CN111546341B - Open-loop motion control method of air bag type soft mechanical arm - Google Patents
Open-loop motion control method of air bag type soft mechanical arm Download PDFInfo
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Abstract
The invention discloses an open-loop motion control method of an air bag type soft mechanical arm, which is characterized in that a soft mechanical arm open-loop kinematic model containing undetermined parameters is established based on theoretical analysis, the undetermined parameters are determined by using a high-precision measurement system and a calibration algorithm after a transformation relation between a soft mechanical arm motion coordinate system and a measurement coordinate system is determined, so that a kinematic model expression after parameter calibration is obtained, the kinematic model expression is simpler, finally, an air pressure input sequence is obtained by performing optimal solution on an objective function, the calculation amount in the optimal solution process is smaller, air pressure is input into each corrugated tubular air bag of the air bag type soft mechanical arm according to the air pressure input sequence to drive the tail end of the mechanical arm to move from the current position to the target position, the requirements of real-time and high efficiency of open-loop motion control can be well met, and the method is suitable for any input pressure, the device is suitable for both low-pressure input and high-pressure input conditions and has high control precision.
Description
Technical Field
The invention relates to the technical field of control of an air bag type soft mechanical arm, in particular to an open-loop motion control method of the air bag type soft mechanical arm.
Background
The soft robot is a continuous robot made of soft material, has continuous deformation capability, and generates smooth curve motion in the main structure of the robot through deformation. At present, the driving modes of the soft robot are various, such as shape memory alloy, electroactive polymer, hydrogel, pneumatic driving, etc. Among them, the pneumatic soft robot is developed earlier and has mature technology, and most probably the application is realized first. In the prior document 1 [ Liu hong Wei, Zhang Xiang, Huang Yi Yong, Cheng Xiao, front-facing airbag type soft mechanical arm kinematics modeling and analysis [ J ] manned aerospace, 2019,3:347-354 ] an airbag type soft mechanical arm system is provided, as shown in fig. 1 and 2, the mechanical arm is formed by connecting three mutually independent soft drivers in series, each soft driver is formed by connecting three mutually independent corrugated pipes in parallel, and a plurality of rigid restraint frames are arranged between the mutually parallel corrugated pipes for improving the rigidity and stability of the mechanical arm. At the position of the rigid restraint frame, the cross sections of the three corrugated pipes are always in one plane. Since the robot arm has 9 mutually independent bellows-like bladders, i.e. 9 independent motion control inputs, the robot arm has 9 degrees of freedom of motion, 2 degrees of freedom of bending and 1 degree of freedom of elongation for each actuator. Therefore, how to precisely control the pneumatic soft robot is very important for the realization of the application.
At present, in the existing literature 2 [ zhangxiang, liu hong wei, liu zhuo qun, etc. ] space intelligent soft mechanical arm dynamics modeling and control [ J ]. intelligent science and technology report, 2019,1(1):52-61 ] dynamics modeling and control research is carried out on the airbag type soft mechanical arm in the literature 1, and a mechanical arm dynamics model is established on the basis of the sectional beam hypothesis of the soft mechanical arm. The model can be used for the open-loop motion control of the soft mechanical arm, but the mathematical expression of the model is very complex and has large calculation amount, and the requirements of real-time performance and high efficiency of the open-loop motion control are difficult to meet.
In addition, prior document 3 [ Zheyuan Gong, Zhexin Xie, Xingbang Yang, et al, design, simulation and Kinematic Modeling of a 3D-motion Soft robot Arm [ C ]. Proceedings of the 2016IEEE International Conference on robots and biometics, Qingdao, China, December 3-7,2016 ] established an open-loop control model of robot motion for a two-segment actuator balloon-type Soft robot Arm, assuming that each actuator bending deformation satisfies a normal curvature assumption, i.e., two curvature parameters are used to describe the spatial state of one Soft actuator. This assumption is true when the input pressure to the air bag is low (about 60kPa or less), and the precision of the open-loop motion control of the soft robot arm is high, but in the high-pressure case, the actuator deformation does not satisfy the constant curvature assumption, so the open-loop motion control error obtained based on this model is large, and at 80kPa, the open-loop motion control error reaches about 4cm, and the open-loop control error rapidly increases as the input pressure increases.
