CN109760051B - Rope length change determination method for rope-driven super-redundancy degree of freedom robot - Google Patents

Rope length change determination method for rope-driven super-redundancy degree of freedom robot Download PDF

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CN109760051B
CN109760051B CN201910041486.6A CN201910041486A CN109760051B CN 109760051 B CN109760051 B CN 109760051B CN 201910041486 A CN201910041486 A CN 201910041486A CN 109760051 B CN109760051 B CN 109760051B
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rope
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vertebral
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CN109760051A (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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Abstract

The invention provides a rope length change determining method for a rope-driven super-redundancy freedom robot, and belongs to the technical field of robot control. Firstly, establishing a coordinate system on a rope drive serial-parallel mechanism of the rope drive super-redundancy freedom degree robot; defining a rope segment vector and obtaining the force of the rope force acting on the rope guide plate by the rope segment vector; then the equivalent rotation of the rope force is obtained by utilizing the force of the rope force acting on the rope guide plate; obtaining a Jacobian matrix through the mapping relation between the rope force and the equivalent moment; and finally, integrating the obtained rope length change rate to obtain the change of the rope length. The invention solves the problem of larger control technology error of the existing rope-driven super-redundancy freedom degree robot. The invention can be used for the control technology of the rope-driven super-redundancy freedom degree robot.

Description

Rope length change determination method for rope-driven super-redundancy degree of freedom robot
Technical Field
The invention relates to a rope length change determining method for a rope-driven super-redundancy freedom robot, and belongs to the technical field of robot control.
Background
Rope-driven super-redundant degree of freedom robot:
the rope-driven ultra-redundant degree of freedom robot is a series-parallel mechanism using ropes as transmission media. The robot is formed by connecting dense moving joints in series, is driven by ropes in parallel, has a large number of degrees of freedom, moves flexibly and has extremely strong moving capability in a narrow and limited environment. Because the rope can only bear unidirectional force and only has unidirectional constraint capacity on the mechanism, the number of the ropes is generally larger than that of the degrees of freedom. Unlike the traditional robot joint motion control method, the robot needs to control the length and speed of the rope. The precondition for controlling this is that the rope needs to meet the motion conditions (rope length and rope speed) when the desired motion is achieved. The super-redundant degree-of-freedom robot described here is a robot in which two-degree-of-freedom universal joints are connected in series.
Inverse kinematics of the rope-driven robot:
the inverse kinematics of the rope-driven robot comprises two parts: the joint space motion state is solved from the operation space motion state (end motion) and the rope motion state is solved from the joint motion state. The method for solving the joint space motion state by the operation space motion state is the same as the inverse kinematics solution method of the traditional redundant robot, namely solving through the Jacobian matrix mapping of a velocity space or solving a numerical solution through a positive kinematics equation.
And the traditional solving method is a rope multi-section accumulation method, establishes a mapping relation between the length of the rope at a single joint and the angle of the joint, solves the problem by using a numerical method, and then superposes all the rope sections to obtain the length of the rope. The method relates to solving a nonlinear equation system, and has the problems of multiple solutions and error accumulation in the multi-segment superposition process.
Disclosure of Invention
The invention provides a method for determining rope length change of a rope-driven super-redundancy freedom degree robot, which aims to solve the problem of large control technology error of the existing rope-driven super-redundancy freedom degree robot.
The invention discloses a method for determining rope length change of a rope-driven super-redundancy freedom degree robot, which is realized by the following technical scheme:
firstly, establishing a coordinate system on a rope drive serial-parallel mechanism of a rope drive super-redundancy freedom degree robot; defining a rope segment vector and obtaining the force of the rope force acting on the rope guide plate by the rope segment vector;
step two, obtaining the equivalent rotation quantity of the rope force by utilizing the force of the rope force acting on the rope guide plate;
thirdly, obtaining a Jacobian matrix through a mapping relation between the rope force and the joint equivalent moment;
step four, combining the angular speed of the rotational degree of freedom and the Jacobian matrix to obtain the change rate of the rope length;
and step five, integrating the rope length change rate obtained in the step four to obtain the change of the rope length.
