CN108406725A - Force feedback man-machine interactive system and method based on electromagnetic theory and mobile tracking - Google Patents
Force feedback man-machine interactive system and method based on electromagnetic theory and mobile tracking Download PDFInfo
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- CN108406725A CN108406725A CN201810130765.5A CN201810130765A CN108406725A CN 108406725 A CN108406725 A CN 108406725A CN 201810130765 A CN201810130765 A CN 201810130765A CN 108406725 A CN108406725 A CN 108406725A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J3/00—Manipulators of master-slave type, i.e. both controlling unit and controlled unit perform corresponding spatial movements
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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
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F3/00—Input arrangements for transferring data to be processed into a form capable of being handled by the computer; Output arrangements for transferring data from processing unit to output unit, e.g. interface arrangements
- G06F3/01—Input arrangements or combined input and output arrangements for interaction between user and computer
- G06F3/017—Gesture based interaction, e.g. based on a set of recognized hand gestures
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Abstract
The present invention proposes force feedback man-machine interactive system and method based on electromagnetic theory and mobile tracking.The present invention allows manipulator to carry out Manipulation of the machine people using gesture motion, while can experience force feedback effect in operation.Interactive system includes five parts such as local control calculator, mobile tracking platform, gesture identification sensor, magnetic force generation device, magnetic force sense device.And exchange method is divided into two parts of control and feedback, wherein control section has used the non-contact gesture of view-based access control model interface to act information in order to control, and feedback fraction has then used contactless power magnetic force as feedback information, to reduce the physical limit being subject to when interaction, additional mobile tracking function simultaneously, ensure that magnetic force generation device and magnetic force sense device can keep relative pose invariance, to reduce because the stress that field decay is brought crosses minor issue.
Description
Technical field
The invention belongs to robot field of human-computer interaction, more particularly to a kind of control based on LeapMotion motion sensing control devices
Technology processed and the man-machine interactive system based on electromagnetic induction technology force feedback technique and its exchange method.
Background technology
With the continuous development of robot technology, human-computer interaction technology is also fed back by original key mouse control, display screen
Interactive mode development of traditional interactive mode towards solid, untethered system.
Have in method, the mainly fixed multiple electromagnet of method of magnetic force direction is controlled, according to the Vector modulation in magnetic field
Rule is passed through the size of electric current by controlling each electromagnet, changes its Distribution of Magnetic Field so that can synthesize correspondence at palm
The magnetic force in direction.The shortcomings that this method is computationally intensive, accuracy is low and there are blind areas.The distribution in electromagnet magnetic field is usual
It is analyzed using finite element method, this is mingled with a large amount of integral operation in the process, and calculation amount is very big, therefore controls process
Real-time just cannot be guaranteed.After analyzing magnetic field, by magnetic field stress, inverse goes out to need to be passed through the size of electric current again, usually
It is calculated using linear interpolation, and the solution of linear interpolation equation group, the case where there is without solution, that is, will appear blind
Area, blind area can also be affected to experiment effect.In addition, influence of the electromagnet due to manufacture craft, can have leakage field, heating etc.
Factor has an impact calculating, therefore the precision calculated also cannot be guaranteed.
In addition, present invention improves over the control modes for generating magnetic force direction control.The present invention is then by Mobile electromagnetic ferropexy
In the end of mobile tracking platform, drives electromagnet to move using tracking platform, change the direction of electromagnet to generate counterparty
To magnetic force.
The present invention is on the basis of having studied existing human-computer interaction technology, it is also proposed that is made with contactless gesture motion
For interactive control mode, feedback system of the non-contact type magnetic as force feedback establishes a set of with electromagnetic theory and shifting
The man-machine interactive system and exchange method of three-dimensional, non-contacting, untethered system based on motion tracking.Use the invention, behaviour
Control person can manually be made using gesture motion to control machine, and on the other hand, machine man-hour institute feedack can also
Manipulator is directly acted on by way of force feedback on hand, and manipulator is enable more intuitively to judge and adjust to interact next time
The step of and order, make interactive process more intuitive.
Invention content
The purpose of the present invention is to provide force feedback man-machine interactive system and method based on electromagnetic theory and mobile tracking,
The man-machine interactive system of three-dimensional, non-contacting, untethered system i.e. based on electromagnetic theory and mobile tracking and interaction side
Method.
Force feedback man-machine interactive system provided by the invention based on electromagnetic theory and mobile tracking comprising：Local control
Calculator, mobile tracking platform, gesture identification sensor, magnetic force generation device and magnetic force sense device processed；Wherein, gesture identification
Sensor uses the infrared sensor LeapMotion equipment based on binocular vision, for detecting and identifying gesture pose data；
Local control calculator then converts gesture data to operational order, is sent to the robot control cabinet of distal end, controls robot
Work, and receive return information；Mobile tracking platform uses the mechanical arm of 6DOF, and magnetic force is fixed on the end of mechanical arm
Generation device makes magnetic force generation device keep the invariance of relative position with hand, converts the calculation amount of field decay to shifting
Motion tracking platform's position and pose variable quantity calculates, and reduces the computation burden of controller；Magnetic force generation device is adjustable using size of current
Electromagnet is passed through electric current as the source for generating magnetic force according to the feedback information of robot, generates suitable magnetic force, is passed to people
Up to feedack；Magnetic force sense device is made of the permanent-magnet material on the gloves and gloves being worn on human hand, is used for behaviour
Author feeds back the magnetic force generated；By contactless gesture ability of posture control robot, simultaneity factor passes through non-contact operator
Robot information is fed back to operator by formula power mode.
Force feedback man-machine interaction method provided by the invention based on electromagnetic theory and mobile tracking, interactive process packet
It includes：
S1, gesture obtain；
S2, force feedback.
The step S1 includes the following steps：
During manipulator is with by gesture and robot interactive, force feedback is generated to human hand, first have to determine
The position of manipulator's hand and posture.Since the human hand data got by LeapMotion are relative to LeapMotion coordinates
System, and be operated in robot pose data in distal environment and be built upon in environment coordinate system, it is therefore desirable to these are counted
According to unified to calculating in a coordinate system.
