CN112140125A - Underwater flexible target grabbing system and accurate force sensing method thereof - Google Patents

Underwater flexible target grabbing system and accurate force sensing method thereof Download PDF

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CN112140125A
CN112140125A CN202011009532.3A CN202011009532A CN112140125A CN 112140125 A CN112140125 A CN 112140125A CN 202011009532 A CN202011009532 A CN 202011009532A CN 112140125 A CN112140125 A CN 112140125A
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strain gauge
resistance strain
finger
knuckle
resistance
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CN112140125B (en
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黄海
徐明浩
张万里
徐杨
李冀永
姜涛
李加强
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Harbin Engineering University
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Harbin Engineering University
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J11/00Manipulators not otherwise provided for
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/16Programme controls
    • B25J9/1602Programme controls characterised by the control system, structure, architecture

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  • Force Measurement Appropriate To Specific Purposes (AREA)

Abstract

The invention belongs to the technical field of underwater robots, and particularly relates to an underwater flexible target grabbing system and an accurate force sensing method thereof. The underwater flexible target grabbing system is mainly used for finishing accurate sensing of grabbing force and lossless and reliable grabbing of an operation target in a complex underwater environment. The sensor senses deformation through an elastic body connected with the paw and the strain bridge, then force signals are converted into electric signals through a circuit system, the electric signals are transmitted to an upper computer after being processed, finally the electric signals are processed through a data decoupling algorithm based on the least square principle, and the final actual grabbing force is obtained after hydrodynamic force and friction are compensated. The accurate force sensing method of the underwater flexible target grabbing system can replace part of complex and expensive pool experiments at the initial design stage of the underwater robot wrist force sensor system, carries out qualitative and quantitative analysis on output under the action of external load, and provides reference for further optimization design of grabbing force sensing and control of an underwater robot.

Description

Underwater flexible target grabbing system and accurate force sensing method thereof
Technical Field
The invention belongs to the technical field of underwater robots, and particularly relates to an underwater flexible target grabbing system and an accurate force sensing method thereof.
Background
Since the latter half of the last century, various force sensing and control systems have gained wide application in the fields of industrial assembly, target grabbing, medical engineering, space exploration, and the like. Due to the underwater sealing limitation, hydrodynamic force and operation depth, the underwater robot uses less force sensing and force control technology when a target is grabbed and operated, and grabbing of the target mainly depends on visual sensing and pose control of the underwater robot and a paw. However, underwater visual observation is affected by particles and ocean currents, and particularly reliable grabbing of a flexible target is difficult to realize by visual observation alone, and force sensing of the existing force sensor is interfered by environmental water flow underwater. In recent years, with implementation of deep and open sea strategies in China, especially with increasing intelligent demands on grabbing and operating of underwater robots, not only a force sensor needs to be equipped on an operating paw of the underwater robot, but also hydrodynamic force and sealing pretightening force need to be considered, so that accurate sensing and grabbing operation control of a flexible target and a dangerous target by a system are realized.
Harbin engineering university has published 3 papers, namely research on a method for measuring the strength of underwater dexterous fingers, and the like, and discusses that a finger-end multi-dimensional force sensor is used for measuring underwater grabbing force and a control method when an underwater target is grabbed. The institute of intelligent machinery and society of Chinese academy of science and academy of sciences published 4 papers such as 'research on dexterous hand contact force control scheme of underwater operation machinery', etc., and discuss contact force measurement and impedance control method for underwater target grabbing. However, although the sensors of the claws are sensitive, the sensors are arranged at the ends of the claws, and are not suitable for sealing to deep water. Moreover, the force sensing and controlling methods disclosed in the documents do not relate to a method for distinguishing the sealing pretightening force from the hydrodynamic force of the movement of the manipulator in the decoupling process, so that the control precision of grabbing the flexible target underwater is limited to a certain extent.
Disclosure of Invention
The invention aims to provide an underwater flexible target grabbing system.
The purpose of the invention is realized by the following technical scheme: the under-actuated multi-finger gripper comprises an under-actuated multi-finger gripper module, a driving module and an information processing module; the under-actuated multi-finger paw module comprises a paw base, two mechanical fingers are respectively arranged on two sides of the paw base, and the four mechanical fingers have the same structure; the mechanical finger comprises an upper knuckle, a lower knuckle and a finger base; the finger base is arranged on the paw module; the lower knuckle comprises a lower knuckle left side plate and a lower knuckle right side plate, an upper knuckle torsion spring is arranged between the upper part of the lower knuckle left side plate and the upper part of the lower knuckle right side plate, and a lower knuckle torsion spring is arranged between the bottom of the lower knuckle left side plate and the bottom of the lower knuckle right side plate; the lower end of the lower joint torsion spring is abutted against the boss of the lower plane of the finger base, and the upper end of the lower joint torsion spring is abutted against the bulge of the right side plate of the lower knuckle; the lower end of the left side plate of the lower knuckle, the lower end of the right side plate of the lower knuckle and the lower joint torsion spring are connected in series through a finger long shaft and are arranged on the finger base; the finger long shaft is provided with a shaft sleeve, and the shaft sleeve is provided with a groove; the upper knuckle comprises an upper knuckle fingerboard; the lower end of the upper knuckle fingerboard, the upper end of the left side plate of the lower knuckle, the upper knuckle torsion spring and the upper end of the right side plate of the lower knuckle are connected in series through a finger knuckle pin shaft; the left end and the right end of the finger joint pin shaft are respectively arranged at the upper end of the left side plate of the lower knuckle and the upper end of the right side plate of the lower knuckle through bearings, the finger joint pin shaft penetrates through the center of the upper joint torsion spring and supports the upper end of the upper joint torsion spring at a bulge part on the inner side of the upper knuckle finger plate, and the lower end of the upper joint torsion spring supports on the finger thin shaft; the finger thin shaft is arranged below the upper knuckle torsion spring, two ends of the finger thin shaft respectively penetrate through positioning holes in the left side plate of the lower knuckle and the right side plate of the lower knuckle and abut against the two plates, a finger guard plate is arranged above the left side plate of the lower knuckle and the right side plate of the lower knuckle, and the left side plate of the lower knuckle and the right side plate of the lower knuckle are connected into a whole by the finger guard plate; the upper part of the upper knuckle fingerboard is provided with an upright post structure, and the outside of the upright post structure is coated with a fingerstall; the upper end of the upper knuckle fingerboard is provided with a tendon rope; the upper end of the tendon rope is fixed at the upper end of the upper knuckle fingerboard, and the lower end of the tendon rope is fixed on the rope pulley cylinder after sequentially bypassing the finger joint pin shaft, the finger thin shaft and the groove on the shaft sleeve; the rope wheel cylinder is connected with a driving main shaft of the driving module; the long finger shafts of the two mechanical fingers positioned on the same side of the paw base are connected;
the information processing module comprises a cross beam elastic body; the cross beam elastic body is of a centrosymmetric structure and comprises a central platform; the center platform is a cube with a square bottom surface, a mounting hole matched with the driving spindle is formed in the center of the center platform, a first main beam is mounted on the front side of the center platform, a second main beam is mounted on the back side of the center platform, a third main beam is mounted on the left side of the center platform, a fourth main beam is mounted on the right side of the center platform, the four main beams are identical in structure, floating beams are mounted at the other ends of the four main beams, and the four floating beams are connected end to end through four groups of fixed platforms; the driving module comprises a watertight shell and a driving steering engine; the driving steering engine is fixed in the watertight shell, and the output end of the driving steering engine is connected with the driving main shaft through a bearing; the cross beam elastic body is arranged on a dynamic sealing cover of the watertight shell; the upper end of the driving main shaft penetrates through the movable sealing cover and the mounting hole in the center of the center platform and then is connected with the rope pulley barrel; four main beams of the cross beam elastic body are pasted with a differential Wheatstone full bridge.