Disclosure of Invention
The invention provides an open-loop motion control method of an air bag type soft mechanical arm, which aims to solve the technical problems that the existing open-loop motion control method of the air bag type soft mechanical arm has very complicated mathematical expression and large calculation amount, is difficult to meet the requirements of real-time performance and high efficiency of open-loop motion control, and has large control error in a high-pressure input environment.
According to one aspect of the invention, the open-loop motion control method of the air bag type soft mechanical arm is provided, the air bag type soft mechanical arm is formed by connecting n soft drivers in series, n is larger than or equal to 1, each soft driver is formed by connecting m corrugated tubular air bags in parallel, m is larger than or equal to 3, a rigid restraint frame is arranged between the adjacent corrugated tubular air bags, and the open-loop motion control method of the air bag type soft mechanical arm comprises the following steps:
step S1: the root part of the air bag type soft mechanical arm is fixedly arranged at the upper end of the cuboid frame, and the air bag type soft mechanical arm naturally droops when no air pressure is input;
step S2: establishing a software mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ;
step S3: establishing a kinematic model of the air bag type soft mechanical arm, wherein the kinematic model comprises the following steps:
wherein the content of the first and second substances,
for the parameter to be determined, PijIndicating the input air pressure of the jth bellows on the ith driver, (x, y, z)TIs a position vector of the tail end of the air bag type soft mechanical arm;
step S4: determining the transformation relation between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ;
step S5: calibrating undetermined parameters in the kinematic model based on a plurality of times of air pressure input measurement results and in combination with a conversion relation between a soft mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ;
step S6: and setting an optimization objective function, carrying out objective function optimization solving based on the kinematic model after parameter calibration and the position vector of the target position point to obtain an air pressure input sequence, and inputting air pressure into each corrugated tubular air bag of the air bag type soft mechanical arm according to the air pressure input sequence to drive the tail end of the mechanical arm to move from the current position to the target position.
Furthermore, the software mechanical arm motion coordinate system 0-xyz takes the center of the bottom of the rectangular frame as an origin o, the horizontal right direction is the positive direction of an x axis, the positive direction of a y axis is obtained by rotating the positive direction of the x axis by 90 degrees anticlockwise, and the positive direction of the z axis points to the height direction; the measurement coordinate system O-ENZ takes the original point of the measurement system as an O point, E points to the east direction, N points to the north direction, and Z points to the height direction.
Further, in step S4, the conversion relationship between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ is determined by measuring the coordinate positions of the six vertices of the rectangular parallelepiped frame.
Further, the step S4 is specifically:
establishing a conversion relation expression between the software mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ, wherein the expression is as follows:
wherein R is an orthogonal rotation matrix, (E)0 N0 Z0)TIs the amount of translation between the two coordinate systems;
the coordinates of the six vertices A, B, C, D, E, F of the rectangular parallelepiped frame are measured, and the measurement results are represented in a measurement coordinate system O-ENZ, where:
wherein, a, b and h respectively represent the length, width and height of the cuboid frame;
the coordinate measurement results of the six vertexes of the rectangular parallelepiped frame are substituted into formula (2) to obtain:
thereby, the following were obtained:
suppose that
The orthogonal rotation matrix R between the two coordinate systems is obtained as:
R＝(QWT)(WWT)-1 (12)；
substituting the formula (12) into the formulas (4) to (9) respectively to obtain (E)0 N0 Z0)TAnd averaged as shown in equation (13):
thereby obtaining a transformation relationship between the two coordinate systems.
Further, in the step S5, the position vector (E) of the end of the soft mechanical arm is obtained by measuring each time of the air pressure input by performing the air pressure input N times, where N is greater than or equal to 3nm +3, and the air pressure combinations input at any two times are not related to each otheri Ni Zi)TAnd the subscript i is 1,2,., N, which represents a measurement serial number, and is used for calibrating the undetermined parameters in the kinematic model based on the N times of measurement results and the conversion relation between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ.
Further, the step S5, based on the N measurement results and the conversion relationship between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ, calibrating the to-be-determined parameter in the kinematic model specifically includes:
the position vector (E) of the end of the soft mechanical arm obtained by each measurementi Ni Zi)TConverting the coordinate system into a mechanical arm motion coordinate system 0-xyz based on a formula (2) to obtain (x)i yi zi)T；
All measurements are taken simultaneously according to equation (1):
wherein (x)i yi zi)TIndicating the end position of the soft mechanical arm at the ith air pressure input, wherein i is 1, 2.