1) definition of coordinate system
World coordinate system is defined as XgYgZg, mobile tracking platform basis coordinates system is defined as XbYbZb.Mobile tracking platform
Ending coordinates system is defined as XeYeZe, LeapMotion coordinate systems are defined as XlYlZl。
X in mobile tracking platform basis coordinates systembYbZbArbitrary point to world coordinate system XgYgZgThe method of middle conversion is as follows：
Assuming that p is a point in space, p is in world coordinate system XgYgZgUnder be expressed as xgygzg, in mobile tracking platform
Basis coordinates system XbYbZbUnder be expressed as xbybzb, then just like down conversion relationship：
Wherein, Tb2g=(Tx,Ty,Tz) indicate X in mobile tracking platform basis coordinates systembYbZbOrigin to world coordinate system
XgYgZgThe translation vector in three directions of translation；Rb2g=(n, o, a), n=(nx,ny,nz)T, o=(ox,oy,oz)T, a=(ax,
ay,az)TIndicate mobile tracking platform basis coordinates system XbYbZbX, Y, Z axis to world coordinate system XgYgZgIn three directions it is remaining
String.It is expressed as using homogeneous equation is converted to：
Formula(2) it can be abbreviated as
pg=Mbgpb (28)
Formula pg=Mbgpb(3) point p is described in mobile tracking platform basis coordinates system XbYbZbWith world coordinate system XgYgZgIt
Between transformation relation.
Similarly, it can obtain：
pb=Mebpe (29)
pe=Mlepl (30)
Wherein, formula pb=Mebpe(4) mobile tracking platform end coordinate system X is describedeYeZeWith mobile tracking platform base
Mark system XbYbZbBetween transformation relation.Formula pe=Mlepl(5) LeapMotion X are describedlYlZlCoordinate system is flat with mobile tracking
Platform ending coordinates system XeYeZeBetween transformation relation.
By pg=Mbgpb(3) pb=Mebpe(4 pe=Mlepl(5) it can obtain：
pg=MbgMebMlepl (31)
Formula pg=MbgMebMlepl(6) it describes from LeapMotion coordinate systems XlYlZlTo world coordinate system XgYgZgChange
Change relationship, wherein MbgFor mobile tracking platform basis coordinates system XbYbZbTo world coordinate system XgYgZgTransformation matrix, it is assumed that the world is sat
Mark system XgYgZgWith mobile tracking platform basis coordinates system XbYbZbIt overlaps, then has：
MebFor from mobile tracking platform end coordinate system XeYeZeTo mobile tracking platform basis coordinates system XbYbZbTransformation matrix.
Mobile tracking platform then has using the robot of 6DOF：
Meb=Meb1Meb2Meb3Meb4Meb5Meb6 (33)
Wherein, MebiIndicate transformation matrix of the mobile tracking platform from (i-1)-th joint to i-th of joint.θiExpression is being sat
Around Z when mark transformationi-1The angle of rotation so that Xi-1And XiIt is mutually parallel；riIt indicates in coordinate transform along Zi-1The distance of translation,
Make Xi-1And XiCollinearly；liIndicate the X in coordinate transformi-1The distance of translation so that Xi-1And XiOrigin overlap；αiIt indicates
Z when coordinate transformi-1Around XiThe angle of rotation so that Zi-1And ZiOrigin overlaps, and direction is consistent.
MleFor from LeapMotion XlYlZlCoordinate system is to mobile tracking platform end coordinate system XeYeZeTransformation matrix.By
The height of the length and LeapMotion itself of electromagnet is differed with mobile tracking platform in LeapMotion, therefore：
Wherein, L is the length of electromagnet, and the height that h is LeapMotion itself.
There is formula pg=MbgMebMleplIt (6), then can be from LeapMotion coordinate system transformation to world coordinate system
XgYgZgIn calculated.
2) conversion of the acquisition of gesture data and coordinate system
The gesture data got from LeapMotion sensors is (x, y, z, θ, α, β), and wherein x, y, z is respectively hand
The palm is in LeapMotion coordinate systems XlYlZlIn three directions position quantity.And θ, α, β are respectively the finger orientation of palm around Zl、
Xl、YlThe angle of reference axis rotation.
Define palm coordinate system XhYhZh, then palm coordinate system and the transformation relation of LeapMotion coordinate systems are：
pl=Mhlph (36)
Wherein：
Therefore, pass through formula pg=MbgMebMlepl(6) and formula pl=MhlphIt (11), can be being got from LeapMotion
Gesture data be transformed into world coordinate system XgYgZgUnder calculated.Similarly, as long as the pose data of the robot distal end
It is unified to arrive world coordinate system XgYgZgUnder, it allows the pose data of robot to be overlapped with manipulator's gesture data, can reach and pass through hand
The purpose of gesture Manipulation of the machine people.
The step S2 includes the following steps：
Step S1 completes the acquisition to gesture data.Step S2 then needs the feedback information according to robot to manipulating
The hand of person generates the magnetic force of a determining size and Orientation, to reach force feedback effect.Magnetic is adjusted including following three steps (1)
The direction of power；(2) size of magnetic force is adjusted；(3) magnetic force is generated.
1) direction that adjustment magnetic force generates
What the adjustment of magnetic force direction was mainly realized by changing the pose of electromagnet.Energization electromagnet is fixed on movement
On the end of tracking platform.Need generate power when, driving mobile tracking platform drive electromagnet movement, make electromagnet the poles N,
The direction of this 3 points of straight lines being linked to be of the poles S with the midpoint of the human hand hand palm of the hand is consistent with the direction of required magnetic force, then can ensure electricity
Magnetic force direction caused by magnet meets the requirements.
In step sl, the data for collecting human hand are (x, y, z, θ, α, β), and wherein x, y, z is respectively palm in coordinate
It is XgYgZgIn three directions position quantity.And the angle that the finger orientation that θ, α, β are respectively palm is rotated around Z, X, Y coordinates axis.
The attitude data for considering human hand is not required here, therefore tri- values of θ, α, β can take 0, indicates as follows using position auto―control：
In order to facilitate expression, the position auto―control M of human handhandAnd all position auto―controls being subsequently noted all have transformed to
World coordinate system XgYgZgLower expression, conversion process is as described in step S1.
Assuming that allow feel by a magnetic force F at this time, the direction of magnetic force is expressed as Fdirection.Wherein, Fdirection
In xOy planes and positive direction of the x-axis angle is ω, is with positive direction of the y-axis angle in yOz planesIn xOz planes just with z-axis
Angular separation is γ.
In order to which the magnetic force for allowing electromagnet to generate meets the requirements, the change for driving tracking platform control electromagnet to carry out position is needed
It changes, conversion process is：
Wherein MeFor the position auto―control of mobile tracking platform end；T is translation matrix；L is the length of electromagnet；H is
The height of LeapMotion sensors；D is distance of the electromagnet to palm.ω is the angle rotated around z-axis；For rao x-axis
The angle of rotation；γ is the angle rotated around y-axis.