The invention also aims to provide an accurate force sensing method of the underwater flexible target grabbing system, which realizes accurate sensing of grabbing force.
The purpose of the invention is realized by the following technical scheme: the method comprises the following steps:
step 1: when the underwater flexible target grabbing system performs lossless and reliable grabbing on a working target, the information processing module obtains an electric signal generated by deformation of the cross beam elastic body, and obtains a grabbing moment M in the vertical direction according to the relation between a force vector received by the cross beam elastic body and a voltage output by the differential Wheatstone full bridgeZ
Step 2: calculating the water resistance moment tau acted on each mechanical finger in the grabbing processD1
Figure BDA0002697111470000021
Wherein ρ is water density; cdIs a coefficient of resistance; r is1The radius of an equivalent cylinder of an upper knuckle of the mechanical finger; r is2The radius of the lower knuckle equivalent cylinder of the mechanical finger; l1The length of an equivalent cylinder of an upper knuckle of the mechanical finger; l2The length of the lower knuckle equivalent cylinder of the mechanical finger;
and step 3: calculating the friction torque of the tendon rope and a shaft sleeve on the long shaft of the finger in the transmission process of the tendon rope;
Figure BDA0002697111470000031
wherein, FBIs the active tension of the tendon rope; zetaβThe friction coefficient of the tendon rope micro-section is shown; r1The radius of the shaft sleeve groove;
and 4, step 4: calculating the grabbing torque of the under-actuated multi-finger paw to complete accurate force sensing of the underwater flexible target grabbing system;
Figure BDA0002697111470000032
the present invention may further comprise:
the method for acquiring the relationship between the force vector received by the cross beam elastic body and the voltage output by the differential Wheatstone full bridge in the step 1 comprises the following steps:
establishing a coordinate system by taking the central position of the cross beam elastic body as an original point, taking two mutually perpendicular main beams of the cross beam elastic body as an x axis and a y axis and taking the vertical direction as a z axis; the differential Wheatstone full bridge consists of resistance strain gauges;
a third resistance strain gauge R3 and a fourth resistance strain gauge R4 are installed on the top surface of the first main beam, a ninth resistance strain gauge R9 and a tenth resistance strain gauge R10 are installed on the bottom surface of the first main beam, and a fifteenth resistance strain gauge R15 and a sixteenth resistance strain gauge R16 are installed on two side surfaces of the first main beam respectively;
a first resistance strain gauge R1 and a second resistance strain gauge R2 are installed on the top surface of the second main beam, a seventh resistance strain gauge R7 and an eighth resistance strain gauge R8 are installed on the bottom surface of the second main beam, and a thirteenth resistance strain gauge R13 and a fourteenth resistance strain gauge R14 are installed on two side surfaces of the second main beam respectively;
a sixth resistance strain gauge R6 is installed on the top surface of the third main beam, a twelfth resistance strain gauge R12 is installed on the bottom surface of the third main beam, a twenty-first resistance strain gauge R21 and a twenty-second resistance strain gauge R22 are installed on one side of the third main beam, and a twenty-third resistance strain gauge R23 and a twenty-fourth resistance strain gauge R24 are installed on the other side of the third main beam;
a fifth resistance strain gauge R5 is installed on the top surface of the fourth main beam, an eleventh resistance strain gauge R11 is installed on the bottom surface of the fourth main beam, a seventeenth resistance strain gauge R17 and an eighteenth resistance strain gauge R18 are installed on one side of the fourth main beam, and a nineteenth resistance strain gauge R19 and a twentieth resistance strain gauge R20 are installed on the other side of the fourth main beam;
all the resistance values are the same, and the fourteenth resistance strain gauge R14, the seventeenth resistance strain gauge R17 and the eighteenth resistance strain gauge R18 are positioned in the same quadrant of the coordinate system; the thirteenth resistive strain gage R13, the twenty-first resistive strain gage R21 and the twenty-second resistive strain gage R22 are located in the same quadrant of the coordinate system; the fifteenth resistive strain gage R15, the twenty-third resistive strain gage R23, and the twenty-fourth resistive strain gage R24 are located in the same quadrant of the coordinate system; the sixteenth resistive strain gage R16, the nineteenth resistive strain gage R19 and the twentieth resistive strain gage R20 are located in the same quadrant of the coordinate system;
the distances from the origin to the first resistance strain gauge R1, the seventh resistance strain gauge R7, the thirteenth resistance strain gauge R13, the fourteenth resistance strain gauge R14, the third resistance strain gauge R3, the ninth resistance strain gauge R9, the fifteenth resistance strain gauge R15, the sixteenth resistance strain gauge R16, the twenty-first resistance strain gauge R21, the twenty-third resistance strain gauge R23, the seventeenth resistance strain gauge R17 and the nineteenth resistance strain gauge R19 are the same;
the distances from the origin to the second resistive strain gauge R2, the eighth resistive strain gauge R8, the sixth resistive strain gauge R6, the twelfth resistive strain gauge R12, the twenty-second resistive strain gauge R22, the twenty-fourth resistive strain gauge R24, the fourth resistive strain gauge R4, the tenth resistive strain gauge R10, the fifth resistive strain gauge R5, the eleventh resistive strain gauge R11, the eighteenth resistive strain gauge R18 and the twentieth resistive strain gauge R20 are the same;
the relationship between the force vector F received by the cross beam elastic body and the voltage output by the differential Wheatstone full bridge is as follows:
Figure BDA0002697111470000041
wherein, Fx、Fy、FzComponent forces of an acting force vector F along an x axis, a y axis and a z axis respectively; mx、My、MzThe moments of the acting force vector F around the x axis, the y axis and the z axis respectively;
Figure BDA0002697111470000042
is the output voltage of a differential Wheatstone full bridge consisting of a thirteenth resistive strain gauge R13, a fourteenth resistive strain gauge R14, a fifteenth resistive strain gauge R15 and a sixteenth resistive strain gauge R16;
Figure BDA0002697111470000043
is the output voltage of a differential Wheatstone full bridge consisting of a nineteenth R19, a seventeenth R17, a twenty-third R23 and a twenty-first R21 resistive strain gauge;
Figure BDA0002697111470000044
the output voltage of a differential Wheatstone full bridge consisting of the seventh resistance strain gauge R7, the first resistance strain gauge R1, the ninth resistance strain gauge R9 and the third resistance strain gauge R3;