Is provided with
Thereby obtaining a transformation matrix in the kinematic model:
inputting the air pressure N times into the sequence (P)11…P1m……Pn1…Pnm)i TEnd of arm position vector (x)i yi zi)TAnd substituting the transformation matrix into formula (1), calculating (x) for each group of measured values0 y0 z0)TAnd taking the average value as the calibrated parameter.
Further, the step S6 is specifically:
let each variable in the kinematic model in equation (1) be expressed as:
the kinematic model is then represented as: r is Ap + r0(21)；
Setting a target position and obtaining a position vector r of the target position in a measuring coordinate system O-ENZtargetConverting the target position vector from a measurement coordinate system O-ENZ into a soft mechanical arm motion coordinate system 0-xyz by using a formula (2);
setting an optimization objective function as f (p), and solving the following optimization problems:
miny＝f(p)
pmin＝(Pmin,Pmin,...Pmin)nm×1 T
pmax＝(Pmax,Pmax,...Pmax)nm×1 T
p＝(P11…P1m……Pn1…Pnm)T
(22)
wherein, PmaxIs the maximum value of the bellows air bag input pressure, PminIs the minimum value of the bellows airbag input pressure;
solving the optimization problem to obtain a pneumatic input sequence P ═ (P)11…P1m……Pn1…Pnm)TAnd inputting air pressure into each corrugated tube-shaped air bag of the air bag type soft mechanical arm according to the air pressure input sequence so as to drive the tail end of the mechanical arm to move from the current position to the target position.
Further, the method also comprises the following steps:
step S7: and evaluating the control accuracy of the open-loop motion control algorithm.
Further, the step S7 is specifically:
measuring to obtain the actual motion position vector r of the tail end of the mechanical arm under the drive of the air pressure input sequence*＝(x*,y*,z*)TAnd calculates its actual motion position vector r*＝(x*,y*,z*)TAnd a target position vector rtarget＝(xtarget,ytarget,ztarget)TAnd evaluating the open-loop motion control accuracy based on the distance calculation result of the two.
Further, a total station or a visual positioning measurement system is used for position measurement in the measurement coordinate system O-ENZ.
The invention has the following effects:
the open-loop motion control method of the air bag type soft mechanical arm of the invention is characterized in that the root part of the air bag type soft mechanical arm is fixedly arranged at the upper end of a cuboid frame, and then a soft mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ are established, and then a soft mechanical arm open-loop kinematics model containing undetermined parameters is established based on theoretical analysis, after determining the transformation relation between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ, determining undetermined parameters by using a high-precision measurement system and a calibration algorithm, thereby obtaining a kinematic model expression after parameter calibration, finally obtaining an air pressure input sequence by optimizing and solving an objective function based on the kinematic model expression after parameter calibration, and inputting air pressure into each corrugated tube-shaped air bag of the air bag type soft mechanical arm according to the air pressure input sequence so as to drive the tail end of the mechanical arm to move from the current position to the target position. The open-loop motion control method of the air bag type soft mechanical arm adopts a simpler kinematics model expression, has smaller calculation amount in the optimization solving process, can well meet the requirements of real-time performance and high efficiency of open-loop motion control, is suitable for any input pressure range, is suitable for both low-pressure input and high-pressure input conditions, and has higher control precision.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic structural diagram of a conventional airbag type soft mechanical arm system.
Figure 2 is a schematic cross-sectional view of the actuator in the balloon-type soft mechanical arm of figure 1.
Fig. 3 is a schematic flow chart of the open-loop motion control method of the balloon type soft mechanical arm according to the preferred embodiment of the present invention.
FIG. 4 is a diagram of the soft robot motion coordinate system 0-xyz and the measurement coordinate system O-ENZ established in step S2 of FIG. 3 according to the preferred embodiment of the present invention.
Detailed Description
The embodiments of the invention will be described in detail below with reference to the accompanying drawings, but the invention can be embodied in many different forms, which are defined and covered by the following description.