The most prominent characteristics and remarkable beneficial effects of the invention are as follows:
the invention relates to a method for determining the change of the length of a rope-driven super-redundant degree of freedom robot, which comprises the steps of solving inverse kinematics from a speed space, obtaining a Jacobian matrix corresponding to the length of the rope and the speed of rotational degree of freedom (joint), further obtaining the change of the length of the rope through integration, and further controlling the rope-driven super-redundant degree of freedom robot. The method is simple in operation, the obtained change value of the length of the rope is unique, the error is small, and therefore the control precision of the rope-driven super-redundancy-degree-of-freedom robot can be improved, and compared with the traditional method, the method can effectively improve the control precision of the rope-driven super-redundancy-degree-of-freedom robot by about 20%.
Drawings
FIG. 1 is a schematic structural diagram of a rope-driven series-parallel mechanism of a rope-driven super-redundant degree of freedom robot;
FIG. 2 is a schematic diagram of coordinate systems established by a rope drive series-parallel mechanism of the rope drive super-redundancy degree of freedom robot;
FIG. 3 is a schematic view of the vertebral segment of the present invention;
FIG. 4 is a flow chart of the present invention;
1. the robot comprises a base, 2, a rope-driven mechanical arm, 21, a vertebral segment, 211, a universal joint, 212, an upper plate, 213, a lower plate and 22, a rope.
Detailed Description
The first embodiment is as follows: the embodiment is described with reference to fig. 1 and 4, and the method for determining the change in the length of the rope-driven super-redundant degree of freedom robot provided by the embodiment specifically includes the following steps:
firstly, establishing a coordinate system on a rope drive serial-parallel mechanism of a rope drive super-redundancy freedom degree robot; defining a rope segment vector and obtaining the force of the rope force acting on the rope guide plate by the rope segment vector;
step two, obtaining the equivalent rotation quantity of the rope force by utilizing the force of the rope force acting on the rope guide plate;
thirdly, obtaining a Jacobian matrix through a mapping relation between the rope force and the joint equivalent moment;
step four, combining the angular speed of the rotational degree of freedom (joint) and the Jacobian matrix to obtain the change rate of the rope length;
and step five, integrating the rope length change rate obtained in the step four to obtain the change of the rope length.
The second embodiment is as follows: the difference between this embodiment and the first embodiment is that the first step specifically includes the following steps:
as shown in fig. 1 and 2, a rope driving series-parallel mechanism of a rope driving super-redundant degree of freedom robot includes: the rope-driven mechanical arm comprises a base 1 and a rope-driven mechanical arm 2 arranged on the base 1; defining any one universal joint 211 on the rope-driven mechanical arm 2 and the part between the universal joint 211 and the next universal joint 211 as a vertebral joint 21; in any vertebral segment 21, the rope guide plate near the universal joint 211 is defined as a lower plate 213, and the rope guide plate far from the universal joint 211 is defined as an upper plate 212; the edges of the upper plate 212 and the lower plate 213 are uniformly provided with the same number of cord holes as the number of cords 22, each cord passing through the lower plate 213 and the upper plate 212 of all the vertebral levels 21 in turn.
As shown in fig. 2 and 3, the center C of the lower plate of the vertebral segmentiEstablishing a vertebral level coordinate system for the origin { Ci-xiyiziI represents the serial number of the vertebral segment, I is 1, 2. I represents the total number of vertebral segments; is defined by the center C of the lower plateiThe direction pointing to the 1 st rope hole on the lower plate is xiThe axial direction, the direction perpendicular to the lower plate, is ziAxial direction, yiThe axis being perpendicular to xiAxis and ziA shaft; establishing a D-H (Denavit Dener and Hartenberg put forward a general method in 1955) coordinate system at the center of the gimbal { On-xnynznN represents a serial number of a rotational degree of freedom, and N is 1, 2. N represents the total number of rotational degrees of freedom, N ═ 2I; that is to say, there are two rotational degrees of freedom in each gimbal center; the vector of the rope hole on the upper plate of the vertebral segment i in the inertial coordinate system { O-XYZ } is recorded as
Figure GDA0002242193010000031
It is in the vertebral level coordinate system { Ci-xiyiziThe vector in (f) is
Figure GDA0002242193010000032
j represents the serial number of the rope, and the serial number of a rope hole for the j rope to pass through on the vertebral segment is also j, j is 1, 2. M is the total number of ropes, N ═3I; the vector of the rope hole on the lower plate of the vertebral segment i in the inertial coordinate system (O-XYZ) is recorded as