Figure BDA0002697111470000045
is the output voltage of a differential Wheatstone full bridge consisting of a fourth resistive strain gauge R4, a tenth resistive strain gauge R10, an eighth resistive strain gauge R8 and a second resistive strain gauge R2;
Figure BDA0002697111470000046
is the output voltage of a differential Wheatstone full bridge consisting of a twelfth resistive strain gage R12, a sixth resistive strain gage R6, a fifth resistive strain gage R5 and an eleventh resistive strain gage R11;
Figure BDA0002697111470000047
is the output voltage of a differential Wheatstone full bridge consisting of a twenty-second resistance strain gauge R22, a twenty-fourth resistance strain gauge R24, a twentieth resistance strain gauge R20 and an eighteenth resistance strain gauge R18; the decoupling matrix C can be obtained by applying a standard force load to the cross beam elastomer to carry out a calibration test.
The invention has the beneficial effects that:
the underwater flexible target grabbing system is mainly used for finishing accurate sensing of grabbing force and lossless and reliable grabbing of a working target in a complex underwater environment. The sensor senses deformation through an elastic body connected with the paw and the strain bridge, then force signals are converted into electric signals through a circuit system, the electric signals are transmitted to an upper computer after being processed, finally the electric signals are processed through a data decoupling algorithm based on the least square principle, and the final actual grabbing force is obtained after hydrodynamic force and friction are compensated. The accurate force sensing method of the underwater flexible target grabbing system can replace part of complex and expensive pool experiments at the initial design stage of the underwater robot wrist force sensor system, performs qualitative and quantitative analysis on output under the action of external load and sends sensing data to a corresponding unit of an upper computer, thereby providing reference for further optimization design of grabbing force sensing and control of an underwater robot.
Drawings
FIG. 1 is a schematic cross beam elastomer coordinate system.
Fig. 2 is a cross beam elastomer mesh division.
FIG. 3(a) is FxAnd (4) distributing the elastic stress on the cross beam elastic body under the action.
FIG. 3(b) is FzAnd (4) distributing the elastic stress on the cross beam elastic body under the action.
FIG. 3(c) is MxAnd (4) distributing the elastic stress on the cross beam elastic body under the action.
FIG. 3(d) is MzAnd (4) distributing the elastic stress on the cross beam elastic body under the action.
Fig. 4(a) is a schematic layout view of a resistance strain gauge on a cross beam elastomer.
FIG. 4(b) is a schematic diagram of a bridge combination of resistance strain gauges.
FIG. 5 is a system flow diagram of an information processing module.
FIG. 6 is a diagram of an experimental device for calibrating an elastomer of a cross beam.
Fig. 7 is a picture of a sea cucumber pinched by the underwater flexible target grabbing system.
FIG. 8 is a graph of base joint torque response.
FIG. 9 is a graph of friction versus hydrodynamic separation.
Figure 10 is a schematic diagram of an under-actuated multi-finger gripper module.
Fig. 11(a) is a sectional view of the driving module.
Fig. 11(b) is a schematic diagram of the driving module.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
An underwater flexible target grabbing system comprises an under-actuated multi-finger gripper module, a driving module and an information processing module; the under-actuated multi-finger paw module comprises paw bases 1-6; two mechanical fingers are respectively arranged on two sides of the paw base, and the four mechanical fingers have the same structure; the mechanical finger comprises a finger base 1-5, an upper knuckle and a lower knuckle; the lower knuckle comprises a lower knuckle left side plate 1-7 and a lower knuckle right side plate 1-10, an upper joint torsion spring 1-14 is arranged between the upper part of the lower knuckle left side plate and the upper part of the lower knuckle right side plate, and a lower joint torsion spring 1-13 is arranged between the bottom of the lower knuckle left side plate and the bottom of the lower knuckle right side plate; the lower end of the lower joint torsion spring is abutted against the boss of the lower plane of the finger base, and the upper end of the lower joint torsion spring is abutted against the bulge of the right side plate of the lower knuckle; the lower end of the left side plate of the lower knuckle, the lower end of the right side plate of the lower knuckle and the lower joint torsion spring are connected in series through long finger shafts 1-4 and are installed on the finger base; the long finger shaft is provided with a long finger shaft sleeve, and the long finger shaft sleeve is provided with a groove; the upper knuckle comprises an upper knuckle fingerboard 1-2; the lower end of the upper knuckle fingerboard, the upper end of the left side plate of the lower knuckle, the upper knuckle torsion spring and the upper end of the right side plate of the lower knuckle are connected in series through a finger knuckle pin shaft; the left end and the right end of the finger joint pin shaft 1-3 are respectively arranged at the upper end of a left side plate of the lower knuckle and the upper end of a right side plate of the lower knuckle through bearings, the finger joint pin shaft penetrates through the center of the upper joint torsion spring and enables the upper end of the upper joint torsion spring to abut against the inner side bulge of the upper knuckle fingerplate, and the lower end of the upper joint torsion spring abuts against the thin finger shaft 1-9; the finger thin shaft is arranged below the upper knuckle torsion spring, two ends of the finger thin shaft respectively penetrate through positioning holes on the left side plate of the lower knuckle and the right side plate of the lower knuckle and abut against the two plates, finger guard plates 1-13 are arranged above the left side plate of the lower knuckle and the right side plate of the lower knuckle, and the left side plate of the lower knuckle and the right side plate of the lower knuckle are connected into a whole by the finger guard plates; the upper part of the upper knuckle fingerboard is provided with an upright post structure, and the outer part of the upright post structure is coated with fingerstalls 1-1; the upper end of the upper knuckle fingerboard is provided with tendon ropes 1-8; the upper end of the tendon rope is fixed at the upper end of the upper knuckle fingerboard, and the lower end of the tendon rope is fixed on the rope pulley barrel 2-8 after sequentially bypassing the finger joint pin shaft, the finger thin shaft and the finger long shaft sleeve groove; the rope wheel cylinder is connected with a driving main shaft of the driving module; the long finger shafts of the two mechanical fingers positioned on the same side of the paw base are connected.
