CN111230882B - Self-adaptive variable impedance control method of fruit sorting parallel robot clamping mechanism - Google Patents

Self-adaptive variable impedance control method of fruit sorting parallel robot clamping mechanism Download PDF

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CN111230882B
CN111230882B CN202010115999.XA CN202010115999A CN111230882B CN 111230882 B CN111230882 B CN 111230882B CN 202010115999 A CN202010115999 A CN 202010115999A CN 111230882 B CN111230882 B CN 111230882B
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clamping mechanism
clamping
parallel robot
fruit sorting
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CN111230882A (en
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高国琴
李雅倩
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Jiangsu University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1612—Programme controls characterised by the hand, wrist, grip control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed

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Abstract

The invention discloses a self-adaptive variable impedance control method for a fruit sorting parallel robot clamping mechanism. The method adopts an impedance controller outer ring and a position controller inner ring to form a cascade control structure, the deviation of expected clamping force and collected actual contact force is used as the input of an outer ring force impedance controller, the outer ring force impedance controller generates a correction value of an inner ring position reference track, and the clamping force control is realized through the self-adaptive variable impedance control of a clamping mechanism of the fruit sorting parallel robot. The self-adaptive variable impedance control algorithm of the fruit sorting parallel robot clamping mechanism provided by the invention has self-adaptability to the movement speed and load change of the clamping mechanism, and can realize the nondestructive clamping of the fruit sorting parallel robot clamping mechanism on the fruit.

Description

Self-adaptive variable impedance control method of fruit sorting parallel robot clamping mechanism
Technical Field
The invention relates to the technical field of agricultural parallel robot control, in particular to a self-adaptive variable impedance control method for clamping serial fruits by a fruit sorting parallel robot, which realizes the nondestructive clamping of the fruit sorting parallel robot to the serial fruits.
Background
The parallel mechanism adopts a closed chain structure, has the advantages of stable structure, high rigidity, high precision, good dynamic performance and the like, and is particularly suitable for fruit sorting operation with higher requirements on grabbing stability. However, the fruits in the cluster are soft and easily damaged, and one of the key problems for realizing nondestructive sorting is how to realize flexible clamping control of the clamping mechanism on the fruits with high performance. The parallel robot gripper mechanism is a mechanism that is in direct contact with the target fruit, and functions like a human hand.
In the text of flexible grabbing force control of an end effector of a fruit and vegetable picking robot (Jiwei, Luomaiwei, Lijunle, agricultural engineering journal, 2014, volume 30, phase 9, pages 19-26), aiming at fruit and vegetable picking of the picking robot, an end effector and driving motor control model is established, and a grabbing moment control method based on generalized proportional integral is designed. But only a GPI moment feedback controller is used, and compared with double-loop control, the force is difficult to accurately track.
In the text of design and gripping force tracking impedance control of a robot flexible gripping test platform (Wangchun, Xiaoshui, agricultural engineering science and report, 2015, volume 31, phase 1, page 58-63), in order to reduce damage of the robot to fruits and vegetables in the picking process, a gripping force tracking impedance control algorithm for gripping the fruits and vegetables by two fingers is provided based on the two-finger gripping direction of a Cartesian space end effector. But the finger force/position control is equivalent to a desired inertia-damping-rigidity model, and the impedance control of fixed impedance model parameters cannot adapt to the change of the fruit quality and position.
Disclosure of Invention
Aiming at the problem of nondestructive clamping of the fruit sorting parallel robot clamping mechanism on the fruits in series, the invention provides the self-adaptive variable impedance control method, which carries out real-time adjustment on the damping parameter based on the deviation of expected clamping force and collected actual contact force, improves the self-adaptability of the system to the clamping speed and the clamping load change, and simultaneously improves the performance of impedance control so as to realize the nondestructive clamping of the fruit sorting parallel robot clamping mechanism on the fruits in series.
The technical scheme adopted by the invention comprises the following steps:
a self-adaptive variable impedance control method of a fruit sorting parallel robot clamping mechanism comprises the following steps:
1) the fruit sorting parallel robot clamping mechanism is used as a controlled object, and the fruit sorting parallel robot clamping mechanism is subjected to kinematic analysis by adopting an analytical method, so that the conversion relation between the rotation angle of the driving joint screw rod and the position of clamping fingers of the clamping mechanism is obtained;
2) establishing a dynamic model of a fruit sorting parallel robot clamping mechanism by adopting a Lagrange method;
3) based on the dynamic model established by the Lagrange method in the step 2), a double-loop control structure is adopted: in the outer ring force control, designing an adaptive variable impedance controller; in the inner ring position control, a smooth sliding mode controller is designed;
4) aiming at an impedance controller for controlling the smooth sliding mode position of the clamping mechanism of the fruit sorting parallel robot in the step 3), designing a self-adaptive variable impedance control algorithm of the clamping mechanism of the fruit sorting parallel robot, and carrying out real-time adjustment on damping parameters based on the deviation between expected clamping force and collected actual contact force;
5) forming a self-adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism based on the step 2), the step 3) and the step 4);
6) the self-adaptive variable impedance control method of the fruit sorting parallel robot clamping mechanism is realized through software programming.