Figure GDA0002242193010000033
It is in the vertebral level coordinate system { Ci-xiyiziThe vector in (f) is
Figure GDA0002242193010000034
The vector from the lower plate rope hole j of the vertebral segment i +1 to the upper plate rope hole j of the vertebral segment i is a rope segment vector
Figure GDA0002242193010000035
The calculation formula is as follows:
Figure GDA0002242193010000036
the vector from the lower plate rope hole j of the vertebral segment i to the upper plate rope hole j of the vertebral segment i-1 is a rope segment vector
Figure GDA0002242193010000037
The calculation formula is as follows:
Figure GDA0002242193010000038
the rope forces acting on the lower and upper plates of the vertebral segment i are then:
Figure GDA0002242193010000039
Figure GDA00022421930100000310
wherein the content of the first and second substances,
Figure GDA00022421930100000311
the force of cord j on the lower plate of vertebra segment i;the force of the cord j on the upper plate of the vertebral segment i;
Figure GDA00022421930100000313
is a vector of rope segment
Figure GDA00022421930100000314
A unit vector of (a);
Figure GDA00022421930100000315
is a vector of rope segment
Figure GDA00022421930100000316
A unit vector of (a); f. ofjIndicating the magnitude of the tension in the rope j.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the second difference between this embodiment and the second embodiment is that the segment vectorUnit vector of
Figure GDA0002242193010000042
Rope segment vectorUnit vector of
Figure GDA0002242193010000044
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the second embodiment is different from the second embodiment in that the equivalent rotation amount of the rope force in the second step is specifically:
wherein S isiRope force generated for rope on vertebral segment iThe equivalent amount of the rotation of the rotor,
Figure GDA0002242193010000046
a force momentum generated at the origin of the vertebral level coordinate system of the vertebral level i for the force of the cord j acting on the vertebral level i; f ═ f1f2… fM]T；
Figure GDA0002242193010000047
Representing the Jacobian matrix mapped by the cable force to the force curl on the ith vertebral level.
Other steps and parameters are the same as those in the second embodiment.
The fifth concrete implementation mode: the fourth difference between the present embodiment and the present embodiment is that
Figure GDA00022421930100000411
The specific calculation process comprises the following steps:
the cable force on the vertebral level is divided into two categories:
A. rope for driving vertebral segment i to move is numbered as follows: j ═ I, I + I,2I + I;
B. the number of the ropes disturbing the movement of the vertebral segments I +1, I +2, … I, I +1, I +2, … 2I,2I +1,2I +2, … 3I;
when cord j is the drive cord for segment i, the only force it exerts on segment i is the force it exerts on the lower plate of segment i, i.e.:
Figure GDA0002242193010000048
at this time, the process of the present invention,
Figure GDA0002242193010000049
the amount of torque generated at the origin of the vertebral level coordinate system for vertebra i is:
Figure GDA00022421930100000410
when cord j is the distracting force of vertebra segment i, its force acting on vertebra segment i is the vector sum of its forces acting on the inferior and inferior plates of vertebra segment i:
Figure GDA0002242193010000051
at this time, the process of the present invention,
Figure GDA0002242193010000052
the amount of torque generated at the origin of the vertebral level coordinate system for vertebra i is:
Figure GDA0002242193010000053
other steps and parameters are the same as those in the first, second or third embodiment.
The sixth specific implementation mode: the difference between this embodiment and the fifth embodiment is that the process of obtaining the jacobian matrix in step three is as follows:
obtained from the formulae (7) and (9)Comprises the following steps:
Sithe calculation method for the conversion to tau is as follows:
Figure GDA0002242193010000056
wherein, tauiIs SiInduced joint equivalent moment; j. the design is a squareiThe Jacobian matrix which is mapped from the force vector on the vertebral level i to the joint equivalent moment comprises the following components:
Figure GDA0002242193010000057
wherein z is0,z1,…z2i-1Is a unit vector, p, of the Z axis of the D-H coordinate system in the inertial coordinate system0,p1,…p2iVector coordinates of an origin of the D-H coordinate system in an inertial coordinate system;
the force rotation quantity borne by all vertebral segments is converted into joint equivalent torque as follows:
Figure GDA0002242193010000058
combined formula (14):
τ＝Jtf (14)
to obtain JtComprises the following steps:
Figure GDA0002242193010000061
wherein, JtA jacobian matrix for mapping the rope force to the joint equivalent moment.
Other steps and parameters are the same as those in the first, second, third, fourth or fifth embodiment.