The driving module comprises a watertight shell 2-9 and a driving steering engine 2-3; the driving steering engine is fixed in the watertight shell, and a steering engine main shaft of the driving steering engine is connected with the steering wheel 2-7; the lower end of the rudder disc is meshed with a gear of a main shaft of the steering engine, and the upper end of the rudder disc is connected with the lower end of the driving main shaft 2-2; the upper end of the driving main shaft is connected with the rope wheel cylinder.
The driving steering engine is enveloped by a steering engine fixing part 2-6, and a concentric positioning disc 2-4 is arranged at the lower end of the steering engine; the concentric positioning plate is matched with a positioning hole at the lower end of the steering engine and is matched with the steering engine fixing piece through a positioning pin, so that the steering engine, the steering engine fixing piece and the concentric positioning plate are integrated; the upper columnar thin wall of the steering engine fixing piece is concentrically matched with a partition plate positioning hole of the watertight shell, and is fixedly connected with the watertight shell by a screw, so that the concentricity of the steering engine and the watertight shell is ensured to meet the requirement; the lower part of the driving main shaft is concentrically matched with a middle partition plate of the watertight shell through a ball bearing, and the upper end of the driving main shaft penetrates through the Glare ring covers 2-10 and the paw base positioning hole and then enters the rope wheel cylinder, so that the dynamic sealing effect of the driving main shaft is ensured while the requirement on concentricity is met; the GREEN cover is internally provided with a GREEN ring, the GREEN ring is arranged in a groove of the GREEN cover, the inner wall of the GREEN ring is attached to the upper end of the driving spindle, and the outer wall of the GREEN ring is attached to the GREEN cover; the Glare ring cover and the watertight shell are sealed through an O-shaped ring 2-5.
A precise force sensing method of an underwater flexible target grabbing system comprises the following steps:
step 1: when the underwater flexible target grabbing system performs lossless and reliable grabbing on a working target, the information processing module obtains an electric signal generated by deformation of the cross beam elastic body, and obtains a grabbing moment M in the vertical direction according to the relation between a force vector received by the cross beam elastic body and a voltage output by the differential Wheatstone full bridgeZ
Step 2: calculating the water resistance moment tau acted on each mechanical finger in the grabbing processD1
Figure BDA0002697111470000061
Wherein ρ is water density; cdIs a coefficient of resistance; r is1The radius of an equivalent cylinder of an upper knuckle of the mechanical finger; r is2The radius of the lower knuckle equivalent cylinder of the mechanical finger; l1The length of an equivalent cylinder of an upper knuckle of the mechanical finger; l2The length of the lower knuckle equivalent cylinder of the mechanical finger;
and step 3: calculating the friction torque of the tendon rope and a shaft sleeve on the long shaft of the finger in the transmission process of the tendon rope;
Figure BDA0002697111470000071
wherein, FBIs the active tension of the tendon rope; zetaβThe friction coefficient of the tendon rope micro-section is shown; r1The radius of the shaft sleeve groove;
and 4, step 4: calculating the grabbing torque of the under-actuated multi-finger paw to complete accurate force sensing of the underwater flexible target grabbing system;
Figure BDA0002697111470000072
the method for acquiring the relationship between the force vector received by the cross beam elastic body and the voltage output by the differential Wheatstone full bridge in the step 1 comprises the following steps:
as shown in fig. 1, a coordinate system is established with the central position of the cross beam elastic body as an origin, two mutually perpendicular main beams of the cross beam elastic body as an x-axis and a y-axis, and a vertical direction as a z-axis; the differential Wheatstone full bridge consists of resistance strain gauges;
as shown in fig. 4(a), a third resistance strain gauge R3 and a fourth resistance strain gauge R4 are mounted on the top surface of the first main beam, a ninth resistance strain gauge R9 and a tenth resistance strain gauge R10 are mounted on the bottom surface of the first main beam, and a fifteenth resistance strain gauge R15 and a sixteenth resistance strain gauge R16 are mounted on both side surfaces of the first main beam;
a first resistance strain gauge R1 and a second resistance strain gauge R2 are installed on the top surface of the second main beam, a seventh resistance strain gauge R7 and an eighth resistance strain gauge R8 are installed on the bottom surface of the second main beam, and a thirteenth resistance strain gauge R13 and a fourteenth resistance strain gauge R14 are installed on two side surfaces of the second main beam respectively;
a sixth resistance strain gauge R6 is installed on the top surface of the third main beam, a twelfth resistance strain gauge R12 is installed on the bottom surface of the third main beam, a twenty-first resistance strain gauge R21 and a twenty-second resistance strain gauge R22 are installed on one side of the third main beam, and a twenty-third resistance strain gauge R23 and a twenty-fourth resistance strain gauge R24 are installed on the other side of the third main beam;
a fifth resistance strain gauge R5 is installed on the top surface of the fourth main beam, an eleventh resistance strain gauge R11 is installed on the bottom surface of the fourth main beam, a seventeenth resistance strain gauge R17 and an eighteenth resistance strain gauge R18 are installed on one side of the fourth main beam, and a nineteenth resistance strain gauge R19 and a twentieth resistance strain gauge R20 are installed on the other side of the fourth main beam;
all the resistance values are the same, and the fourteenth resistance strain gauge R14, the seventeenth resistance strain gauge R17 and the eighteenth resistance strain gauge R18 are positioned in the same quadrant of the coordinate system; the thirteenth resistive strain gage R13, the twenty-first resistive strain gage R21 and the twenty-second resistive strain gage R22 are located in the same quadrant of the coordinate system; the fifteenth resistive strain gage R15, the twenty-third resistive strain gage R23, and the twenty-fourth resistive strain gage R24 are located in the same quadrant of the coordinate system; the sixteenth resistive strain gage R16, the nineteenth resistive strain gage R19 and the twentieth resistive strain gage R20 are located in the same quadrant of the coordinate system;