Further, in the step 1), performing kinematic analysis on the parallel robot clamping mechanism by using an analytical method, and obtaining a position conversion relation between a rotation angle of the driving joint screw and clamping fingers of the clamping mechanism, to obtain:
Figure GDA0003476073720000021
in the formula, psIs a lead screw lead; theta is the rotation angle of the driving joint screw rod; l1Is the length of the driven rod; e is the structural length of the slider; x is the position of the clamping finger of the clamping mechanism in the X-axis direction; d0The initial position of the slide block from the origin of coordinates; l3The structure length of the clamping finger from the sliding seat in the Y-axis direction is adopted; l5The clamping fingers are away from the sliding seat in the structural length in the X-axis direction.
Further, in the step 2), the dynamic model established by the lagrangian method is as follows:
Figure GDA0003476073720000022
wherein M (q) is an inertia matrix,
Figure GDA00034760737200000210
the terms of Copenforces and centrifugal forces, G (Q) the terms of gravity, and Q the generalized driving force;
the pose of the pinch finger is given by q ═ x, and the kinetic model can be converted into:
Figure GDA0003476073720000023
wherein m (x) is a symmetric positive definite inertial matrix,
Figure GDA0003476073720000024
the terms Copenforces and centrifugal forces, g (x) the terms gravity,
Figure GDA0003476073720000025
and
Figure GDA0003476073720000026
the actual speed and the acceleration of the clamping fingers of the clamping mechanism are respectively, and tau is the driving torque of the active joint screw rod;
further, in the step 3), in the outer ring force control, a relationship between a force applied to the gripping fingers of the gripping mechanism and a difference between an actual position and a desired position of the gripping fingers is expressed by establishing a second order differential equation, and the desired target impedance is as follows:
Figure GDA0003476073720000027
in the formula, md、bd、kdRespectively representing equivalent mass, damping and rigidity parameters of the clamping mechanism; x, x,
Figure GDA0003476073720000028
And
Figure GDA0003476073720000029
the actual displacement, speed and acceleration of the clamping fingers of the clamping mechanism are respectively; x is the number ofd、
Figure GDA0003476073720000031
And
Figure GDA0003476073720000032
respectively the expected displacement, velocity and acceleration of the gripping fingers of the gripping mechanism; f. ofdA desired contact force applied to the fruit for the gripper fingers; f. ofeActually collecting contact force for the pressure sensor;
the designed adaptive variable impedance controller comprises the following components:
Figure GDA0003476073720000033
in the formula (f)d(t) a desired contact force applied to the fruit by the gripper fingers; f. ofe(t) actually collecting contact force by the pressure sensor; m and b respectively represent equivalent mass parameters and damping parameters of the clamping mechanism;
Figure GDA0003476073720000034
Figure GDA0003476073720000035
e(t)＝xd(t) -x (t), wherein:
Figure GDA0003476073720000036
Figure GDA00034760737200000322
respectively showing the current expected attitude acceleration error (m/s2) and the current speed error (m/s) of the clamping finger of the clamping mechanism,
Figure GDA0003476073720000038
Figure GDA0003476073720000039
respectively represent the tiny change amounts of the expected attitude acceleration error (m/s2) and the speed error (m/s) of the clamping fingers of the clamping mechanism,
Figure GDA00034760737200000310
and
Figure GDA00034760737200000311
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism;
Figure GDA00034760737200000312
and
Figure GDA00034760737200000313
respectively the expected speed and acceleration of the gripper fingers; Δ b (t) is the designed adaptation law;
in the inner ring position control, the designed sliding mode surface of the smooth sliding mode controller is as follows:
Figure GDA00034760737200000314
in the formula: e (t) qd(t)-q(t)，
Figure GDA00034760737200000315
Lambda is an adjustable parameter and satisfies the Hall Woltz stability condition, qd(t)、
Figure GDA00034760737200000316
For the expected pose (m), velocity (m/s) and acceleration (m/s2) of the pinch finger, e (t),
Figure GDA00034760737200000317
The expected pose error (m) and the speed error (m/s) of the clamping finger.
Deriving S (t), and subjecting e (t),
Figure GDA00034760737200000318
substituting to obtain:
Figure GDA00034760737200000319
taking a constant velocity approach law:
Figure GDA00034760737200000320
in the formula: k (t) is a switching gain indicating a rate at which a moving point of the system approaches a switching plane S equal to 0;
since the sgn (s (t)) function has a problem of chattering in an actual control system, in order to reduce chattering, the function sgn (s (t)) is replaced by a continuous function a (t)) and there are:
Figure GDA00034760737200000321
further, in the step 4), based on the impedance controller for controlling the smooth sliding mode position of the clamping mechanism of the fruit sorting parallel robot, an adaptive variable impedance control algorithm for the clamping mechanism of the fruit sorting parallel robot is designed, and damping parameters are adjusted in real time based on the deviation between the expected clamping force and the collected actual contact force, and the designed adaptive law is as follows:
Figure GDA0003476073720000041
wherein b represents the equivalent damping parameter of the clamping mechanism, Δ b (t) is the adaptive law of the designed damping parameter,
Figure GDA0003476073720000042
representing the current expected pose velocity error (m/s) of the clamping finger of the clamping mechanism, phi (t) is the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force collected by the pressure sensor in the previous sampling period, λ is the sampling period of the controller, and σ is the update rate.
