is that the step 1 specifically includes following procedure:
Any one universal joint and the universal joint to the part between next universal joint are defined as a vertebra section;Any vertebra section In, the rope guide plate close to universal joint is lower plate, and the rope guide plate far from universal joint is upper plate;
With the lower plate center C of vertebra sectioniVertebra section coordinate system { C is established for origini-xiyizi, the serial number of i expression vertebra section, i=1, 2,…,I;The total number of I expression vertebra section;Definition is by lower plate center CiThe direction for being directed toward the 1st cord hole in lower plate is xiAxis direction, Direction perpendicular to lower plate is ziAxis direction, yiAxis is both perpendicular to xiAxis and ziAxis;D-H coordinate is established at universal center It is { On-xnynzn, n indicates the serial number of rotational freedom, n=1,2 ..., N;N indicates the total number of rotational freedom, N=2I; Vector of the cord hole in inertial coodinate system { O-XYZ } on the upper plate of vertebra section i is denoted asIt is in vertebra section coordinate system { Ci- xiyiziIn vector beJ indicates the serial number of rope, and the serial number for the cord hole that j rope passes through on vertebra section is also j, j=1, 2,…,M;M is the sum of rope, N=3I;Vector of the cord hole in inertial coodinate system { O-XYZ } in the lower plate of vertebra section i It is denoted asIt is in vertebra section coordinate system { Ci-xiyiziIn vector be
Vector from the upper plate cord hole j of the lower plate cord hole j to vertebra section i of vertebra section i+1 is rope section vectorIts calculation formula is:
Vector from the upper plate cord hole j of the lower plate cord hole j to vertebra section i-1 of vertebra section i is rope section vectorIts calculation formula is:
Then act on the rope active force in the lower plate and upper plate of vertebra section i are as follows:
Wherein,The active force in the lower plate of vertebra section i is acted on for rope j;It is acted on for rope j on the upper plate of vertebra section i Active force;For rope section vectorUnit vector;For rope section vectorUnit vector;fjIndicate the pulling force of rope j Size.
3. the rope lengths that a kind of rope drives ultra-redundant degree of freedom robot according to claim 2 change the method for determination, special Sign is, rope section vectorUnit vectorRope section vectorUnit vector
4. the rope lengths that a kind of rope drives ultra-redundant degree of freedom robot according to claim 2 change the method for determination, special Sign is, the equivalent spinor of rope force described in step 2 specifically:
Wherein, SiFor on vertebra section i rope generate rope force equivalent spinor,The power on vertebra section i is acted in vertebra for rope j Save the force screw generated at the vertebra section coordinate origin of i;F=[f1 f2 … fM]TIt indicates from rope force to i-th of vertebra section The Jacobian matrix of upper force screw mapping.
5. the rope lengths that a kind of rope drives ultra-redundant degree of freedom robot according to claim 4 change the method for determination, special Sign is, describedSpecific calculating process include:
Rope force suffered by vertebra section is divided into two classes:
A, the rope of driving vertebra section i movement, number are as follows: j=i, I+i, 2I+i;
B, vertebra section i+1, i+2 are interfered ..., the rope number of I movement is j=i+1, i+2 ... I, I+i+1, I+i+2 ... 2I, 2I+ i+1,2I+i+2,…3I;
When rope j is the driving rope of vertebra section i, the power on vertebra section i is acted on are as follows:
At this point,The force screw generated at the vertebra section coordinate origin of vertebra section i are as follows:
When rope j is the perturbed force of vertebra section i, the power on vertebra section i is acted on are as follows:
At this point,The force screw generated at the vertebra section coordinate origin of vertebra section i are as follows:
6. the rope lengths that a kind of rope drives ultra-redundant degree of freedom robot according to claim 5 change the method for determination, special Sign is, Jacobian matrix described in step 3 are as follows:
It is obtained by formula (7), (9)Are as follows:
SiIt is converted into the calculation method of τ are as follows:
Wherein, τiFor SiThe equivalent driving moment of caused joint space;JiIt is the force vector on vertebra section i to joint equivalent moment The Jacobian matrix of mapping, consisting of:
Wherein, z0,z1,…z2i-1For unit vector of the Z axis in inertial space of D-H coordinate system, p0,p1,…p2iFor D-H coordinate Phasor coordinate of the origin of system in inertial coodinate system;
Force screw suffered by whole vertebra sections is converted into the equivalent moment of joint space are as follows:
Convolution (14):
τ=Jtf (14)
Obtain JtAre as follows:
Wherein, JtThe force Jacobian matrix mapped for rope force to joint equivalent moment.
7. according to claim 2,3,4,5 or a kind of 6 rope lengths variation determinations of rope drive ultra-redundant degree of freedom robot Method, which is characterized in that the detailed process that long change of rope rate is obtained described in step 4 includes:
Rope is firmly replaced, can be obtained using the principle of virtual work:
δ is variation operator, τnIndicate the size of the equivalent moment of n-th of rotational freedom as caused by rope;qnIndicate n-th The angular speed of a rotational freedom;
By formula (2) andIt obtainsThen formula (17) can rewrite are as follows:
Due toljFor the length of rope j, then formula (18) can convert are as follows:
fTδ l=τTδq (19)
Wherein, δ l=[δ l1 δl2 … δlM]T;τ=[τ1 τ2 … τN]T
Formula (14) is brought into (19) and is obtained:
δ l=Jt Tδq (21)
Since all constraints are scleronomic constraint, steady constraint, long change of rope rateRelationship between the angular speed of rotational freedom Are as follows:
Wherein,Subscript " " is indicated to time derivation.
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CN112975925A (en) * 2021-02-08 2021-06-18 西安电子科技大学 Rope-driven snakelike mechanical arm motion data processing method containing rope hole gaps
CN114714342A (en) * 2022-04-24 2022-07-08 哈尔滨工业大学(深圳) Device for measuring hysteresis deformation of driving rope of rope-driven flexible arm and compensation control method thereof
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CN117697765B (en) * 2024-02-05 2024-04-16 泓浒(苏州)半导体科技有限公司 Method and system for improving conveying accuracy of wafer mechanical arm based on sensing feedback

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