In this experiment porch, mobile tracking platform uses the mechanical arm of 6DOF.Obtain mobile tracking platform end
Position auto―control MeAfterwards, by the anti-solution operation in robot kinematics, to solve the size of each joint angle.Solve anti-solution operation
Method it is very much, have the inverse transformation method of Paul, the geometric method of Lee and Ziegler, spinor theory method, neural network method etc..This
Most common Pual inverse transformation methods are used in system.Since length is limited, the algorithm is not described in detail herein.
Operation is solved by counter, after calculating and setting the size of each joint angle of mobile tracking platform, drives mobile tracking
Platform moves to specified corresponding position, and the magnetic force of generation can be made to meet direction requirement.
2) size that adjustment magnetic force generates
C) calculating of energization solenoid electromagnetic force
Using direct current, it is assumed that the magnetic permeable material of energization solenoid uniformly and isotropism, ignores the magnetic hysteresis of permeability magnetic material
Effect does not consider influences of the Wen Sheng of circle energization generation to coil magnetic potential and permeability magnetic material magnetic resistance.Wait for that solenoid energization reaches steady
After fixed, the magnetic force of generation is：
Wherein, φ is working gas gap magnetic flux, unit Wb；B is magnetic induction intensity, unit T.μ0For space permeability,
Value is 4 π × 10-7Wb/A·m；S is magnetic circuit sectional area, unit m2。
Do not consider that air gap existing for leakage field and other connecting portions, main air gap are armature travel, at this time DC electromagnet
Air gap (iron core stroke) magnetic induction density B be：
Wherein, N is coil number, and unit is circle；U is supply voltage, unit V；μ0For space permeability, it is worth for 4 π × 10-7Wb/A·m；I is current strength, unit A；R is wire resistor, unit Ω；δ is gas length, unit m.By formula(16) and likes(15) it can obtain：
Since there are leakage field phenomenons for electromagnet, after in view of the factor, magnetic force can be calculated plus magnetic leakage factor, because
This formula(17) it can be converted to：
Wherein KfFor magnetic leakage factor, its value is determined by the physical property of electromagnet itself, and work is made according to electromagnet
The quality of skill, value can change in 1-10, and in Electromagnetic Design, general value is 1.2-5.0.
D) electromagnet is passed through the calculating of size of current
Different electric currents is loaded on one group of coil, and the magnetic field in different size direction can be generated at the every bit in space.
Formula(18) it describes and provides solenoid current, it is asked to generate the calculation formula of magnetic force size.On the contrary, if desired
The magnetic field in certain size direction is generated at certain point, then to solve needs and load great electric current respectively on this group of coil.
Hereinafter, description to be passed through to the computational methods of electric current.
First, arbitrary current source can inspire magnetic field in space.The magnetic induction that the current elements generate at the point P of space
The size of intensity is directly proportional to the size of current elements, with electric current where place arrive P points position vector and current elements between angle
Sine it is directly proportional, and square being inversely proportional at a distance from current elements to P points.It can be described as with equation：
Wherein, I is size of current, and unit is A；L is path of integration, and dl is the atomic element of elementary current, μ0For Vacuum Magnetic
Conductance, value are 4 π × 10-7Tm/A；R is distance；The unit vector of site to be asked is merely desired to for current source.
Formula(19) it is as follows to be write as integrated form：
The size of the magnetic induction intensity generated at the point P of space due to arbitrary current elements and the size of current elements are at just
Than.Can be by infinite more current source arrangement form conducting wire, then the conducting wire of arbitrary shape excites at the point P of space magnetic field and lead
Electric current in is directly proportional.It is expressed as with equation：
Wherein,It is integral of the linear coefficient to current path of electric current, i.e.,：
And be vector by electric current excitation electromagnetic field field strength, meet vector superposed principle.There is the mutual of multiple current sources
Under the influence of, the magnetic field in space at certain point P is equal to the vector superposed of the electromagnetic field that all current sources excite at this point respectively.Cause
This can be by each circle coil as an electric current loop for energization solenoid.Under more electric current field source environment in three dimensions,
The magnetic field intensity of certain point and each field source electric current are in a linear relationship.Therefore by formula(21) it is ordinary circumstance to expand,
Have：
Formula(23) magnetic field of certain point P and field source electric current in space are described
Linear relationship.Wherein, n is the number of current source sources；I1,I2,…,InRespectively the 1st, 2 ..., the size of current of n current source,
Unit is A；Bx,By,BzGo out component of the vector sum in the magnetic field inspired on 3 directions in point P for n current source, unit is
T；Aix,Aiy,AizComponent of the linear coefficient in magnetic field on 3 directions is generated on spatial point P for i-th of current source；Matrix A
For electric current magnetic field linear coefficient matrix in spatial point.
Magnetic field amount Bx,By,BzBy being provided in robot feedback information, electric current magnetic field linear coefficient matrices A can be by spatial point
Formula(22) it calculates separately and obtains.Therefore with I1,I2,…,InFor unknown number, solve equation(23), the solution acquired is the electric current being added in required for generating magnetic field on coil.
Obviously, according to equation(23) size of current is solved, equation might not have
Solution.Because current field linear coefficient matrix A may have the case where determinant is 0.Generate current field linear coefficient square
Battle array A may have the position that determinant is 0 and be known as unreachable region.
In order to eliminate the unreachable region for influencing experiment effect, the mobile tracking platform of step S2 is introduced.Due in step
In rapid S2, the end of solenoid and mobile tracking platform is fixed, electromagnet can reach it with mobile tracking platform
Desired position and posture, therefore unreachable region can be eliminated.Moreover, in step s 2, mobile tracking platform can be with behaviour
Control person hand is mobile and changes pose, it is ensured that electromagnet with manipulate the relative position set about and fix, i.e., the two poles of the earth of electromagnet are always
Towards palm.Therefore in the calculation, it need to only consider electromagnetism generated magnetic force in two extreme directions after powered up.And in the reality
It tests in platform, has only used an electromagnet, therefore current source number n is set as 1, therefore have：
B=Bz=AzI (49)
It solves：
I=Az -1Bz (50)
Required I is the size of required electrical current.
3) magnetic force is generated
By step 1) and 2) after, it is flat the mobile tracking for acquiring and electromagnet being made to reach specific position and direction has been calculated
The angle of the joint angle in six joints of platform, and need the electric current for being passed through electromagnet.Therefore, in this step, local control meter
It calculates device and generates platform transmission order to mobile tracking platform and magnetic force respectively, allow it to be moved to specified position and generate magnetic
Power, the operator for having worn magnetic force sense device just can experience the effect of force feedback.It as a result, can be anti-by the information of robot
It feeds human hand.