Further, in the step 5), the adaptive variable impedance controller is configured to:
Figure GDA0003476073720000043
in the formula fd(t) desired contact force applied to the fruit by the gripper fingers, fe(t) is the actual collected contact force of the pressure sensor, m and b respectively represent the equivalent mass parameter and the damping parameter of the clamping mechanism, delta b (t) is the self-adaptive law of the designed damping parameter,
Figure GDA0003476073720000044
e(t)＝xd(t) -x (t), wherein:
Figure GDA0003476073720000045
respectively showing the current expected attitude acceleration error (m/s2) and the current speed error (m/s) of the clamping finger of the clamping mechanism,
Figure GDA0003476073720000046
respectively representing the slight changes of the expected attitude acceleration error (m/s2) and the speed error (m/s) of the clamping fingers of the clamping mechanismThe chemical quantity is changed,
Figure GDA00034760737200000411
and
Figure GDA0003476073720000048
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism,
Figure GDA0003476073720000049
and
Figure GDA00034760737200000410
respectively the expected speed and acceleration of the gripper fingers, phi (t) the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force collected by the pressure sensor in the previous sampling period, λ is the sampling period of the controller, and σ is the update rate.
The invention provides a self-adaptive variable impedance control method of a fruit sorting parallel robot clamping mechanism for the first time, which is applied to realizing the nondestructive clamping of the fruit sorting parallel robot clamping mechanism on fruits in series, and has the characteristics and beneficial effects that:
1. the fruit sorting parallel robot clamping mechanism is subjected to kinematic analysis, and then a Lagrange method is adopted to establish a dynamic model of the fruit sorting parallel robot clamping mechanism, so that the dynamic model with various uncertainties such as parameter change, unmodeled dynamics and external interference can be obtained.
2. An impedance control method for smooth sliding mode position control of a fruit sorting parallel robot clamping mechanism based on a Lagrange method dynamic model is introduced, the problem of buffeting generated by discontinuity of sliding mode control in impedance control of traditional sliding mode position control is solved, and the control performance of the parallel robot clamping mechanism can be improved.
3. Aiming at impedance control parameters of smooth sliding mode position control of a fruit sorting parallel robot clamping mechanism based on a Lagrange method dynamic model, damping parameters are adjusted in real time based on deviation of expected clamping force and collected actual contact force, the adaptivity of the system to clamping speed and clamping load change is improved, and meanwhile the performance of impedance control is improved.
Drawings
Fig. 1 is a structure diagram of a fruit sorting parallel robot clamping mechanism.
In the figure: 1. connecting block 2, sliding screw rod 3, sliding block 4, driving motor 5, pressure sensor 6, bottom connecting plate 7, left clamping finger 8, right clamping finger 9, driven rod 10, sliding seat 11 and spring
Fig. 2 is a schematic block diagram of an adaptive variable impedance control system.
Fig. 3 is a simplified structure of a fruit sorting parallel robot clamping mechanism.
Fig. 4 is a general structure diagram of a fruit sorting parallel robot control system.
Fig. 5 is a fruit sorting parallel robot clamping mechanism clamping finger expected motion track.
FIG. 6 shows the expected movement track 1, 0.5kg bunch finger movement tracking error.
Fig. 7 is a graph of the expected movement trajectory 1, 0.5kg bunch grip force.
FIG. 8 shows the expected motion trajectory 2, 0.5kg bunch finger motion tracking error.
FIG. 9 is a graph of the expected movement trajectory 1, 0.8kg bunch grip force.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The technical scheme adopted by the invention comprises the following steps:
1) the fruit sorting parallel robot clamping mechanism is used as a controlled object, and the fruit sorting parallel robot clamping mechanism is subjected to kinematic analysis by adopting an analytical method, so that the conversion relation between the rotation angle of the driving joint screw rod and the position of clamping fingers of the clamping mechanism is obtained;
2) establishing a dynamic model of a fruit sorting parallel robot clamping mechanism by adopting a Lagrange method;
3) based on the dynamic model established by the Lagrange method in the step 2), a double-ring control structure is adopted in the outer ring force control: designing an impedance controller; in the inner ring position control, a smooth sliding mode controller is designed.
4) Aiming at the step 3) based on the impedance controller for controlling the smooth sliding mode position of the clamping mechanism of the fruit sorting parallel robot, a self-adaptive variable impedance control algorithm of the clamping mechanism of the fruit sorting parallel robot is designed, and the damping parameters are adjusted in real time based on the deviation between the expected clamping force and the collected actual contact force. Self-adaptive variable impedance controller for fruit sorting parallel robot clamping mechanism based on dynamic model established by adopting Lagrange method and based on impedance controller in outer loop control and smooth sliding mode controller in inner loop position control
5) Forming a self-adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism based on the step 2), the step 3) and the step 4);
6) the self-adaptive variable impedance control method of the fruit sorting parallel robot clamping mechanism is realized through software programming.
As shown in fig. 1, in the figure: 1. the device comprises a connecting block 2, a sliding screw rod (the upper end is connected with a belt, the lower end is connected with a sliding block) 3, a sliding block 4, a driving motor 5, a pressure sensor 6, a bottom connecting plate 7, a left clamping finger 8, a right clamping finger 9, a driven rod 10, a sliding seat 11 and a spring. Fig. 3 is a simplified structure of a fruit sorting parallel robot clamping mechanism.