As shown in fig. 3, a preferred embodiment of the present invention provides an open-loop motion control method for an airbag-type soft mechanical arm, which is used to control the motion of the airbag-type soft mechanical arm, where the airbag-type soft mechanical arm is formed by connecting n soft drivers in series, n is greater than or equal to 1, each soft driver is formed by connecting m bellows-shaped air bags in parallel, m is greater than or equal to 3, and a rigid constraining frame is disposed between adjacent bellows-shaped air bags, so that the rigidity and stability of the mechanical arm are improved, and the structures at the positions of the rigid constraining frame in the motion process of the mechanical arm have the same spatial orientation. It is understood that the structure of the balloon-type soft arm system is similar to that of the balloon-type soft arm system in fig. 1, except that the number of soft actuators connected in series is not specifically limited, and the number of bellows-shaped balloons connected in parallel in each soft actuator is not specifically limited. The open-loop motion control method of the air bag type soft mechanical arm specifically comprises the following steps:
step S1: the root part of the air bag type soft mechanical arm is fixedly arranged at the upper end of the cuboid frame, and the air bag type soft mechanical arm naturally droops when no air pressure is input;
step S2: establishing a software mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ;
step S3: establishing a kinematic model of the air bag type soft mechanical arm, wherein the kinematic model comprises the following steps:
wherein the content of the first and second substances,
for the parameter to be determined, PijIndicating the input air pressure of the jth bellows on the ith driver, (x, y, z)TIs a position vector of the tail end of the air bag type soft mechanical arm;
step S4: determining the transformation relation between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ;
step S5: calibrating undetermined parameters in the kinematic model based on a plurality of times of air pressure input measurement results and in combination with a conversion relation between a soft mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ;
step S6: and setting an optimization objective function, carrying out objective function optimization solving based on the kinematic model after parameter calibration and the position vector of the target position point to obtain an air pressure input sequence, and inputting air pressure into each corrugated tubular air bag of the air bag type soft mechanical arm according to the air pressure input sequence to drive the tail end of the mechanical arm to move from the current position to the target position.
It can be understood that, in the method for controlling the open-loop motion of the airbag-type soft mechanical arm according to the preferred embodiment, the root of the airbag-type soft mechanical arm is fixedly installed at the upper end of the rectangular frame, the motion coordinate system 0-xyz and the measurement coordinate system O-ENZ of the airbag-type soft mechanical arm are established, the open-loop kinematics model of the airbag-type soft mechanical arm containing the undetermined parameters is established based on theoretical analysis, the undetermined parameters are determined by using the high-precision measurement system and the calibration algorithm after the transformation relationship between the motion coordinate system 0-xyz and the measurement coordinate system O-ENZ is determined, so as to obtain the kinematics model expression after the parameter calibration, finally, the air pressure input sequence is obtained by optimizing and solving the target function based on the kinematics model expression after the parameter calibration, and air pressure is input into each corrugated tubular airbag of the airbag-type soft mechanical arm according to the air pressure input sequence so as to drive the tail end of the airbag-type soft And (4) placing. The open-loop motion control method of the air bag type soft mechanical arm adopts a simpler kinematics model expression, has smaller calculation amount in the optimization solving process, can well meet the requirements of real-time performance and high efficiency of open-loop motion control, is suitable for any input pressure range, is suitable for both low-pressure input and high-pressure input conditions, and has higher control precision.
It can be understood that, in the step S1, the root of the airbag-type soft mechanical arm is fixedly installed on the rectangular frame, and the rectangular frame is horizontally placed and fixed on the ground, when no air pressure is input, the airbag-type soft mechanical arm naturally droops, and when the airbag-type soft mechanical arm is inflated, the mechanical arm can perform bending, stretching and other actions.
It can be understood that, as shown in fig. 4, in the step S2, the soft mechanical arm motion coordinate system 0-xyz takes the bottom center of the rectangular parallelepiped frame as an origin o, the horizontal right direction is the positive x-axis direction, the positive y-axis direction is obtained by rotating 90 ° counterclockwise from the positive x-axis direction, and the positive z-axis direction points to the height direction, forming a right-hand rectangular coordinate system; the measurement coordinate system O-ENZ takes the original point of the measurement system as an O point, E points to the east direction, N points to the north direction, and Z points to the height direction, so that a right-hand rectangular coordinate system is formed. Wherein, a total station or a visual positioning measurement system is adopted to measure the position in the measurement coordinate system O-ENZ.