Compared with prior art, the present invention having the following advantages that and technique effect：
Present invention improves over the control modes for generating magnetic force direction.The present invention puts down Mobile electromagnetic ferropexy in mobile tracking
The end of platform drives electromagnet to move, changes the direction of electromagnet to generate the magnetic force of corresponding direction using tracking platform.This
Sample can mitigate calculation amount being converted in the solution of robot kinematics to the calculating of magnetic field analysis.Meanwhile because
Mobile tracking platform is used, it is ensured that the relative position of electromagnet and human hand is constant, and towards always towards human hand, can be with
Solve the problems, such as the field decay generated due to factors such as leakage field, heatings on other directions of electromagnet.
Description of the drawings
Fig. 1 is composition and the signal transmission signal of the force feedback man-machine interactive system based on electromagnetic theory and mobile tracking
Figure.
Fig. 2 is the block diagram of the force feedback man-machine interactive system based on electromagnetic theory and mobile tracking.
Fig. 3 is the coordinate system expression figure of system in embodiment；
Fig. 4 is that magnetic force generates direction schematic diagram.
Specific implementation mode
The present invention is described in further detail with reference to embodiments, and embodiments of the present invention are not limited thereto,
Place is not described in detail especially if having below, is that those skilled in the art can refer to prior art realization or understand.
If Fig. 1 is composition and the signal transmission signal of the force feedback man-machine interactive system based on electromagnetic theory and mobile tracking
Figure.Fig. 2 is the block diagram of the force feedback man-machine interactive system based on electromagnetic theory and mobile tracking.Based on electromagnetic theory with it is mobile with
The force feedback man-machine interactive system of track comprising：Local control calculator, mobile tracking platform, gesture identification sensor, magnetic force
Generation device and magnetic force sense device；Wherein, gesture identification sensor uses the infrared sensor based on binocular vision
LeapMotion equipment, for detecting and identifying gesture pose data；Local control calculator then converts gesture data to behaviour
It orders, is sent to the robot control cabinet of distal end, control machine is manually made, and receives return information；Mobile tracking platform makes
With the mechanical arm of 6DOF, magnetic force generation device is fixed on the end of mechanical arm, and magnetic force generation device is made to keep phase with hand
To the invariance of position, converts the calculation amount of field decay to mobile tracking platform's position and pose variable quantity and calculate, reduce controller
Computation burden；Magnetic force generation device uses the adjustable electromagnet of size of current as the source for generating magnetic force, according to robot
Feedback information is passed through electric current, generates suitable magnetic force, and feedack is conveyed to people；Magnetic force sense device is by being worn over human hand
On gloves and gloves on permanent-magnet material constitute, for operator feed back generate magnetic force；Operator passes through non-contact
Robot information is fed back to operator by the gesture ability of posture control robot of formula, simultaneity factor by contactless power mode.
The exchange method of this example includes the following steps：
S1, gesture obtain；
S2, force feedback.
The step S1 includes the following steps：
During manipulator is with by gesture and robot interactive, force feedback is generated to human hand, first have to determine
The position of manipulator's hand and posture.Since the human hand data got by LeapMotion are relative to LeapMotion coordinates
System, and be operated in robot pose data in distal environment and be built upon in environment coordinate system, it is therefore desirable to these are counted
According to unified to calculating in a coordinate system.
3) definition of coordinate system
World coordinate system is defined as XgYgZg, mobile tracking platform basis coordinates system is defined as XbYbZb.Mobile tracking platform
Ending coordinates system is defined as XeYeZe, 301 coordinate systems of LeapMotion are defined as XlYlZl.Their expression such as Fig. 3.
X in mobile tracking platform basis coordinates systembYbZbArbitrary point to world coordinate system XgYgZgThe method of middle conversion is as follows：
Assuming that p is a point in space, p is in world coordinate system XgYgZgUnder be expressed as xgygzg, in mobile tracking platform
Basis coordinates system XbYbZbUnder be expressed as xbybzb, then just like down conversion relationship：
Wherein, Tb2g=(Tx,Ty,Tz) indicate X in mobile tracking platform basis coordinates systembYbZbOrigin to world coordinate system
XgYgZgThe translation vector in three directions of translation；Rb2g=(n, o, a), n=(nx,ny,nz)T, o=(ox,oy,oz)T, a=(ax,
ay,az)TIndicate mobile tracking platform basis coordinates system XbYbZbX, Y, Z axis to world coordinate system XgYgZgIn three directions it is remaining
String.It is expressed as using homogeneous equation is converted to：
Formula(2) it can be abbreviated as
pg=Mbgpb (53)
Formula pg=Mbgpb(3) point p is described in mobile tracking platform basis coordinates system XbYbZbWith world coordinate system XgYgZgIt
Between transformation relation.
Similarly, it can obtain：
pb=Mebpe (54)
pe=Mlepl (55)
Wherein, formula pb=Mebpe(4) mobile tracking platform end coordinate system X is describedeYeZeWith mobile tracking platform base
Mark system XbYbZbBetween transformation relation.Formula pe=Mlepl(5) LeapMotion X are describedlYlZlCoordinate system is flat with mobile tracking
Platform ending coordinates system XeYeZeBetween transformation relation.
By pg=Mbgpb(3) pb=Mebpe(4 pe=Mlepl(5) it can obtain：
pg=MbgMebMlepl (56)
Formula pg=MbgMebMlepl(6) it describes from LeapMotion coordinate systems XlYlZlTo world coordinate system XgYgZgChange
Change relationship, wherein MbgFor mobile tracking platform basis coordinates system XbYbZbTo world coordinate system XgYgZgTransformation matrix, it is assumed that the world is sat
Mark system XgYgZgWith mobile tracking platform basis coordinates system XbYbZbIt overlaps, then has：
MebFor from mobile tracking platform end coordinate system XeYeZeTo mobile tracking platform basis coordinates system XbYbZbTransformation matrix.
Mobile tracking platform then has using the robot of 6DOF：
Meb=Meb1Meb2Meb3Meb4Meb5Meb6 (58)
Wherein, MebiIndicate transformation matrix of the mobile tracking platform from (i-1)-th joint to i-th of joint.θiExpression is being sat
Around Z when mark transformationi-1The angle of rotation so that Xi-1And XiIt is mutually parallel；riIt indicates in coordinate transform along Zi-1The distance of translation,
Make Xi-1And XiCollinearly；liIndicate the X in coordinate transformi-1The distance of translation so that Xi-1And XiOrigin overlap；αiIt indicates
Z when coordinate transformi-1Around XiThe angle of rotation so that Zi-1And ZiOrigin overlaps, and direction is consistent.