Firstly, performing kinematic analysis on a fruit sorting parallel robot clamping mechanism to obtain the position conversion relation between the rotation angle of a driving joint screw rod and clamping fingers of the clamping mechanism; secondly, establishing a dynamic model of the fruit sorting parallel robot clamping mechanism by adopting a Lagrange method; then, in the outer ring force control, an impedance controller is designed; in the inner ring position control, a sliding mode surface S is designed according to the existence and the reaching condition of a sliding mode, and a smooth sliding mode controller is designed. Then, aiming at impedance control parameters of smooth sliding mode position control of the fruit sorting parallel robot clamping mechanism based on a Lagrange method dynamic model, real-time adjustment of the deviation of expected clamping force and collected actual contact force is carried out on the damping parameters, and design of an adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism is completed; and finally, realizing the self-adaptive variable impedance control of the fruit sorting parallel robot clamping mechanism through software programming. The specific method comprises the following steps:
1. solving the position conversion relation between the rotation angle of the driving joint screw rod and the clamping finger of the clamping mechanism
Selecting a pose parameter q ═ X of a clamping finger of a clamping mechanism of the parallel robot as a generalized coordinate of the system, wherein X is the displacement (unit is m) of the clamping finger of the clamping mechanism in the X-axis direction; and (3) performing kinematic analysis on the mechanism by adopting an analytical method to obtain the position conversion relation between the rotation angle of the driving joint screw rod and the clamping fingers of the clamping mechanism.
Figure GDA0003476073720000061
In the formula, psIs a lead screw lead; theta is the rotation angle (unit is rad) of the driving joint screw rod; l1Is the length of the driven rod (unit is m); e is the structural length of the slider (in m). X is the position of the clamping finger of the clamping mechanism in the X-axis direction (unit is m); d0Is the initial position (in m) of the slider from the origin of coordinates.
2. Dynamic model for establishing fruit sorting parallel robot clamping mechanism by adopting Lagrange method
Figure GDA0003476073720000062
Wherein M (q) is an inertia matrix,
Figure GDA0003476073720000063
the terms Copenforces and centrifugal forces, G (Q) the gravitational terms, and Q the generalized driving force.
The pose of the pinch finger is given by q ═ x, and the kinetic model can be converted into:
Figure GDA0003476073720000071
wherein m (x) is a symmetric positive definite inertial matrix,
Figure GDA0003476073720000072
the terms Copenforces and centrifugal forces, g (x) the terms gravity,
Figure GDA0003476073720000073
and
Figure GDA0003476073720000074
the actual speed and the acceleration of the clamping fingers of the clamping mechanism are respectively, and tau is the driving torque of the driving joint screw rod. In order to convert the generalized force into the joint driving force, the following transformation is needed:
Figure GDA0003476073720000075
3. based on a fruit sorting parallel robot clamping mechanism dynamic model established by a Lagrange method, in the outer ring force control, a second order differential equation is established to express the relation between the force applied to a clamping finger of the clamping mechanism and the difference of an actual position deviating from an expected position, and the expected target impedance is as follows:
Figure GDA0003476073720000076
in the formula, md、bd、kdRespectively representing equivalent mass, damping and rigidity parameters of the clamping mechanism; x, x,
Figure GDA0003476073720000077
And
Figure GDA0003476073720000078
respectively the actual displacement (in m), velocity (in m/s) and acceleration (in m/s) of the gripper fingers2)；xd、
Figure GDA0003476073720000079
And
Figure GDA00034760737200000710
respectively the desired displacement (in m), velocity (in m/s) and acceleration (in m/s) of the gripper fingers2)；fdA desired contact force (in N) applied to the fruit for the gripper fingers; f. ofeThe actual contact force (in N) is collected for the pressure sensor.
The designed adaptive variable impedance controller comprises the following components:
Figure GDA00034760737200000711
in the formula (f)d(t) desired contact force applied to the fruit by the gripper fingers, fe(t) the pressure sensor actually collects the contact force, m and b respectively represent the equivalent mass parameter and the damping parameter of the clamping mechanism,
Figure GDA00034760737200000712
Figure GDA00034760737200000713
e(t)＝xd(t) -x (t), wherein:
Figure GDA00034760737200000714
Figure GDA00034760737200000723
respectively showing the current expected attitude acceleration error (m/s2) and the current speed error (m/s) of the clamping finger of the clamping mechanism,
Figure GDA00034760737200000716
Figure GDA00034760737200000717
respectively represent the tiny change amounts of the expected attitude acceleration error (m/s2) and the speed error (m/s) of the clamping fingers of the clamping mechanism,
Figure GDA00034760737200000724
and
Figure GDA00034760737200000719
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism,
Figure GDA00034760737200000720
and
Figure GDA00034760737200000721
respectively the expected speed and the acceleration of the clamping fingers of the clamping mechanism, and deltab (t) is a designed adaptive law.
In the inner ring position control, the designed sliding mode surface of the smooth sliding mode controller is as follows:
Figure GDA00034760737200000722
wherein e (t) qd(t)-q(t)，
Figure GDA0003476073720000081
Lambda is an adjustable parameter and meets the Hall Woltz stability condition; q. q.sd(t)、
Figure GDA0003476073720000082
Is the expected pose (m), velocity (m/s) and acceleration (m/s2) of the clamping finger; e (t),
Figure GDA0003476073720000083
The expected pose error (m) and the speed error (m/s) of the clamping finger.
The derivation of equation (7) and the addition of e (t),
Figure GDA0003476073720000084
substituting to obtain:
Figure GDA0003476073720000085
taking a constant velocity approach law:
Figure GDA0003476073720000086
where k (t) is a switching gain, which indicates a rate at which the moving point of the system approaches the switching plane S equal to 0.