It can be understood that, in the step S3, the total number of nm independent input air pressures P are provided by the air bag type soft mechanical armijWherein i 1, 2.. n denotes a driver number, j 1, 2.. m denotes a bellows-shaped airbag number, and PijThe input air pressure of the jth bellows-shaped air bag on the ith driver is represented, and the position vector of the end of the soft mechanical arm in the motion coordinate system 0-xyz of the soft mechanical arm can be represented as (x, y, z)T. For each driver in the air bag type soft mechanical arm, the driver can be divided into a series of micro-elements along the direction of the central axis, and the motion of each micro-element is represented as bending and stretching under the action of the air pressure of the cavity, so that the micro-elements can be assumed to be elastic beams, and a linear relation exists between the position coordinates of the tail ends of the micro-elements and the air pressure. Because the coordinates of the tail end position of the air bag type soft mechanical arm are the superposition of all infinitesimal bending and stretching motions, the tail end position of the soft mechanical arm and all air pressures have a linear relation, and thus the kinematic model of the air bag type soft mechanical arm can be expressed as follows:
wherein the content of the first and second substances,
the parameters to be determined need to be obtained by fitting experimental measurement data.
In this embodiment, the open-loop motion control method of the airbag-type soft mechanical arm includes performing theoretical analysis on the airbag-type soft mechanical arm formed by connecting a plurality of drivers in series, and equating each driver to be a infinitesimal, and then based on an elastic beam analysis mechanism, a linear relationship exists between a position coordinate of the tail end of each infinitesimal and air pressure, so that a linear relationship also exists between the tail end position of the entire airbag-type soft mechanical arm and all air pressures, thereby establishing the above-mentioned kinematic model.
It is understood that the conversion relationship between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ is determined by measuring the coordinate positions of the six vertices of the rectangular parallelepiped frame in step S4.
Specifically, in the step S4, in order to measure the conversion relationship between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ, the coordinates of the vertices of the 6 rectangular parallelepiped frames A, B, C, D, E, F are measured by using a total station, a visual positioning measurement system, or the like, wherein the measurement result is expressed in the O-ENZ coordinate system. It is understood that other six vertices may be selected in other embodiments of the present invention, and the selection of the vertex positions is not specifically limited herein. The soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ are right-handed rectangular coordinate systems, so that the transformation relation between the two coordinate systems comprises rotation and translation, and a transformation relation expression between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ can be established, wherein the expression is as follows:
wherein R is an orthogonal rotation matrix reflecting the rotation relationship between two coordinate systems, (E)0 N0 Z0)TThe translation relationship between the two coordinate systems is reflected for the amount of translation between the two coordinate systems.
And then measuring by a total station or a visual positioning measurement system to obtain coordinates of six vertexes A, B, C, D, E, F of the cuboid frame, wherein the measurement result is expressed in a measurement coordinate system O-ENZ, and specifically comprises the following steps:
wherein, a, b and h respectively represent the length, width and height of the cuboid frame.
Then, the coordinate measurement results of the six vertexes of the rectangular parallelepiped frame are substituted into the formula (2) to obtain:
thereby, the following were obtained:
suppose that
So as to obtain an orthogonal rotation matrix R between the motion coordinate system 0-xyz of the soft mechanical arm and the measurement coordinate system O-ENZ as follows:
R＝(QWT)(WWT)-1 (12)；
substituting the formula (12) into the formulas (4) to (9) respectively to obtain (E)0 N0 Z0)TAnd then taking the average value thereof, as shown in formula (13):
then calculating the average value0 N0 Z0)TAnd substituting into the formula (2) to obtain a transformation relational expression between the two coordinate systems.
It can be understood that in the gas bag type soft mechanical arm kinematics model given by the formula (1), the undetermined parameters are 3nm +3 in total, and at least more than 3nm +3 groups of measurements are needed to determine the undetermined parameters. Therefore, in the step S5, N times of air pressure input are performed, N is larger than or equal to 3nm +3, and the air pressure combination of any two times of input (P)11…P1m……Pn1…Pnm)i TIs not related to each other, and the position vector (E) of the end of the soft mechanical arm can be obtained by measuring with the measuring system at each time of air pressure inputi Ni Zi)TThe index i ═ 1, 2., N, which represents the measurement sequence number, the position vector being represented in the measurement coordinate system O-ENZ, the parameter to be determined in the kinematic model being calibrated on the basis of the N measurements in combination with the expression of the transformation relationship between the two coordinate systems determined in the above step S4.