MleFor from LeapMotion XlYlZlCoordinate system is to mobile tracking platform end coordinate system XeYeZeTransformation matrix.By
The height for having differed the length and LeapMotion itself of electromagnet 302 with mobile tracking platform in LeapMotion 301, because
This：
Wherein, L is the length of electromagnet, and the height that h is LeapMotion itself.
There is formula pg=MbgMebMleplIt (6), then can be from LeapMotion coordinate system transformation to world coordinate system
XgYgZgIn calculated.
4) conversion of the acquisition of gesture data and coordinate system
The gesture data got from LeapMotion sensors is (x, y, z, θ, α, β), and wherein x, y, z is respectively hand
The palm is in LeapMotion coordinate systems XlYlZlIn three directions position quantity.And θ, α, β are respectively the finger orientation of palm around Zl、
Xl、YlThe angle of reference axis rotation.
Define palm coordinate system XhYhZh, then palm coordinate system and the transformation relation of LeapMotion coordinate systems are：
pl=Mhlph (61)
Wherein：
Therefore, pass through formula pg=MbgMebMlepl(6) and formula pl=MhlphIt (11), can be being got from LeapMotion
Gesture data be transformed into world coordinate system XgYgZgUnder calculated.Similarly, as long as the pose data of the robot distal end
It is unified to arrive world coordinate system XgYgZgUnder, it allows the pose data of robot to be overlapped with manipulator's gesture data, can reach and pass through hand
The purpose of gesture Manipulation of the machine people.
The step S2 includes the following steps：
Step S1 completes the acquisition to gesture data.Step S2 then needs the feedback information according to robot to manipulating
The hand of person generates the magnetic force of a determining size and Orientation, to reach force feedback effect.Magnetic is adjusted including following three steps (1)
The direction of power；(2) size of magnetic force is adjusted；(3) magnetic force is generated.
3) direction that adjustment magnetic force generates
What the adjustment of magnetic force direction was mainly realized by changing the pose of electromagnet.Energization electromagnet 302 is fixed on
On the end of mobile tracking platform.When needing to generate power, driving mobile tracking platform drives electromagnet movement, makes electromagnet
The poles N, the direction of this 3 points of straight lines being linked to be of the poles S with the midpoint of 401 palm of the hand of human hand are consistent with the direction of required magnetic force, then can protect
Magnetic force direction meets the requirements caused by card electromagnet.Such as Fig. 4.
In step sl, the data for collecting human hand are (x, y, z, θ, α, β), and wherein x, y, z is respectively palm in coordinate
It is XgYgZgIn three directions position quantity.And the angle that the finger orientation that θ, α, β are respectively palm is rotated around Z, X, Y coordinates axis.
The attitude data for considering human hand is not required here, therefore tri- values of θ, α, β can take 0, indicates as follows using position auto―control：
In order to facilitate expression, the position auto―control M of human handhandAnd all position auto―controls being subsequently noted all have transformed to
World coordinate system XgYgZgLower expression, conversion process is as described in step S1.
Assuming that allow feel by a magnetic force F at this time, the direction of magnetic force is expressed as Fdirection.Wherein, Fdirection
In xOy planes and positive direction of the x-axis angle is ω, is with positive direction of the y-axis angle in yOz planesIn xOz planes just with z-axis
Angular separation is γ.
In order to which the magnetic force for allowing electromagnet to generate meets the requirements, the change for driving tracking platform control electromagnet to carry out position is needed
It changes, conversion process is：
Wherein MeFor the position auto―control of mobile tracking platform end；T is translation matrix；L is the length of electromagnet；H is
The height of LeapMotion sensors；D is distance of the electromagnet to palm.ω is the angle rotated around z-axis；For rao x-axis
The angle of rotation；γ is the angle rotated around y-axis.
In this experiment porch, mobile tracking platform uses the mechanical arm of 6DOF.Obtain mobile tracking platform end
Position auto―control MeAfterwards, by the anti-solution operation in robot kinematics, to solve the size of each joint angle.Solve anti-solution operation
Method it is very much, have the inverse transformation method of Paul, the geometric method of Lee and Ziegler, spinor theory method, neural network method etc..This
Most common Pual inverse transformation methods are used in system.Since length is limited, the algorithm is not described in detail herein.
Operation is solved by counter, after calculating and setting the size of each joint angle of mobile tracking platform, drives mobile tracking
Platform moves to specified corresponding position, and the magnetic force of generation can be made to meet direction requirement.
4) size that adjustment magnetic force generates
E) calculating of energization solenoid electromagnetic force
Using direct current, it is assumed that the magnetic permeable material of energization solenoid uniformly and isotropism, ignores the magnetic hysteresis of permeability magnetic material
Effect does not consider influences of the Wen Sheng of circle energization generation to coil magnetic potential and permeability magnetic material magnetic resistance.Wait for that solenoid energization reaches steady
After fixed, the magnetic force of generation is：
Wherein, φ is working gas gap magnetic flux, unit Wb；B is magnetic induction intensity, unit T.μ0For space permeability,
Value is 4 π × 10-7Wb/A·m；S is magnetic circuit sectional area, unit m2。
Do not consider that air gap existing for leakage field and other connecting portions, main air gap are armature travel, at this time DC electromagnet
Air gap (iron core stroke) magnetic induction density B be：
Wherein, N is coil number, and unit is circle；U is supply voltage, unit V；μ0For space permeability, it is worth for 4 π × 10-7Wb/A·m；I is current strength, unit A；R is wire resistor, unit Ω；δ is gas length, unit m.By formula(16) and likes(15) it can obtain：
Since there are leakage field phenomenons for electromagnet, after in view of the factor, magnetic force can be calculated plus magnetic leakage factor, because
This formula(17) it can be converted to：
Wherein KfFor magnetic leakage factor, its value is determined by the physical property of electromagnet itself, and work is made according to electromagnet
The quality of skill, value can change in 1-10, and in Electromagnetic Design, general value is 1.2-5.0.
F) electromagnet is passed through the calculating of size of current
Different electric currents is loaded on one group of coil, and the magnetic field in different size direction can be generated at the every bit in space.
Formula(18) it describes and provides solenoid current, it is asked to generate the calculation formula of magnetic force size.On the contrary, if desired
The magnetic field in certain size direction is generated at certain point, then to solve needs and load great electric current respectively on this group of coil.