Since the sgn (s (t)) function has a problem of chattering in an actual control system, the function sgn (s (t)) is replaced with a continuous function a (t) for reducing chattering. Then equation (9) is:
Figure GDA0003476073720000087
4. the self-adaptive law of the damping parameters for the self-adaptive variable impedance control is designed as follows:
Figure GDA0003476073720000088
wherein b represents the equivalent damping parameter of the clamping mechanism, Δ b (t) is the adaptive law of the designed damping parameter,
Figure GDA0003476073720000089
representing the current expected pose velocity error (m/s) of the clamping finger of the clamping mechanism, phi (t) is the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force collected by the pressure sensor in the previous sampling period, λ is the sampling period of the controller, and σ is the update rate.
5. A dynamic model of the fruit sorting parallel robot clamping mechanism is established by adopting a Lagrange method, and an adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism is formed by an impedance controller in outer loop control and a smooth sliding mode controller in inner loop position control.
The self-adaptive variable impedance control law of the fruit sorting parallel robot clamping mechanism is as follows:
Figure GDA0003476073720000091
in the formula fd(t) desired contact force applied to the fruit by the gripper fingers, fe(t) is the actual collected contact force of the pressure sensor, m and b respectively represent the equivalent mass parameter and the damping parameter of the clamping mechanism, delta b (t) is the self-adaptive law of the designed damping parameter,
Figure GDA0003476073720000092
e(t)＝xd(t) -x (t), wherein:
Figure GDA0003476073720000093
respectively showing the current expected attitude acceleration error (m/s2) and the current speed error (m/s) of the clamping finger of the clamping mechanism,
Figure GDA0003476073720000094
respectively represent the tiny change amounts of the expected attitude acceleration error (m/s2) and the speed error (m/s) of the clamping fingers of the clamping mechanism,
Figure GDA00034760737200000910
and
Figure GDA0003476073720000096
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism,
Figure GDA0003476073720000097
and
Figure GDA0003476073720000098
respectively the expected speed and acceleration of the gripper fingers, phi (t) the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force collected by the pressure sensor in the previous sampling period, λ is the sampling period of the controller, and σ is the update rate.
6. And the self-adaptive variable impedance control of the clamping mechanism of the fruit sorting parallel robot is realized through software programming.
Because the clamping mechanism of the fruit sorting parallel robot adopts the alternating current servo motor to directly connect with the lead screw through the belt to realize the axial movement of the slide block. Therefore, the controller output τ determined in step 2 needs to be converted to obtain the actual required torque of the active joint driving motor.
The servo motor torque is:
Figure GDA0003476073720000099
where eta is the belt transmission efficiency, tau0Is the driving force of the motor.
Writing a self-adaptive variable impedance control algorithm software program based on the fruit sorting parallel robot clamping mechanism, sending a voltage analog quantity obtained by the digital/analog conversion of a calculation result (namely the torque required by a driving motor) through a control system to a servo driver corresponding to the motor, and controlling the motor to drive a lead screw, thereby driving the fruit sorting parallel robot clamping mechanism to realize the serial fruit clamping of the fruit sorting parallel robot.
Examples of the invention are provided below:
example 1
The invention provides a self-adaptive variable impedance control method of a fruit sorting parallel robot clamping mechanism, aiming at the problem that the fruit sorting parallel robot clamping mechanism can clamp serial fruits in a nondestructive mode. Fig. 2 shows a schematic diagram of an adaptive variable impedance control of a fruit sorting parallel robot gripping mechanism, and the control method has the following specific implementation modes:
1. solving the position conversion relation between the rotation angle of the driving joint screw rod and the clamping finger of the clamping mechanism
In fig. 2, a driven rod length constraint equation is adopted, and a mechanism kinematics equation can be obtained according to the structural arrangement of the clamping mechanism:
Figure GDA0003476073720000101
in the formula (I), the compound is shown in the specification,
Figure GDA0003476073720000102
represents a unit vector along the X axis;
Figure GDA0003476073720000103
represents a unit vector along the Y axis; d is the position of the intermediate slider relative to the origin of the coordinate system (in m); r ═ x 0)TPinch finger position point B1A position vector of (a); e is the structural length of the slider (in m); l1，u1Respectively the rod length (in m) and the unit vector of the driven rod; l3The structure length (unit is m) of the clamping finger from the sliding seat in the Y-axis direction; l5The distance between the clamping fingers and the sliding seat is the structural length (in m) in the X-axis direction.
Rewriting formula (17) to
Figure GDA0003476073720000104
Multiplying both ends by respective transpositions to obtain:
x2+Ex+F＝0 (15)
wherein E is-2 (E-l)5)，F＝(d-l3)2+(e-l5)2-l1 2。
Depending on the assembly mode of the mechanism, equation (18) can be solved:
Figure GDA0003476073720000105
and (3) solving the position conversion relation between the rotation angle of the driving joint screw rod and the clamping finger of the clamping mechanism, and obtaining:
Figure GDA0003476073720000106
in the formula, psIs a lead screw lead; theta is the rotation angle (unit divided rad) of the driving joint screw rod; l1Is the length of the driven rod (unit is m); e is the structural length of the slider (in m). X is the position of the clamping finger of the clamping mechanism in the X-axis direction (unit is m); d0Is the initial position (in m) of the slide block from the origin of coordinates; l3The structure length (unit is m) of the clamping finger from the sliding seat in the Y-axis direction; l5The distance between the clamping fingers and the sliding seat is the structural length (in m) in the X-axis direction.