In step S5, the process of calibrating the to-be-determined parameter in the kinematic model based on the N measurement results and the conversion relationship between the soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ specifically includes:
firstly, the position vector (E) of the end of the soft mechanical arm obtained by each measurement is obtainedi Ni Zi)TTransforming into a mechanical arm motion coordinate system 0-xyz based on formula (2) to obtain (x)i yi zi)T；
And then all the measurement results are obtained simultaneously according to the formula (1):
wherein (x)i yi zi)TIndicates the end position of the robot arm at the ith pneumatic input, i 1,20 y0 z0)TIs the undetermined parameter in equation (1). Is provided with
Thereby obtaining a transformation matrix in the kinematic model (i.e., equation (1)):
then inputting the air pressure N times into the sequence (P)11…P1m……Pn1…Pnm)i TEnd of arm position vector (x)i yizi)TAnd substituting the transformation matrix into formula (1), and calculating to obtain an (x) value for each group of measured values0 y0 z0)TThen taking the average value as the parameter in the above-mentioned kinematic model, and
it can be solved by equations (15) to (17). Thus, the kinematic model of the air bag type soft mechanical arm is determined by an experimental measurement method.
It can be understood that the design of the open-loop motion control algorithm of the air bag type soft mechanical arm is to optimally design the pressure input combination of each air bag in the soft mechanical arm under the condition of a given target point position, and the tail end of the mechanical arm is moved to the target point position under the driving of the pressure combination. The step S6 specifically includes:
let each variable in the kinematic model in equation (1) be expressed as:
the kinematic model of the balloon-type soft mechanical arm can be expressed as: r is Ap + r0(21)。
In the design of the open-loop motion control algorithm of the air bag type soft mechanical arm, a target position is set first and a position vector r of the target position in a measurement coordinate system O-ENZ is obtainedtargetAnd then transforming the target position vector from the measurement coordinate system O-ENZ to the soft mechanical arm motion coordinate system 0-xyz by using a formula (2).
And then setting an optimization objective function as f (p), and then converting the design of the air bag type soft mechanical arm open-loop motion control algorithm into the solution of the following optimization problem:
miny＝f(p)
pmin＝(Pmin,Pmin,...Pmin)nm×1 T
pmax＝(Pmax,Pmax,...Pmax)nm×1 T
p＝(P11…P1m……Pn1…Pnm)T (22)
wherein, PmaxIs the maximum value of the bellows air bag input pressure, PminIs the minimum value of the bellows bladder input pressure, the optimization objective function f (p) may be set manually, such as minimum total air pressure input, minimum length of movement between the current position and the target position, etc. For example, taking the total barometric pressure input as a minimum as an optimization goal, then:
and solving the optimization problem by using a sequence quadratic optimization method to obtain a pneumatic input sequence P ═ (P)11…P1m……Pn1…Pnm)TAnd inputting air pressure into each corrugated tube-shaped air bag of the air bag type soft mechanical arm according to the air pressure input sequence so as to drive the tail end of the mechanical arm to move from the current position to the target position. The sequence quadratic optimization method is an algorithm mature in the optimization field, and the specific process is not described herein again. In addition, other advantages existing in the prior art can be adopted in other embodiments of the inventionThe optimization method is not specifically limited herein, and the optimization problem is solved.
The method for controlling the open-loop motion of the air bag type soft mechanical arm can be understood that the design of the open-loop motion control algorithm is converted into the solution of the target optimization problem by converting the kinematics model, the data calculation amount involved in the open-loop motion control algorithm is greatly reduced, and the control precision is higher.
It can be understood that the open-loop motion control method of the airbag type soft mechanical arm further comprises the following steps:
step S7: and evaluating the control accuracy of the open-loop motion control algorithm.