the distances from the origin to the first resistance strain gauge R1, the seventh resistance strain gauge R7, the thirteenth resistance strain gauge R13, the fourteenth resistance strain gauge R14, the third resistance strain gauge R3, the ninth resistance strain gauge R9, the fifteenth resistance strain gauge R15, the sixteenth resistance strain gauge R16, the twenty-first resistance strain gauge R21, the twenty-third resistance strain gauge R23, the seventeenth resistance strain gauge R17 and the nineteenth resistance strain gauge R19 are the same;
the distances from the origin to the second resistive strain gauge R2, the eighth resistive strain gauge R8, the sixth resistive strain gauge R6, the twelfth resistive strain gauge R12, the twenty-second resistive strain gauge R22, the twenty-fourth resistive strain gauge R24, the fourth resistive strain gauge R4, the tenth resistive strain gauge R10, the fifth resistive strain gauge R5, the eleventh resistive strain gauge R11, the eighteenth resistive strain gauge R18 and the twentieth resistive strain gauge R20 are the same;
the relationship between the force vector F received by the cross beam elastic body and the voltage output by the differential Wheatstone full bridge is as follows:
Figure BDA0002697111470000081
wherein, Fx、Fy、FzComponent forces of an acting force vector F along an x axis, a y axis and a z axis respectively; mx、My、MzThe moments of the acting force vector F around the x axis, the y axis and the z axis respectively;
as shown in figure 4(b) of the drawings,
Figure BDA0002697111470000082
is the output voltage of a differential Wheatstone full bridge consisting of a thirteenth resistive strain gauge R13, a fourteenth resistive strain gauge R14, a fifteenth resistive strain gauge R15 and a sixteenth resistive strain gauge R16;
Figure BDA0002697111470000083
is the output voltage of a differential Wheatstone full bridge consisting of a nineteenth resistance strain gauge R19, a seventeenth resistance strain gauge R17, a twenty-third resistance strain gauge R23 and a twenty-first resistance strain gauge R21;
Figure BDA0002697111470000084
is the output voltage of a differential Wheatstone full bridge consisting of a seventh resistance strain gauge R7, a first resistance strain gauge R1, a ninth resistance strain gauge R9 and a third resistance strain gauge R3;
Figure BDA0002697111470000085
is the output voltage of a differential Wheatstone full bridge consisting of a fourth resistance strain gauge R4, a tenth resistance strain gauge R10, an eighth resistance strain gauge R8 and a second resistance strain gauge R2;
Figure BDA0002697111470000086
is the output of a differential Wheatstone full bridge consisting of a twelfth resistive strain gage R12, a sixth resistive strain gage R6, a fifth resistive strain gage R5 and an eleventh resistive strain gage R11A voltage;
Figure BDA0002697111470000087
is the output voltage of a differential Wheatstone full bridge consisting of a twenty-second resistance strain gauge R22, a twenty-fourth resistance strain gauge R24, a twentieth resistance strain gauge R20 and an eighteenth resistance strain gauge R18; the decoupling matrix C can be obtained by performing calibration test on the cross beam elastomer by applying a standard force load.
The underwater flexible target grabbing system is mainly used for finishing accurate sensing of grabbing force and lossless and reliable grabbing of a working target in a complex underwater environment, and comprises a set of elastic sensitive structure units, a hardware processing circuit system and a sensor decoupling compensation Method under laboratory conditions, wherein the elastic sensitive structure units are designed based on a Finite Element Method (FEM) and are suitable for an underwater robot wrist force sensor system in a submarine high-humidity high-salt environment. The sensor senses deformation through an elastic body connected with the paw and a strain bridge, force signals are converted into electric signals through a circuit system, the electric signals are transmitted to an upper computer after being processed, the electric signals are processed through a data decoupling algorithm based on the least square principle, and the final actual grabbing force is obtained after water power and friction are compensated. The accurate force sensing method of the underwater flexible target grabbing system can replace part of complex and expensive pool experiments at the initial design stage of the underwater robot wrist force sensor system, performs qualitative and quantitative analysis on output under the action of external load and sends sensing data to a corresponding unit of an upper computer, and further provides reference for further optimization design of grabbing force sensing and control of an underwater robot.
According to the invention, the force acting on the end effector is picked up, collected, transmitted and processed to obtain six linearly independent components on each axis, so that the precise sensing of the grabbing force is realized.
A hardware part of the underwater flexible object grabbing system mainly comprises a transmission driving part, a grabbing structure part and a force sense information part. The under-actuated paw is driven by a steering engine to open and close, and the power transmission mode is worm and gear transmission. The elastic body, the strain gauge, the amplifying circuit and the information acquisition and processing plate are positioned in the watertight shell, and the anodic oxidation aluminum alloy shell provides sealing and collision protection for the elements in the shell. After the paw is stressed, the force is transmitted to the cross beam elastic body to deform the cross beam elastic body, and a force signal is converted into an electric signal through the resistance strain gauges symmetrically distributed on the cross beam elastic body. Wherein the one end snap-on of elastomer is on the steering wheel output shaft, the foil gage is fixed on the cross strain beam of elastomer, amplifier circuit is direct to link to each other with the foil gage, information acquisition preliminary treatment board passes through the interface and links to each other with amplifier circuit, thereby accomplish the collection and the processing work of signal, the other end of elastomer links to each other with the basic joint main shaft of underactuated multi-finger gripper, underactuated multi-finger gripper passes through the steering wheel drive by the basic joint main shaft, realize the underactuated snatching motion of gripper, the foil gage can be according to the drive snatching force that the strain perception of elastomer cross beam received like this. Through the calibration and the decoupling processing of the cross beam and the calculation and separation of the hydrodynamic force in the direction during the decoupling, the gripping force of the gripper on the target can be accurately obtained, and the accurate gripping control of the under-actuated multi-finger gripper on the flexible target is realized.