2. Dynamic model for establishing fruit sorting parallel robot clamping mechanism by adopting Lagrange method
Figure GDA0003476073720000111
Wherein M (q) is an inertia matrix,
Figure GDA0003476073720000112
the terms Copenforces and centrifugal forces, G (Q) the gravitational terms, and Q the generalized driving force.
The pose of the pinch finger is given by q ═ x, and the kinetic model can be converted into:
Figure GDA0003476073720000113
wherein m (x) is a symmetric positive definite inertial matrix,
Figure GDA0003476073720000114
the terms Copenforces and centrifugal forces, g (x) the terms gravity,
Figure GDA0003476073720000115
and
Figure GDA0003476073720000116
the actual speed and the acceleration of the clamping fingers of the clamping mechanism are respectively, and tau is the driving torque of the driving joint screw rod.
In order to convert the generalized force into the joint driving force, the following transformation is needed:
Figure GDA0003476073720000117
3. based on a fruit sorting parallel robot clamping mechanism dynamic model established by a Lagrange method, in the outer ring force control, a second order differential equation is established to express the relation between the force applied to a clamping finger of the clamping mechanism and the difference of an actual position deviating from an expected position, and the expected target impedance is as follows:
Figure GDA0003476073720000118
in the formula, md、bd、kdRespectively representing equivalent mass, damping and rigidity parameters of the clamping mechanism; x, x,
Figure GDA0003476073720000119
And
Figure GDA00034760737200001110
respectively the actual displacement (in m), velocity (in m/s) and acceleration (in m/s) of the gripper fingers2)；xd、
Figure GDA00034760737200001111
And
Figure GDA00034760737200001112
respectively the desired displacement (in m), velocity (in m/s) and acceleration (in m/s) of the gripper fingers2)；fdA desired contact force (in N) applied to the fruit for the gripper fingers; f. ofeThe actual contact force (in N) is collected for the pressure sensor.
The designed adaptive variable impedance controller comprises the following components:
Figure GDA00034760737200001113
in the formula (f)d(t) is a gripper mechanism clampRefers to the desired contact force applied to the fruit, fe(t) the pressure sensor actually collects the contact force, m and b respectively represent the equivalent mass parameter and the damping parameter of the clamping mechanism,
Figure GDA00034760737200001114
Figure GDA00034760737200001115
e(t)＝xd(t) -x (t), wherein:
Figure GDA00034760737200001116
Figure GDA00034760737200001120
respectively showing the current expected attitude acceleration error (m/s2) and the current speed error (m/s) of the clamping finger of the clamping mechanism,
Figure GDA00034760737200001118
Figure GDA00034760737200001119
respectively represent the tiny change amounts of the expected attitude acceleration error (m/s2) and the speed error (m/s) of the clamping fingers of the clamping mechanism,
Figure GDA00034760737200001215
and
Figure GDA0003476073720000122
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism,
Figure GDA0003476073720000123
and
Figure GDA0003476073720000124
respectively the expected speed and the acceleration of the clamping fingers of the clamping mechanism, and deltab (t) is a designed adaptive law.
In the inner ring position control, the designed sliding mode surface of the smooth sliding mode controller is as follows:
Figure GDA0003476073720000125
wherein e (t) qd(t)-q(t)，
Figure GDA0003476073720000126
Lambda is an adjustable parameter and meets the Hall Woltz stability condition; q. q.sd(t)、
Figure GDA0003476073720000127
Is the expected pose (m), velocity (m/s) and acceleration (m/s2) of the clamping finger; e (t),
Figure GDA0003476073720000128
The expected pose error (m) and the speed error (m/s) of the clamping finger.
The derivation of formula (23) and the addition of e (t),
Figure GDA0003476073720000129
substituting to obtain:
Figure GDA00034760737200001210
taking a constant velocity approach law:
Figure GDA00034760737200001211
where k (t) is a switching gain, which indicates a rate at which the moving point of the system approaches the switching plane S equal to 0.
Since the sgn (s (t)) function has a problem of chattering in an actual control system, the function sgn (s (t)) is replaced with a continuous function a (t) for reducing chattering. Then equation (25) is:
Figure GDA00034760737200001212
4. the self-adaptive law of the damping parameters for the self-adaptive variable impedance control is designed as follows:
Figure GDA00034760737200001213
wherein b represents the equivalent damping parameter of the clamping mechanism, Δ b (t) is the adaptive law of the designed damping parameter,
Figure GDA00034760737200001214
representing the current expected pose velocity error (m/s) of the clamping finger of the clamping mechanism, phi (t) is the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force collected by the pressure sensor in the previous sampling period, λ is the sampling period of the controller, and σ is the update rate.
5. A dynamic model of the fruit sorting parallel robot clamping mechanism is established by adopting a Lagrange method, and an adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism is formed by an impedance controller in outer loop control and a smooth sliding mode controller in inner loop position control.
The self-adaptive variable impedance control law of the fruit sorting parallel robot clamping mechanism is as follows:
Figure GDA0003476073720000131
in the formula fd(t) desired contact force applied to the fruit by the gripper fingers, fe(t) is the actual collected contact force of the pressure sensor, m and b respectively represent the equivalent mass parameter and the damping parameter of the clamping mechanism, delta b (t) is the self-adaptive law of the designed damping parameter,
Figure GDA0003476073720000132
e(t)＝xd(t) -x (t), wherein:
Figure GDA0003476073720000133
respectively shows the acceleration errors of the current expected pose of the clamping fingers of the clamping mechanismDifference (m/s2) and velocity error (m/s),
Figure GDA0003476073720000134
respectively represent the tiny change amounts of the expected attitude acceleration error (m/s2) and the speed error (m/s) of the clamping fingers of the clamping mechanism,
Figure GDA00034760737200001310
and
Figure GDA0003476073720000136
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism,
Figure GDA0003476073720000137
and
Figure GDA0003476073720000138
respectively the expected speed and acceleration of the gripper fingers, phi (t) the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force collected by the pressure sensor in the previous sampling period, λ is the sampling period of the controller, and σ is the update rate.