Hereinafter, description to be passed through to the computational methods of electric current.
First, arbitrary current source can inspire magnetic field in space.The magnetic induction that the current elements generate at the point P of space
The size of intensity is directly proportional to the size of current elements, with electric current where place arrive P points position vector and current elements between angle
Sine it is directly proportional, and square being inversely proportional at a distance from current elements to P points.It can be described as with equation：
Wherein, I is size of current, and unit is A；L is path of integration, and dl is the atomic element of elementary current, μ0For Vacuum Magnetic
Conductance, value are 4 π × 10-7Tm/A；R is distance；The unit vector of site to be asked is merely desired to for current source.
Formula(19) it is as follows to be write as integrated form：
The size of the magnetic induction intensity generated at the point P of space due to arbitrary current elements and the size of current elements are at just
Than.Can be by infinite more current source arrangement form conducting wire, then the conducting wire of arbitrary shape excites at the point P of space magnetic field and lead
Electric current in is directly proportional.It is expressed as with equation：
Wherein,It is integral of the linear coefficient to current path of electric current, i.e.,：
And be vector by electric current excitation electromagnetic field field strength, meet vector superposed principle.There is the mutual of multiple current sources
Under the influence of, the magnetic field in space at certain point P is equal to the vector superposed of the electromagnetic field that all current sources excite at this point respectively.Cause
This can be by each circle coil as an electric current loop for energization solenoid.Under more electric current field source environment in three dimensions,
The magnetic field intensity of certain point and each field source electric current are in a linear relationship.Therefore by formula(21) it is ordinary circumstance to expand,
Have：
Formula(23) magnetic field of certain point P and field source electric current in space are described
Linear relationship.Wherein, n is the number of current source sources；I1,I2,…,InRespectively the 1st, 2 ..., the size of current of n current source,
Unit is A；Bx,By,BzGo out component of the vector sum in the magnetic field inspired on 3 directions in point P for n current source, unit is
T；Aix,Aiy,AizComponent of the linear coefficient in magnetic field on 3 directions is generated on spatial point P for i-th of current source；Matrix A
For electric current magnetic field linear coefficient matrix in spatial point.
Magnetic field amount Bx,By,BzBy being provided in robot feedback information, electric current magnetic field linear coefficient matrices A can be by spatial point
Formula(22) it calculates separately and obtains.Therefore with I1,I2,…,InFor unknown number, solve equation(23), the solution acquired is the electric current being added in required for generating magnetic field on coil.
Obviously, according to equation(23) size of current is solved, equation might not have
Solution.Because current field linear coefficient matrix A may have the case where determinant is 0.Generate current field linear coefficient square
Battle array A may have the position that determinant is 0 and be known as unreachable region.
In order to eliminate the unreachable region for influencing experiment effect, the mobile tracking platform of step S2 is introduced.Due in step
In rapid S2, the end of solenoid and mobile tracking platform is fixed, electromagnet can reach it with mobile tracking platform
Desired position and posture, therefore unreachable region can be eliminated.Moreover, in step s 2, mobile tracking platform can be with behaviour
Control person hand is mobile and changes pose, it is ensured that electromagnet with manipulate the relative position set about and fix, i.e., the two poles of the earth of electromagnet are always
Towards palm.Therefore in the calculation, it need to only consider electromagnetism generated magnetic force in two extreme directions after powered up.And in the reality
It tests in platform, has only used an electromagnet, therefore current source number n is set as 1, therefore have：
B=Bz=AzI (74)
It solves：
I=Az -1Bz (75)
Required I is the size of required electrical current.
3) magnetic force is generated
By step 1) and 2) after, it is flat the mobile tracking for acquiring and electromagnet being made to reach specific position and direction has been calculated
The angle of the joint angle in six joints of platform, and need the electric current for being passed through electromagnet.Therefore, in this step, local control meter
It calculates device and generates platform transmission order to mobile tracking platform and magnetic force respectively, allow it to be moved to specified position and generate magnetic
Power, the operator for having worn magnetic force sense device just can experience the effect of force feedback.It as a result, can be anti-by the information of robot
It feeds human hand.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, it is other it is any without departing from the spirit and principles of the present invention made by changes, modifications, substitutions, combinations, simplifications,
Equivalent substitute mode is should be, is included within the scope of the present invention.
Claims (7)
1. the force feedback man-machine interactive system based on electromagnetic theory and mobile tracking, it is characterised in that including：Local control calculates
Device, mobile tracking platform, gesture identification sensor, magnetic force generation device and magnetic force sense device；Wherein, gesture identification sensor
Using the infrared sensor LeapMotion equipment based on binocular vision, for detecting and identifying gesture pose data；Local control
Calculator processed then converts gesture data to operational order, is sent to the robot control cabinet of distal end, and control machine is manually made, and
Receive return information；Mobile tracking platform uses the mechanical arm of 6DOF, and magnetic force is fixed on the end of mechanical arm and generates dress
It sets, so that magnetic force generation device is kept the invariance of relative position with hand, convert the calculation amount of field decay to mobile tracking
Platform's position and pose variable quantity calculates, and reduces the computation burden of controller；Magnetic force generation device uses the adjustable electromagnet of size of current
Electric current is passed through according to the feedback information of robot as the source for generating magnetic force, generates suitable magnetic force, conveys and feeds back to people
Information；Magnetic force sense device is made of the permanent-magnet material on the gloves and gloves being worn on human hand, for anti-to operator
Present the magnetic force generated；Operator passes through contactless power side by contactless gesture ability of posture control robot, simultaneity factor
Robot information is fed back to operator by formula.
2. the force feedback man-machine interaction method based on electromagnetic theory and mobile tracking, it is characterised in that using described in claim 1
The force feedback man-machine interactive system based on electromagnetic theory and mobile tracking, exchange method be divided into control and feedback two parts,
Control section has used the non-contact gesture of view-based access control model interface to act information in order to control, using based on infrared vision
LeapMotion is as gesture identification sensor；Feedback fraction has then used contactless power magnetic force as feedback information, uses
Direction adjustable mobile tracking platform fixes the adjustable electromagnet of size of current as magnetic force generation device, big to generate
Small, the adjustable magnetic force in direction feeds back robot information.
3. the force feedback man-machine interaction method according to claim 2 based on electromagnetic theory and mobile tracking, feature exist
Include in the feedback fraction：The feedback information for collecting distant place robot after handling the feedback information, is calculated and is produced
Bear size, the suitable magneticaction in direction on hand, allows operator that can experience force feedback in operator.