Wherein, the step S7 specifically includes:
the pressure input sequence P (P) of the end of the air bag type soft mechanical arm is measured by a measuring system11…P1m……Pn1…Pnm)TActual motion position vector r under drive*＝(x*,y*,z*)TAnd calculates its actual motion position vector r*＝(x*,y*,z*)TAnd a target position vector rtarget＝(xtarget,ytarget,ztarget)TThe distance between:
and then evaluating the open-loop motion control accuracy based on the distance calculation result of the two. The level of accuracy at which the open loop motion control is based can be assessed by setting different thresholds, for example, a high control accuracy level when the calculated distance between the two is less than a first threshold, a medium control accuracy level when the calculated distance is between the first threshold and a second threshold, and a low control accuracy level when the calculated distance is greater than the second threshold, wherein the first threshold is less than the second threshold. Once the open-loop motion control accuracy level is evaluated to be low, the whole air bag type soft mechanical arm system needs to be checked, for example, whether factors influencing the control accuracy, such as air leakage, structural looseness and the like exist. Of course, other ways of performing control accuracy grading may also be used in other embodiments of the present invention.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. An open-loop motion control method of an air bag type soft mechanical arm, the air bag type soft mechanical arm is formed by connecting n soft drivers in series, n is more than or equal to 1, each soft driver is formed by connecting m corrugated tubular air bags in parallel, m is more than or equal to 3, a rigid restraint frame is arranged between the adjacent corrugated tubular air bags, and the method is characterized in that,
the open-loop motion control method of the air bag type soft mechanical arm comprises the following steps:
step S1: the root part of the air bag type soft mechanical arm is fixedly arranged at the upper end of the cuboid frame, and the air bag type soft mechanical arm naturally droops when no air pressure is input;
step S2: establishing an air bag type soft mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ;
step S3: establishing a kinematic model of the air bag type soft mechanical arm, wherein the kinematic model comprises the following steps:
wherein the content of the first and second substances,
for the parameter to be determined, PijIndicating the input air pressure of the jth bellows on the ith driver, (x, y, z)TIs a position vector of the tail end of the air bag type soft mechanical arm;
step S4: determining the transformation relation between the motion coordinate system 0-xyz of the air bag type soft mechanical arm and the measurement coordinate system O-ENZ;
step S5: inputting a measurement result based on a plurality of times of air pressure and calibrating undetermined parameters in the kinematics model by combining a conversion relation between an air bag type soft mechanical arm motion coordinate system 0-xyz and a measurement coordinate system O-ENZ;
step S6: and setting an optimized objective function, carrying out objective function optimization solving based on the kinematic model after parameter calibration and the position vector of the target position point to obtain an air pressure input sequence, and inputting air pressure into each corrugated tube-shaped air bag of the air bag type soft mechanical arm according to the air pressure input sequence to drive the tail end of the air bag type soft mechanical arm to move from the current position to the target position.
2. The open-loop motion control method of a balloon-type soft mechanical arm as claimed in claim 1,
the motion coordinate system 0-xyz of the air bag type soft mechanical arm takes the center of the bottom of the rectangular frame as an original point o, the horizontal right direction is the positive direction of an x axis, the positive direction of a y axis is obtained by anticlockwise rotating for 90 degrees from the positive direction of the x axis, and the positive direction of a z axis points to the height direction; the measurement coordinate system O-ENZ takes the original point of the measurement system as an O point, E points to the east direction, N points to the north direction, and Z points to the height direction.
3. The open-loop motion control method of a balloon-type soft mechanical arm as claimed in claim 1,
in the step S4, the coordinate positions of the six vertexes of the rectangular parallelepiped frame are measured to determine the conversion relationship between the motion coordinate system 0-xyz of the balloon type soft mechanical arm and the measurement coordinate system O-ENZ.
4. The open-loop motion control method of a balloon-type soft mechanical arm as claimed in claim 3,
the step S4 specifically includes:
establishing a transformation relation expression between the air bag type soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ, wherein the expression is as follows:
wherein R is an orthogonal rotation matrix, (E)0 N0 Z0)TIs the amount of translation between the two coordinate systems;
the coordinates of the six vertices A, B, C, D, E, F of the rectangular parallelepiped frame are measured, and the measurement results are represented in a measurement coordinate system O-ENZ, where:
wherein, a, b and h respectively represent the length, width and height of the cuboid frame;
the coordinate measurement results of the six vertexes of the rectangular parallelepiped frame are substituted into formula (2) to obtain:
thereby, the following were obtained:
suppose that
The orthogonal rotation matrix R between the two coordinate systems is obtained as:
R＝(QWT)(WWT)-1 (12)；
substituting the formula (12) into the formulas (4) to (9) respectively to obtain (E)0 N0 Z0)TAnd averaged as shown in equation (13):
thereby obtaining a transformation relationship between the two coordinate systems.