6. The self-adaptive variable impedance control method of the fruit sorting parallel robot clamping mechanism is realized through software programming.
Because the clamping mechanism of the fruit sorting parallel robot adopts the alternating current servo motor to directly connect with the lead screw through the belt to realize the axial movement of the slide block. Therefore, the controller output τ determined in step 2 needs to be converted to obtain the actual required torque of the active joint driving motor.
Specifically, the drive motor torque is determined by the belt transmission mechanical efficiency η of 0.95:
Figure GDA0003476073720000139
(unit is n.m).
The fruit sorting parallel robot adopts a distributed control system of an upper computer (PC) and a lower computer (UMAC multi-axis motion controller), and the overall structural schematic diagram of the control system is shown in FIG. 4. The control system operation process: the method comprises the steps that an upper computer (PC) completes tasks such as system initialization, code compiling and the like, a serial port of the upper computer (PC) reads an actual collected pressure value in real time, an attitude adjusting instruction is sent to a UMAC controller in real time through an Ethernet port (Ethernet) according to an instruction requirement sent by a main control center, the UMAC processes related instructions in real time, differential pulse instruction control of a servo driver and reading of six paths of differential encoder information are achieved through an ACC-24E2A board card, corresponding joints of a parallel robot are controlled to generate corresponding displacement and rotation at an instruction speed, finally, position and speed information of an active joint are fed back to the UMAC through an encoder, and a result is returned to the PC after the UMAC completes a control function.
VC + +6.0 is used as a software development platform, and an upper computer application program is designed based on a Pcomm32W.dll dynamic link library provided by MFC and Delta Tau companies, so that the functions of system initialization, data management, code compilation, real-time monitoring of mechanism states and the like are mainly realized.
Developing a UMAC servo algorithm program according to a self-adaptive variable impedance control algorithm of the designed fruit sorting parallel robot clamping mechanism, and developing a mechanism motion program according to a required expected motion track and an expected clamping force; the self-adaptive variable impedance control algorithm program of the fruit sorting parallel robot clamping mechanism is downloaded into the UMAC, the related parameters of the UMAC are set, and the parallel robot clamping mechanism can be obtained by executing the motion program of the mechanism, so that fruit clamping is realized according to the expected motion track and the expected clamping force.
Fig. 5 is a fruit sorting parallel robot clamping mechanism clamping finger expected motion track.
The motion track of the clamping fingers of the clamping mechanism of the fruit sorting parallel robot is shown in figure 5; under the expected movement track 1, the movement tracking error of the clamping fingers of the 0.5kg grape bunch is shown in fig. 6, and the clamping force curve of the 0.5kg grape bunch is shown in fig. 7; under the expected movement track 2, the tracking error of the movement of the clamping fingers of the 0.5kg grape bunch is shown in fig. 8, and the clamping force curve of the 0.8kg grape bunch is shown in fig. 9.
Fig. 6 and 7 show that when the system has the lumped disturbance, the self-adaptive variable impedance control algorithm of the fruit sorting parallel robot clamping mechanism can enable the fruit sorting parallel robot clamping mechanism control system to have higher position tracking accuracy and enable the output force of the clamping mechanism to reach the expected set force more quickly and with low overshoot. Comparing fig. 6 and fig. 8 shows that when the moving speed of the gripping fingers of the gripping mechanism is changed, the adaptive variable impedance control algorithm of the gripping mechanism of the fruit sorting parallel robot improves the adaptability of the control system to the change of the gripping speed and the system can still keep higher position tracking accuracy because the damping parameter b is adaptively adjusted along with delta f. Comparing fig. 7 and fig. 9 shows that when the fruit quality is changed, the adaptive variable impedance control algorithm of the clamping mechanism of the fruit sorting parallel robot improves the adaptability of the control system to the load change because the damping parameter b is adaptively adjusted along with Δ f, and the output force of the clamping mechanism can still reach the expected set force quickly and with low overshoot.
It should be understood that the above-described embodiments are illustrative only and are not limiting upon the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereto that may occur to those skilled in the art upon reading the present disclosure.