The seventh embodiment: the difference between this embodiment and the second, third, fourth, fifth or sixth embodiment is that the specific process of obtaining the rope length change rate in the fourth step includes:
the rope force is replaced, and the principle of virtual work is utilized to obtain the following result:
is obtained by the formula (4)
Figure GDA0002242193010000063
And bringing it into formula (16) with formula (3):
Figure GDA0002242193010000064
delta is a variation operator, taunRepresents the magnitude of the equivalent moment of the nth rotational degree of freedom (joint) caused by the rope; q. q.snAn angular velocity representing the nth rotational degree of freedom;
is composed of(2) And
Figure GDA0002242193010000065
to obtain
Figure GDA0002242193010000066
Equation (17) can be rewritten as:
Figure GDA0002242193010000067
due to the fact that
Figure GDA0002242193010000068
ljFor the length of rope j, equation (18) can be converted into:
fTδl＝τTδq (19)
wherein δ l ═ δ l [ δ l ═ δ l1δl2… δlM]T；τ＝[τ1τ2… τN]T；δq＝[δq1δq2… δqN]T；
Substituting formula (14) into (19) yields:
fTδl＝fTJt Tδq (20)
obtained by the formula (20):
δl＝Jt Tδq (21)
since all constraints are constant constraints, the rate of change of the rope length
Figure GDA0002242193010000069
The relationship with the angular velocity of the rotational degree of freedom is:
Figure GDA00022421930100000610
wherein the content of the first and second substances,the superscript "·" indicates derivation with respect to time.
Solving forThe key to the inverse kinematics relationship (22) is to solve the Jacobian matrix JtFrom the formula (14), JtCan be obtained through the mapping relation between the rope force and the equivalent moment.
Other steps and parameters are the same as those in the first to sixth embodiments.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (1)

1. A method for determining the length change of a rope-driven super-redundancy freedom robot is characterized by comprising the following steps:
firstly, establishing a coordinate system on a rope drive serial-parallel mechanism of a rope drive super-redundancy freedom degree robot; defining a rope segment vector and obtaining the force of the rope force acting on the rope guide plate by the rope segment vector, wherein the specific process comprises the following steps:
defining any universal joint and the part between the universal joint and the next universal joint as a vertebral joint; in any vertebral segment, the rope guide plate close to the universal joint is a lower plate, and the rope guide plate far away from the universal joint is an upper plate;
with the center C of the lower plate of the vertebral segmentiEstablishing a vertebral level coordinate system for the origin { Ci-xiyiziI represents the serial number of the vertebral segment, I is 1, 2. I represents the total number of vertebral segments; is defined by the center C of the lower plateiThe direction pointing to the 1 st rope hole on the lower plate is xiThe axial direction, the direction perpendicular to the lower plate, is ziAxial direction, yiThe axis being perpendicular to xiAxis and ziA shaft; establishing a D-H coordinate system { O } at the center of the gimbaln-xnynznN represents a serial number of a rotational degree of freedom, and N is 1, 2. N represents the total number of rotational degrees of freedom, N ═ 2I; the vector of the rope hole on the upper plate of the vertebral segment i in the inertial coordinate system { O-XYZ } is recorded as
Figure FDA0002242192000000011
It is in the vertebral level coordinate system { Ci-xiyiziThe vector in (f) isj represents the serial number of the rope, and the serial number of a rope hole for the j rope to pass through on the vertebral segment is also j, j is 1, 2. M is the total number of ropes, and M is 3I; the vector of the rope hole on the lower plate of the vertebral segment i in the inertial coordinate system (O-XYZ) is recorded as
Figure FDA0002242192000000013
It is in the vertebral level coordinate system { Ci-xiyiziThe vector in (f) is
Figure FDA0002242192000000014
The vector from the lower plate rope hole j of the vertebral segment i +1 to the upper plate rope hole j of the vertebral segment i is a rope segment vector
Figure FDA0002242192000000015
The calculation formula is as follows:
Figure FDA0002242192000000016
the vector from the lower plate rope hole j of the vertebral segment i to the upper plate rope hole j of the vertebral segment i-1 is a rope segment vector
Figure FDA0002242192000000017
The calculation formula is as follows:
Figure FDA0002242192000000018
the rope forces acting on the lower and upper plates of the vertebral segment i are then:
Figure FDA0002242192000000019
Figure FDA00022421920000000110
wherein the content of the first and second substances,
Figure FDA00022421920000000111