4. the force feedback man-machine interaction method according to claim 3 based on electromagnetic theory and mobile tracking, feature exist
In：During manipulator is with by gesture and robot interactive, force feedback is generated to human hand, first have to determine manipulator
The position of hand and posture；Due to the human hand data got by LeapMotion be relative to LeapMotion coordinate systems,
And it is operated in robot pose data in distal environment and is built upon in environment coordinate system, it is therefore desirable to which these data are unified
To being calculated in a coordinate system；It specifically includes：
World coordinate system is defined as XgYgZg, mobile tracking platform basis coordinates system is defined as XbYbZb；Mobile tracking platform end
Coordinate system is defined as XeYeZe, LeapMotion coordinate systems are defined as XlYlZl；
X in mobile tracking platform basis coordinates systembYbZbArbitrary point to world coordinate system XgYgZgThe method of middle conversion is as follows：
If p is a point in space, p is in world coordinate system XgYgZgUnder be expressed as xgygzg, in mobile tracking platform basis coordinates
It is XbYbZbUnder be expressed as xbybzb, then just like down conversion relationship：
Wherein, Tb2g=(Tx,Ty,Tz) indicate X in mobile tracking platform basis coordinates systembYbZbOrigin to world coordinate system XgYgZg
The translation vector in three directions of translation；Use Rb2g=(n, o, a), n=(nx,ny,nz)T, o=(ox,oy,oz)T, a=(ax,ay,
az)TIndicate mobile tracking platform basis coordinates system XbYbZbX, Y, Z axis to world coordinate system XgYgZgIn three directions cosine；Make
It is expressed as with homogeneous equation is converted to：
FormulaIt can be abbreviated as：
pg=Mbgpb (3)
Formula pg=Mbgpb(3) point p is described in mobile tracking platform basis coordinates system XbYbZbWith world coordinate system XgYgZgBetween change
Change relationship；
Similarly, it can obtain：
pb=Mebpe (4)
pe=Mlepl (5)
Wherein, formula pb=Mebpe(4) mobile tracking platform end coordinate system X is describedeYeZeWith mobile tracking platform basis coordinates system
XbYbZbBetween transformation relation；Formula pe=Mlepl(5) LeapMotionX is describedlYlZlCoordinate system and mobile tracking platform end
Hold coordinate system XeYeZeBetween transformation relation；
By pg=Mbgpb(3)pb=Mebpe(4pe=Mlepl(5) it can obtain：
pg=MbgMebMlepl (6)
Formula pg=MbgMebMlepl(6) it describes from LeapMotion coordinate systems XlYlZlTo world coordinate system XgYgZgTransformation close
System, wherein MbgFor mobile tracking platform basis coordinates system XbYbZbTo world coordinate system XgYgZgTransformation matrix, it is assumed that world coordinate system
XgYgZgWith mobile tracking platform basis coordinates system XbYbZbIt overlaps, then has：
MebFor from mobile tracking platform end coordinate system XeYeZeTo mobile tracking platform basis coordinates system XbYbZbTransformation matrix；It is mobile
Tracking platform then has using the mechanical arm of 6DOF：
Meb=Meb1Meb2Meb3Meb4Meb5Meb6 (8)
Wherein, MebiIndicate transformation matrix of the mobile tracking platform from (i-1)-th joint to i-th of joint；θiIt indicates to become in coordinate
Around Z when changingi-1The angle of rotation so that Xi-1And XiIt is mutually parallel；riIt indicates in coordinate transform along Zi-1The distance of translation so that
Xi-1And XiCollinearly；liIndicate the X in coordinate transformi-1The distance of translation so that Xi-1And XiOrigin overlap；αiIt indicates in coordinate
Z when transformationi-1Around XiThe angle of rotation so that Zi-1And ZiOrigin overlaps, and direction is consistent；
MleFor from the X of LeapMotionlYlZlCoordinate system is to mobile tracking platform end coordinate system XeYeZeTransformation matrix；Due to
LeapMotion has differed the height of the length and LeapMotion itself of electromagnet with mobile tracking platform, therefore：
Wherein, L is the length of electromagnet, and the height that h is LeapMotion itself；
There is formula pg=MbgMebMleplIt (6), then can be from LeapMotion coordinate system transformations to world coordinate system XgYgZgIn into
Row calculates；
The acquisition of gesture data and the conversion of coordinate system specifically include：
The gesture data got from LeapMotion sensors is (x, y, z, θ, α, β), and wherein x, y, z is respectively that palm exists
LeapMotion coordinate systems XlYlZlIn three directions position quantity；And θ, α, β are respectively the finger orientation of palm around Zl、Xl、Yl
The angle of reference axis rotation；
Define palm coordinate system XhYhZh, then palm coordinate system and the transformation relation of LeapMotion coordinate systems are：
pl=Mhlph (11)
Wherein：
Therefore, pass through formula pg=MbgMebMlepl(6) and formula pl=MhlphIt (11), can be the hand got from LeapMotion
Gesture data are transformed into world coordinate system XgYgZgUnder calculated；Similarly, as long as the pose data of the robot of distal end are also unified
To world coordinate system XgYgZgUnder, it allows the pose data of robot to be overlapped with manipulator's gesture data, just can reach and be grasped by gesture
The purpose of man-controlled mobile robot.