5. The open-loop motion control method of the balloon-type soft mechanical arm of claim 4,
in the step S5, the position vector (E) of the tail end of the air bag type soft mechanical arm is obtained by measuring each air pressure input by N times of air pressure input, wherein N is more than or equal to 3nm +3, and the air pressure combinations input at any two times are not related to each otheri Ni Zi)TAnd the subscript i is 1,2,., N and represents a measurement serial number, and the undetermined parameters in the kinematics model are calibrated based on the N times of measurement results and the conversion relation between the air bag type soft mechanical arm motion coordinate system 0-xyz and the measurement coordinate system O-ENZ.
6. The open-loop motion control method of a balloon-type soft mechanical arm according to claim 5,
the process of calibrating the undetermined parameters in the kinematics model based on the N measurement results and the conversion relationship between the motion coordinate system 0-xyz of the airbag type soft mechanical arm and the measurement coordinate system O-ENZ in the step S5 specifically includes:
the position vector (E) of the tail end of the air bag type soft mechanical arm obtained by each measurementi Ni Zi)TIs transformed into an air bag type soft mechanical arm motion coordinate system 0-xyz based on a formula (2) to obtain (x)i yi zi)T；
All measurements are taken simultaneously according to equation (1):
wherein (x)i yi zi)TIndicating the end position of the air bag type soft mechanical arm when the ith air pressure is input, wherein i is 1, 2.
Setting:
thereby obtaining a transformation matrix in the kinematic model:
inputting the air pressure N times into the sequence (P)11 … P1m … … Pn1 … Pnm)i TAir bag type soft machineryArm end position vector (x)i yi zi)TAnd substituting the transformation matrix into formula (1), calculating (x) for each group of measured values0 y0 z0)TAnd taking the average value as the calibrated parameter.
7. The open-loop motion control method of a balloon-type soft mechanical arm of claim 6,
the step S6 specifically includes:
let each variable in the kinematic model in equation (1) be expressed as:
the kinematic model is then represented as: r is Ap + r0 (21)；
Setting a target position and obtaining a position vector r of the target position in a measuring coordinate system O-ENZtargetConverting the target position vector from a measurement coordinate system O-ENZ into a motion coordinate system 0-xyz of the air bag type soft mechanical arm by using a formula (2);
setting an optimization objective function as f (p), and solving the following optimization problems:
min y＝f(p)
pmin＝(Pmin,Pmin,...Pmin)nm×1 T
pmax＝(Pmax,Pmax,...Pmax)nm×1 T
p＝(P11 … P1m … … Pn1 … Pnm)T (22)
wherein, PmaxIs the maximum value of the bellows air bag input pressure, PminIs the minimum value of the bellows airbag input pressure;
solving the optimization problem to obtain a pneumatic input sequence P ═ (P)11 … P1m … … Pn1 … Pnm)TAnd inputting air pressure into each corrugated tube-shaped air bag of the air bag type soft mechanical arm according to the air pressure input sequence so as to drive the tail end of the air bag type soft mechanical arm to move from the current position to the target position.
8. The open-loop motion control method of a balloon-type soft mechanical arm as claimed in claim 7,
further comprising the steps of:
step S7: and evaluating the control accuracy of the open-loop motion control algorithm.
9. The open-loop motion control method of a balloon-type soft mechanical arm of claim 8,
the step S7 specifically includes:
measuring to obtain the actual motion position vector r of the tail end of the air bag type soft mechanical arm driven by the air pressure input sequence*＝(x*,y*,z*)TAnd calculates its actual motion position vector r*＝(x*,y*,z*)TAnd a target position vector rtarget＝(xtarget,ytarget,ztarget)TAnd evaluating the open-loop motion control accuracy based on the distance calculation result of the two.
10. The open-loop motion control method of a balloon-type soft mechanical arm as claimed in claim 1,
and measuring the position in the measuring coordinate system O-ENZ by adopting a total station or a visual positioning measuring system.
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