The underwater target grabbing force sensing method mainly comprises the steps that acquisition and collection of multi-dimensional force information are achieved through an elastic sensing unit and a sensing circuit, the elastic sensing unit converts contact force into displacement change, and the sensing circuit is responsible for converting displacement into electric signals to be output. To solve the problem of underwater sealing, the sensitive unit and hardware support circuitry are mounted in an anodized aluminum housing. In order to improve the detection precision, the bridge part adopts four waterproof strain gauges to form a differential Wheatstone full bridge to be attached to each surface of the elastomer cross beam, and the relationship between the elastomer strain and the bridge output is established. And a proper amplification factor is set according to the voltage acquisition range of the data acquisition circuit, the small sensor signals are transmitted and conditioned to stm32 for processing through an instrument amplification chip AD620, and data are transmitted to an upper computer through a universal serial interface bus, so that the grabbing force in each direction is obtained through decoupling calculation.
A processing algorithm part firstly measures and records voltage data of each channel obtained by a standard weight calibration experiment on an upper computer. The calibration and decoupling process of the cross strain beam follows a strain and bridge output formula:
Figure BDA0002697111470000101
establishing the relation between the resistance value change and the bridge circuit output according to the characteristics of the full bridge circuit:
Figure BDA0002697111470000102
wherein KSThe sensitivity coefficient of the resistance strain gauge is; the magnitude of the strain at the patch position; the initial resistance values of the strain gauges are the same, the pasting positions of the strain gauges are symmetrical, so that the resistance value variation of each resistance strain gauge is the same, and the bridge circuit output is obtained:
Uout=KsE
in order to accurately obtain the relation between the input six-dimensional force vector and the output voltage vector, the output data of each channel is analyzed by applying a standard force load to the simple calibration device. The calibration method comprises the following steps:
1) and (3) loading any acting force on the sensor by using a force vector F, wherein the input and the output of the six channels satisfy the following relation:
Figure BDA0002697111470000103
wherein, F is an input force vector of six rows and one column; c is a calibration decoupling matrix; u is a six-row one-column output voltage vector.
2) Thirty-six groups of standard forces are input into the wrist force sensor and are arranged according to a certain sequence, and output voltage vectors corresponding to the input are arranged in sequence, so that the method comprises the following steps:
F6*36=C6*6U6*36
wherein, F6*36Is an input force matrix; u shape6*36Is a matrix of output voltages.
3) According to the least square theoryThe minimum norm solution is obtained by calculating the decoupling matrix, and the corresponding sensor system has the minimum strain energy (U.U)T) The decoupling matrix calculated under the condition of full rank is most accurate, and the finally obtained decoupling matrix is as follows:
C=F·UT·(U·UT)-1
at this point, a solution under decoupling can be obtained by inputting a set of spatially arbitrary forces again.
d. The hydrodynamic separation approximately equates the knuckles of each finger to a cylinder. When an object moves relatively in a viscous fluid, water resistance is generated and is divided into tangential resistance and normal resistance. The direction of the tangential resistance is tangent to the surface of the object, the normal resistance generated by water is mainly considered, and the water resistance and the resistance moment acting on the knuckle of each finger in the grabbing process are as follows:
Figure BDA0002697111470000104
Figure BDA0002697111470000111
wherein rho- -water density, kg/mm3
Cd-coefficient of drag;
vn(x) -cylinder surface normal velocity, mm/s;
r- -radius of cylinder, mm;
dx-thickness of the slice unit
Due to water resistance coefficient CdIs non-linearly changed with some parameters, and the empirical value is used to obtain Cd1.1. The grabbing paw structure finger consists of two sections of cylindrical structures, and the water resistance relation of the base joint (joint 1) under the overall influence is obtained by comprehensively analyzing the combined action of the hydrodynamic force of each section of knuckle structure as follows:
Figure BDA0002697111470000112
e. the invention analyzes the transmission process to eliminate the influence of friction loss and establishes a transmission friction model of the tendon rope and the cylinder. The following friction exists during tendon cord transfer: firstly, friction between the finger joint shaft and the bearing is very small and can be ignored; secondly, the internal friction of the tendon rope is ignored in the pulling process; thirdly, the friction between the tendon rope and the strut, here the dominant friction, is only used to build a friction compensation model, and the friction torque at the joint is as follows:
Figure BDA0002697111470000113
in the formula, FBIs the active tension of the tendon rope;
Figure BDA0002697111470000114
the friction torque of the tendon rope and the shaft sleeve on the long shaft of the finger is obtained; r1The radius of the groove of the shaft sleeve on the long axis of the finger; zetaβIs the coefficient of friction of the rope micro-segment. The gripper that this patent designed snatchs the structure and comprises four identical fingers, because the symmetry of structure just needs to obtain the final holistic power of grabbing size of grabbing of whole structure on the basis of calculating a finger resistance moment, and its expression is:
Figure BDA0002697111470000115
fig. 2 is a diagram of network division of the elastic body by using a finite element method, and the network is automatically divided by using a smart sizing function to adapt to the complex geometric shape of the elastic body.
In fig. 3(a) to 3(d), ANSYS software is used for reproducing the stress condition of the elastic body under the action of several external forces, the properties and the constraints of the elastic body material are defined in the software, a certain force load is applied to the elastic body material, the analysis result is displayed through a stress distribution cloud chart, and a strain foil patch position scheme is provided according to the analysis result.
Fig. 4(a) is a schematic position diagram of the strain gauge, fig. 4(b) is a schematic bridge mode diagram, six sets of electric bridges respectively measure six force components, and according to analysis of the stress result of the elastic body, the position of the strain gauge patch is arranged at different positions of different crossbeams to improve the precision and is close to a center table area with larger deformation to the greatest extent.
Fig. 5 is a schematic circuit diagram of a hardware circuit part, and a weak differential signal output by a strain bridge is amplified by using an instrument amplification chip AD 620.
Fig. 6 shows a printed circuit board fitted in a watertight protective housing with an elastic sensitive unit, the circuit board being circular in shape for ease of arrangement.
Fig. 7 illustrates the acquisition process of the sensor, and the strain gauge is used to complete the conversion from the force signal to the electric signal, and the bridge signal is picked up and transmitted to the upper computer through the serial interface.
FIG. 8 is a laboratory simple sensor calibration loading experiment device, which utilizes a special loading cap to match with a thin line, a pulley and a weight to change the magnitude and direction of loading force. The cross beam elastomer calibration loading experiment process is as follows:
1) electrifying a power supply, and recording the reading size of each output channel during no load;
2) the height of the fixed pulley is adjusted to ensure that the height of the mooring point of the pulley and the thin wire on the loading cap is consistent so as to ensure that the thin wire and the table top of the workbench are kept horizontal;
3) a plurality of equidistant loading points are divided within the range of the elastic body of the cross beam
4) According to the division condition in the step (3), gradually increasing the input standard force according to the principle that the loading capacity is from small to large, and storing and recording each group of input and output by upper computer software;
5) after the maximum measurement range of the sensor is reached, gradually reducing the inverse range of the input value, and simultaneously recording the output voltage corresponding to the input force value;
6) and (5) repeating the steps (4) and (5) for multiple times to carry out reciprocating calibration measurement on the sensor according to the positive and negative strokes to list corresponding tables, averaging the measurement results under the same input, and drawing an input-output curve.