5. the force feedback man-machine interaction method according to claim 3 based on electromagnetic theory and mobile tracking, feature exist
In：The feedback fraction generates the hand of operator according to the feedback information of robot the magnetic force of one determining size and Orientation,
To reach force feedback effect, including following three steps：
(1) direction of magnetic force is adjusted
Energization electromagnet is fixed on the end of mobile tracking platform；When needing to generate power, mobile tracking platform band is driven
Dynamic electromagnet movement makes the poles N of electromagnet, the direction of this 3 points of straight lines being linked to be of the poles S and the midpoint of the human hand hand palm of the hand and required
The direction of magnetic force is consistent, then can guarantee that magnetic force direction caused by electromagnet meets the requirements；
The data for collecting human hand are (x, y, z, θ, α, β), and wherein x, y, z is respectively palm in coordinate system XgYgZgIn three sides
To position quantity；And the angle that the finger orientation that θ, α, β are respectively palm is rotated around Z, X, Y coordinates axis；Consideration is not required here
The attitude data of human hand, therefore tri- values of θ, α, β can take 0, indicate as follows using position auto―control：
The position auto―control M of human handhandAnd all position auto―controls being subsequently noted all have transformed to world coordinate system XgYgZg
Lower expression；
If to allow feel by a magnetic force F at this time, the direction of magnetic force is expressed as Fdirection；Wherein, FdirectionIn xOy planes
Interior and positive direction of the x-axis angle is ω, is with positive direction of the y-axis angle in yOz planesIt is pressed from both sides with z-axis positive direction in xOz planes
Angle is γ；
In order to which the magnetic force for allowing electromagnet to generate meets the requirements, the transformation for driving tracking platform control electromagnet to carry out position is needed,
Conversion process is：
Wherein MeFor the position auto―control of mobile tracking platform end；T is translation matrix；L is the length of electromagnet；H is
The height of LeapMotion sensors；D is distance of the electromagnet to palm；ω is the angle rotated around z-axis；For rao x-axis
The angle of rotation；γ is the angle rotated around y-axis；
Obtain the position auto―control M of mobile tracking platform endeAfterwards, by the anti-solution operation in robot kinematics, to solve each pass
Save the size at angle；Solve operation by counter, after calculating and setting the size of each joint angle of mobile tracking platform, driving it is mobile with
Track platform moves to specified corresponding position, and the magnetic force of generation can be made to meet direction requirement；
(2) size that adjustment magnetic force generates, specifically includes：
A) calculating of energization solenoid electromagnetic force
Using direct current, after solenoid energization reaches and stablizes, the magnetic force of generation is：
Wherein, φ is working gas gap magnetic flux, unit Wb；B is magnetic induction intensity, unit T；μ0For space permeability, it is worth for 4 π
×10-7Wb/A·m；S is magnetic circuit sectional area, unit m2；
Do not consider that air gap existing for leakage field and other connecting portions, main air gap are armature travel, at this time the gas of DC electromagnet
Gap, that is, iron core stroke magnetic induction density B is：
Wherein, N is coil number, and unit is circle；U is supply voltage, unit V；μ0For space permeability, it is worth for 4 π × 10-7Wb/
A·m；I is current strength, unit A；R is wire resistor, unit Ω；δ is gas length, unit m；By formulaAnd formulaIt can obtain：
Since there are leakage field phenomenons for electromagnet, after in view of the factor, magnetic force, therefore formula can be calculated plus magnetic leakage factorIt can be converted to：
Wherein KfFor magnetic leakage factor, its value is determined by the physical property of electromagnet itself, according to the good of electromagnet manufacture craft
Bad, value changes in 1-10；
B) electromagnet is passed through the calculating of size of current
Different electric currents is loaded on one group of coil, and the magnetic field in different size direction can be generated at the every bit in space；FormulaExpression is providing solenoid current, it is asked to generate the calculation formula of magnetic force size；If on the contrary, needing
To locate to generate the magnetic field for being sized direction on one point, then demand solves needs and loads great electricity respectively on this group of coil
Stream；
(3) magnetic force is generated
Behind step (1) and (2), the mobile tracking platform for acquiring and electromagnet being made to reach specific position and direction has been calculated
The angle of the joint angle in six joints, and need the electric current for being passed through electromagnet；Therefore, in this step, local control calculates
Device generates platform to mobile tracking platform and magnetic force respectively and sends order, allows it to be moved to specified position and generates magnetic force,
The operator for having worn magnetic force sense device just can experience the effect of force feedback；The information of robot can be fed back as a result,
To human hand.
6. the force feedback man-machine interaction method according to claim 5 based on electromagnetic theory and mobile tracking, feature exists
Great electric current is loaded respectively on this group of coil in step (2) needs that solve, and is specifically included：
First, arbitrary current elements can inspire magnetic field in space, the magnetic induction intensity which generates at one point P of space
Size it is directly proportional to the size of current elements, with electric current where place arrive P points position vector and current elements between angle just
String is directly proportional, and square being inversely proportional at a distance from current elements to P points；It is described as with equation：
Wherein, I is size of current, and unit is A；L is path of integration, and dl is the atomic element of elementary current, μ0For space permeability,
Value is 4 π × 10-7Tm/A；R is distance；The unit vector of site to be asked is merely desired to for current source；
FormulaIt is as follows to be write as integrated form：
The size of the magnetic induction intensity generated at one point P of space due to arbitrary current elements is directly proportional to the size of current elements；It can
By infinite more current source arrangement form conducting wire, then in the conducting wire of arbitrary shape excites at the point P of space magnetic field and guiding
Electric current it is directly proportional；It is expressed as with equation：
Wherein,It is integral of the linear coefficient to current path of electric current, i.e.,：
And be vector by electric current excitation electromagnetic field field strength, meet vector superposed principle；There is influencing each other for multiple current elements
Under, the magnetic field in space at a point P is equal to the vector superposed of the electromagnetic field that all current elements excite at this point respectively；Therefore,
For energization solenoid, by each circle coil as an electric current loop；Under more electric current field source environment in three dimensions, the magnetic of a bit
Field intensity and each field source electric current are in a linear relationship；Therefore by formulaIt is ordinary circumstance to expand, and is had：
FormulaIllustrate the linear pass in the magnetic field and field source electric current of a point P in space
System；Wherein, n is the number of current source sources；I1,I2,…,InRespectively the 1st, 2 ..., the size of current of n current source, unit is
A；Bx,By,BzGo out component of the vector sum in the magnetic field inspired on 3 directions, unit T in point P for n current source；Aix,
Aiy,AizComponent of the linear coefficient in magnetic field on 3 directions is generated on spatial point P for i-th of current source；Matrix A is space
Electric current magnetic field linear coefficient matrix on point；
Magnetic field amount Bx,By,BzBy being provided in robot feedback information, electric current magnetic field linear coefficient matrices A can be by formula in spatial pointIt calculates separately and obtains；Therefore with I1,I2,…,InFor unknown number, solve equationThe solution acquired is the electricity being added in required for generating magnetic field on coil
Stream.
7. the force feedback man-machine interaction method according to claim 6 based on electromagnetic theory and mobile tracking, feature exist
In due to fixing the end of solenoid and mobile tracking platform, electromagnet can reach it with mobile tracking platform and want
Position and posture, therefore unreachable region can be eliminated；Mobile tracking platform can change position as manipulator's hand is mobile
Appearance, it is ensured that the relative position that electromagnet is set about with manipulation is fixed, i.e., the two poles of the earth of electromagnet are always towards palm；Therefore it is calculating
In, it need to only consider electromagnetism generated magnetic force in two extreme directions after powered up；If only having used an electromagnet, i.e. electric current
Source number n is set as 1, has：
B=Bz=AzI (24)
It solves：
I=Az -1Bz (25)
Required I is the size of required electrical current.
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