the force of cord j on the lower plate of vertebra segment i;
Figure FDA00022421920000000112
the force of the cord j on the upper plate of the vertebral segment i;
Figure FDA00022421920000000113
is a vector of rope segment
Figure FDA00022421920000000114
A unit vector of (a);
Figure FDA00022421920000000115
is a vector of rope segment
Figure FDA00022421920000000116
Unit vector of, rope segment vector
Figure FDA00022421920000000117
Unit vector ofRope segment vectorUnit vector of
Figure FDA00022421920000000120
fjRepresenting the magnitude of the tension of the rope j;
step two, utilize the rope force to act on the equivalent momentum of the rope force of the rope deflector, the concrete process includes:
wherein S isiThe equivalent amount of rotation of the rope force generated by the rope on the vertebral segment i,
Figure FDA0002242192000000022
a force momentum generated at the origin of the vertebral level coordinate system of the vertebral level i for the force of the cord j acting on the vertebral level i; f ═ f1f2… fM]T；A Jacobian matrix representing a mapping of the force momentum from the cable force to the ith vertebral level;
the above-mentioned
Figure FDA0002242192000000024
The specific calculation process comprises the following steps:
the cable force on the vertebral level is divided into two categories:
A. rope for driving vertebral segment i to move is numbered as follows: j ═ I, I + I,2I + I;
B. the number of the ropes disturbing the movement of the vertebral segments I +1, I +2, … I, I +1, I +2, … 2I,2I +1,2I +2, … 3I;
when cord j is the drive cord for vertebra i, the forces acting on vertebra i are:
at this time, the process of the present invention,
Figure FDA0002242192000000026
the amount of torque generated at the origin of the vertebral level coordinate system for vertebra i is:
Figure FDA0002242192000000027
when the cord j is the distracting force of the vertebra segment i, the forces acting on the vertebra segment i are:
Figure FDA0002242192000000028
at this time, the process of the present invention,
Figure FDA0002242192000000029
the amount of torque generated at the origin of the vertebral level coordinate system for vertebra i is:
Figure FDA00022421920000000210
step three, obtaining a Jacobian matrix through a mapping relation between the rope force and the joint equivalent moment, wherein the specific process comprises the following steps:
obtained from the formulae (7) and (9)Comprises the following steps:
Figure FDA0002242192000000031
Sithe calculation method for the conversion to tau is as follows:
Figure FDA0002242192000000032
wherein, tauiIs SiInduced joint equivalent moment; j. the design is a squareiThe Jacobian matrix which is mapped from the force vector on the vertebral level i to the joint equivalent moment comprises the following components:
Figure FDA0002242192000000033
wherein z is0,z1,…z2i-1Z in D-H coordinate systemUnit vector of axis in inertial frame, p0,p1,...p2iVector coordinates of an origin of the D-H coordinate system in an inertial coordinate system;
the force rotation quantity borne by all vertebral segments is converted into joint equivalent torque as follows:
Figure FDA0002242192000000034
combined formula (14):
τ＝Jtf (14)
to obtain JtComprises the following steps:
wherein, JtA Jacobian matrix for mapping the rope force to the joint equivalent moment;
step four, combining the angular speed of the rotational freedom degree and the Jacobian matrix to obtain the rope length change rate, and the concrete process comprises the following steps:
the rope force is replaced, and the principle of virtual work is utilized to obtain the following result:
Figure FDA0002242192000000036
delta is a variation operator, taunThe magnitude of the equivalent moment representing the nth rotational degree of freedom caused by the rope; q. q.snAn angular velocity representing the nth rotational degree of freedom;
is represented by the formula (2) andto obtain
Figure FDA0002242192000000042
Equation (17) can be rewritten as:
Figure FDA0002242192000000043
due to the fact that
Figure FDA0002242192000000044
ljFor the length of rope j, equation (18) can be converted into:
fTδl＝τTδq (19)
wherein δ l ═ δ l [ δ l ═ δ l1δl2… δlM]T；τ＝[τ1τ2… τN]T；δq＝[δq1δq2… δqN]T(ii) a Substituting formula (14) into (19) yields:
δl＝Jt Tδq (21)
since all constraints are constant constraints, the rate of change of the rope length
Figure FDA0002242192000000045
The relationship with the angular velocity of the rotational degree of freedom is:
Figure FDA0002242192000000046
wherein the content of the first and second substances,
Figure FDA0002242192000000047
superscript "·" denotes derivation over time;
and step five, integrating the rope length change rate obtained in the step four to obtain the change of the rope length.
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