Starting from 0Kg, the initial weight of the force-loaded weight equally divides the full-scale 100N into 5 distance points and increases and decreases according to the increment interval of 2 Kg; the torque is applied to the elastic body by two sets of pulleys and weights in a mode of a pair of large reverse force pairs, the full range 100 N.m is equally divided into 5 distance points, and the distance is changed according to increment intervals of 2 N.m.
Fig. 9 is a diagram of a manipulator grabbing a holothurian object, after a sensor, a related circuit part and a shell are assembled to be consistent, the manipulator is controlled by an upper computer to grab the holothurian object, and meanwhile grabbing data obtained by a channel is collected on the upper computer of the upper computer so as to be convenient for subsequent processing.
FIG. 10 is a graph of the base joint torque response, using the correlation data obtained in FIG. 9 to obtain in software a corresponding image of the base joint torque over time during the capture process.
Fig. 11 is a curve of separating the gripping friction force from the hydrodynamic force, and the torque measured by the sensor is compensated by using the method for analyzing the friction loss torque and the water resistance torque according to the present invention, so as to obtain the actual gripping torque after compensating the friction force and the hydrodynamic force.
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 (3)

1. An underwater flexible target grabbing system is characterized in that: the under-actuated multi-finger gripper comprises an under-actuated multi-finger gripper module, a driving module and an information processing module; the under-actuated multi-finger paw module comprises a paw base, two mechanical fingers are respectively arranged on two sides of the paw base, and the four mechanical fingers are identical in structure; the mechanical finger comprises an upper knuckle, a lower knuckle and a finger base; the finger base is arranged on the paw module; the lower knuckle comprises a lower knuckle left side plate and a lower knuckle right side plate, an upper knuckle torsion spring is arranged between the upper part of the lower knuckle left side plate and the upper part of the lower knuckle right side plate, and a lower knuckle torsion spring is arranged between the bottom of the lower knuckle left side plate and the bottom of the lower knuckle right side plate; the lower end of the lower joint torsion spring is abutted against the boss of the lower plane of the finger base, and the upper end of the lower joint torsion spring is abutted against the bulge of the right side plate of the lower knuckle; the lower end of the left side plate of the lower knuckle, the lower end of the right side plate of the lower knuckle and the lower joint torsion spring are connected in series through a finger long shaft and are arranged on the finger base; the finger long shaft is provided with a shaft sleeve, and the shaft sleeve is provided with a groove; the upper knuckle comprises an upper knuckle fingerboard; the lower end of the upper knuckle fingerboard, the upper end of the left side plate of the lower knuckle, the upper knuckle torsion spring and the upper end of the right side plate of the lower knuckle are connected in series through a finger knuckle pin shaft; the left end and the right end of the finger joint pin shaft are respectively arranged at the upper end of the left side plate of the lower knuckle and the upper end of the right side plate of the lower knuckle through bearings, the finger joint pin shaft penetrates through the center of the upper joint torsion spring and supports the upper end of the upper joint torsion spring at a bulge part on the inner side of the upper knuckle finger plate, and the lower end of the upper joint torsion spring supports on the finger thin shaft; the finger thin shaft is arranged below the upper knuckle torsion spring, two ends of the finger thin shaft respectively penetrate through positioning holes in the left side plate of the lower knuckle and the right side plate of the lower knuckle and abut against the two plates, a finger protection plate is arranged above the left side plate of the lower knuckle and the right side plate of the lower knuckle, and the left side plate of the lower knuckle and the right side plate of the lower knuckle are connected into a whole by the finger protection plate; the upper part of the upper knuckle fingerboard is provided with an upright post structure, and the outside of the upright post structure is coated with a fingerstall; the upper end of the upper knuckle fingerboard is provided with a tendon rope; the upper end of the tendon rope is fixed at the upper end of the upper knuckle fingerboard, and the lower end of the tendon rope is fixed on the rope pulley cylinder after sequentially bypassing the finger joint pin shaft, the finger thin shaft and the groove on the shaft sleeve; the rope wheel cylinder is connected with a driving main shaft of the driving module; the long finger shafts of the two mechanical fingers positioned on the same side of the paw base are connected;
the information processing module comprises a cross beam elastic body; the cross beam elastic body is of a centrosymmetric structure and comprises a center platform; the center platform is a cube with a square bottom surface, a mounting hole matched with the driving spindle is formed in the center of the center platform, a first main beam is mounted on the front side of the center platform, a second main beam is mounted on the back side of the center platform, a third main beam is mounted on the left side of the center platform, a fourth main beam is mounted on the right side of the center platform, the four main beams are identical in structure, floating beams are mounted at the other ends of the four main beams, and the four floating beams are connected end to end through four groups of fixed platforms; the driving module comprises a watertight shell and a driving steering engine; the driving steering engine is fixed in the watertight shell, and the output end of the driving steering engine is connected with the driving main shaft through a bearing; the cross beam elastic body is arranged on a dynamic sealing cover of the watertight shell; the upper end of the driving main shaft penetrates through the movable sealing cover and the mounting hole in the center of the center platform and then is connected with the rope pulley barrel; four main beams of the cross beam elastic body are pasted with a differential Wheatstone full bridge.