Claims (2)

1. A self-adaptive variable impedance control method of a fruit sorting parallel robot clamping mechanism is characterized by comprising the following steps:
1) the fruit sorting parallel robot clamping mechanism is used as a controlled object, and the fruit sorting parallel robot clamping mechanism is subjected to kinematic analysis by adopting an analytical method, so that the conversion relation between the rotation angle of the driving joint screw rod and the position of clamping fingers of the clamping mechanism is obtained;
2) establishing a dynamic model of a fruit sorting parallel robot clamping mechanism by adopting a Lagrange method;
3) based on the dynamic model established by the Lagrange method in the step 2), a double-loop control structure is adopted: in the outer ring force control, designing an adaptive variable impedance controller; in the inner ring position control, a smooth sliding mode controller is designed; the self-adaptive variable impedance controller and the smooth sliding mode controller form an impedance controller for controlling the position of the smooth sliding mode;
4) aiming at an impedance controller based on smooth sliding mode position control of a clamping mechanism of the fruit sorting parallel robot in the step 3), designing a self-adaptive variable impedance control algorithm of the clamping mechanism of the fruit sorting parallel robot, and carrying out real-time adjustment on damping parameters based on deviation of expected contact force and collected actual contact force;
5) forming a self-adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism based on the step 2), the step 3) and the step 4);
6) the self-adaptive variable impedance control method of the fruit sorting parallel robot clamping mechanism is realized through software programming;
in the step 2), the dynamic model established by adopting the Lagrange method is as follows:
Figure FDA0003487738720000011
wherein M (q) is an inertia matrix,
Figure FDA0003487738720000012
the terms of Copenforces and centrifugal forces, G (Q) the terms of gravity, and Q the generalized driving force;
and q is equal to x and is the pose of the clamping finger of the clamping mechanism, and the dynamic model can be converted into the following steps:
Figure FDA0003487738720000013
wherein m (x) is a symmetric positive definite inertial matrix,
Figure FDA0003487738720000014
the terms Copenforces and centrifugal forces, g (x) the terms gravity,
Figure FDA0003487738720000015
and
Figure FDA0003487738720000016
the actual speed and the actual acceleration of the clamping fingers of the clamping mechanism are respectively, and tau is the driving torque of the active joint screw rod;
in the step 3), in the outer ring force control, a second order differential equation is established to express the relationship between the force applied to the clamping fingers of the clamping mechanism and the difference of the actual position deviating from the expected position, and the expected target impedance is as follows:
Figure FDA0003487738720000017
in the formula, md、bd、kdRespectively representing an equivalent mass parameter, an equivalent damping parameter and an equivalent stiffness parameter of the clamping mechanism; x, x,
Figure FDA0003487738720000021
And
Figure FDA0003487738720000022
respectively the actual displacement, the actual speed and the actual acceleration of the clamping fingers of the clamping mechanism; x is the number ofd、
Figure FDA0003487738720000023
And
Figure FDA0003487738720000024
respectively the expected displacement, the expected speed and the expected acceleration of the clamping fingers of the clamping mechanism; f. ofdA desired contact force applied to the fruit for the gripper fingers; f. ofeActual contact force collected for the pressure sensor;
the designed adaptive variable impedance controller comprises the following components:
Figure FDA0003487738720000025
in the formula (f)d(t) a desired contact force applied to the fruit by the gripper fingers; f. ofe(t) is the actual contact force collected by the pressure sensor; m and b respectively represent equivalent mass parameters and equivalent damping parameters of the clamping mechanism;
Figure FDA0003487738720000026
Figure FDA0003487738720000027
e(t)＝xd(t) -x (t), wherein:
Figure FDA0003487738720000028
Figure FDA0003487738720000029
respectively showing the acceleration error and the speed error of the current expected pose of the clamping finger of the clamping mechanism,
Figure FDA00034877387200000210
respectively representing the tiny variation of the acceleration error and the tiny variation of the speed error of the expected pose of the clamping finger of the clamping mechanism,
Figure FDA00034877387200000223
and
Figure FDA00034877387200000212
respectively the speed and the acceleration of the clamping fingers of the clamping mechanism;
Figure FDA00034877387200000213
and
Figure FDA00034877387200000214
respectively the expected speed and the expected acceleration of the clamping fingers of the clamping mechanism; Δ b (t) is the designed damping parameter adaptation law;
in the inner ring position control, the designed sliding mode surface of the smooth sliding mode controller is as follows:
Figure FDA00034877387200000215
in the formula: e (t) qd(t)-q(t)，
Figure FDA00034877387200000216
Lambda is an adjustable parameter and satisfies the Hall Woltz stability condition, qd(t)、
Figure FDA00034877387200000217
E (t) desired pose, desired velocity and desired acceleration of the pinch finger,
Figure FDA00034877387200000218
Errors in the expected pose of the gripping fingers and speed errors;
deriving S (t), and subjecting e (t),
Figure FDA00034877387200000219
substituting to obtain:
Figure FDA00034877387200000220
taking a constant velocity approach law:
Figure FDA00034877387200000221
in the formula: k (t) is a switching gain indicating a rate at which the moving point approaches the sliding mode surface S — 0;
replacing sgn (s (t)) with a continuous function a (t) to reduce buffeting, then:
Figure FDA00034877387200000222
in the step 4), based on an impedance controller for controlling the smooth sliding mode position of the clamping mechanism of the fruit sorting parallel robot, a self-adaptive variable impedance control algorithm of the clamping mechanism of the fruit sorting parallel robot is designed, damping parameters are adjusted in real time based on the deviation between the expected contact force and the collected actual contact force, and the designed self-adaptive law is as follows:
Figure FDA0003487738720000031
where Φ (t) is the update rate, fd(t- λ) is the desired contact force applied to the fruit by the gripper fingers of the gripper mechanism of the previous sampling cycle, fe(t- λ) is the actual contact force acquired by the pressure sensor in the previous sampling period, λ is the sampling period, and σ is the update rate.
2. The adaptive variable impedance control method of the fruit sorting parallel robot clamping mechanism according to claim 1, characterized in that: in the step 5), the self-adaptive variable impedance controller of the fruit sorting parallel robot clamping mechanism comprises:
Figure FDA0003487738720000032
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