2. The method for accurately sensing force of an underwater flexible object gripping system based on the underwater flexible object gripping system of claim 1, comprising the steps of:
step 1: when the underwater flexible target grabbing system performs lossless and reliable grabbing on an operation target, the information processing module acquires an electric signal generated by deformation of the cross beam elastic body, and acquires grabbing moment M in the vertical direction according to the relation between a force vector received by the cross beam elastic body and voltage output by the differential Wheatstone full bridgeZ
Step 2: calculating the water resistance moment tau acted on each mechanical finger in the grabbing processD1
Figure FDA0002697111460000021
Wherein ρ is water density; cdIs a coefficient of resistance; r is1The radius of an equivalent cylinder of an upper knuckle of the mechanical finger; r is2The radius of the lower knuckle equivalent cylinder of the mechanical finger; l1The length of an equivalent cylinder of an upper knuckle of the mechanical finger; l2The length of the lower knuckle equivalent cylinder of the mechanical finger;
and step 3: calculating the friction torque of the tendon rope and a shaft sleeve on the long shaft of the finger in the transmission process of the tendon rope;
Figure FDA0002697111460000022
wherein, FBIs the active tension of the tendon rope; zetaβThe friction coefficient of the tendon rope micro-section is shown; r1The radius of the shaft sleeve groove;
and 4, step 4: calculating the grabbing torque of the under-actuated multi-finger paw to complete accurate force sensing of the underwater flexible target grabbing system;
Figure FDA0002697111460000023
3. the method of claim 2, wherein the force sensing system comprises: the method for acquiring the relationship between the force vector received by the cross beam elastic body and the voltage output by the differential Wheatstone full bridge in the step 1 comprises the following steps:
establishing a coordinate system by taking the central position of the cross beam elastic body as an original point, taking two mutually perpendicular main beams of the cross beam elastic body as an x axis and a y axis and taking the vertical direction as a z axis; the differential Wheatstone full bridge consists of resistance strain gauges;
a third resistance strain gauge R3 and a fourth resistance strain gauge R4 are installed on the top surface of the first main beam, a ninth resistance strain gauge R9 and a tenth resistance strain gauge R10 are installed on the bottom surface of the first main beam, and a fifteenth resistance strain gauge R15 and a sixteenth resistance strain gauge R16 are installed on two side surfaces of the first main beam respectively;
a first resistance strain gauge R1 and a second resistance strain gauge R2 are installed on the top surface of the second main beam, a seventh resistance strain gauge R7 and an eighth resistance strain gauge R8 are installed on the bottom surface of the second main beam, and a thirteenth resistance strain gauge R13 and a fourteenth resistance strain gauge R14 are installed on two side surfaces of the second main beam respectively;
a sixth resistance strain gauge R6 is installed on the top surface of the third main beam, a twelfth resistance strain gauge R12 is installed on the bottom surface of the third main beam, a twenty-first resistance strain gauge R21 and a twenty-second resistance strain gauge R22 are installed on one side of the third main beam, and a twenty-third resistance strain gauge R23 and a twenty-fourth resistance strain gauge R24 are installed on the other side of the third main beam;
a fifth resistance strain gauge R5 is installed on the top surface of the fourth main beam, an eleventh resistance strain gauge R11 is installed on the bottom surface of the fourth main beam, a seventeenth resistance strain gauge R17 and an eighteenth resistance strain gauge R18 are installed on one side of the fourth main beam, and a nineteenth resistance strain gauge R19 and a twentieth resistance strain gauge R20 are installed on the other side of the fourth main beam;
all the resistance values are the same, and the fourteenth resistance strain gauge R14, the seventeenth resistance strain gauge R17 and the eighteenth resistance strain gauge R18 are positioned in the same quadrant of the coordinate system; the thirteenth resistive strain gage R13, the twenty-first resistive strain gage R21 and the twenty-second resistive strain gage R22 are located in the same quadrant of the coordinate system; the fifteenth R15, the twenty-third R23 and the twenty-fourth R24 resistance strain gauges are located in the same quadrant of the coordinate system; the sixteenth resistive strain gage R16, the nineteenth resistive strain gage R19 and the twentieth resistive strain gage R20 are located in the same quadrant of the coordinate system;
the distances from the origin to the first resistance strain gauge R1, the seventh resistance strain gauge R7, the thirteenth resistance strain gauge R13, the fourteenth resistance strain gauge R14, the third resistance strain gauge R3, the ninth resistance strain gauge R9, the fifteenth resistance strain gauge R15, the sixteenth resistance strain gauge R16, the twenty-first resistance strain gauge R21, the twenty-third resistance strain gauge R23, the seventeenth resistance strain gauge R17 and the nineteenth resistance strain gauge R19 are the same;
the distances from the origin to the second resistance strain gauge R2, the eighth resistance strain gauge R8, the sixth resistance strain gauge R6, the twelfth resistance strain gauge R12, the twenty-second resistance strain gauge R22, the twenty-fourth resistance strain gauge R24, the fourth resistance strain gauge R4, the tenth resistance strain gauge R10, the fifth resistance strain gauge R5, the eleventh resistance strain gauge R11, the eighteenth resistance strain gauge R18 and the twentieth resistance strain gauge R20 are the same;
the relationship between the force vector F received by the cross beam elastic body and the voltage output by the differential Wheatstone full bridge is as follows:
Figure FDA0002697111460000031
wherein, Fx、Fy、FzComponent forces of an acting force vector F along an x axis, a y axis and a z axis respectively; mx、My、MzThe moments of the acting force vector F around the x axis, the y axis and the z axis respectively;
Figure FDA0002697111460000032
is the output voltage of a differential Wheatstone full bridge consisting of a thirteenth resistive strain gauge R13, a fourteenth resistive strain gauge R14, a fifteenth resistive strain gauge R15 and a sixteenth resistive strain gauge R16;
Figure FDA0002697111460000033
is the output voltage of a differential Wheatstone full bridge consisting of a nineteenth resistance strain gauge R19, a seventeenth resistance strain gauge R17, a twenty-third resistance strain gauge R23 and a twenty-first resistance strain gauge R21;
Figure FDA0002697111460000034
is the output voltage of a differential Wheatstone full bridge consisting of a seventh resistance strain gauge R7, a first resistance strain gauge R1, a ninth resistance strain gauge R9 and a third resistance strain gauge R3;
Figure FDA0002697111460000035
is the output voltage of a differential Wheatstone full bridge consisting of a fourth resistive strain gauge R4, a tenth resistive strain gauge R10, an eighth resistive strain gauge R8 and a second resistive strain gauge R2;
Figure FDA0002697111460000036
is the output voltage of a differential Wheatstone full bridge consisting of a twelfth resistive strain gage R12, a sixth resistive strain gage R6, a fifth resistive strain gage R5 and an eleventh resistive strain gage R11;
Figure FDA0002697111460000037
is the output voltage of a differential Wheatstone full bridge consisting of a twenty-second resistance strain gauge R22, a twenty-fourth resistance strain gauge R24, a twentieth resistance strain gauge R20 and an eighteenth resistance strain gauge R18; the decoupling matrix C can be obtained by applying a standard force load to the cross beam elastomer to carry out a calibration test.
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