CN106344026A - Portable human joint parameter estimation method based on IMU (inertial measurement unit) - Google Patents

Abstract

The invention provides a portable human joint parameter estimation method based on an IMU (inertial measurement unit) and relates to a human joint parameter estimation method in order to solve the problems of low precision, high price, inconvenient operation, high time consumption and the like in the prior art. The method comprises steps as follows: step one, a human arm is equivalent to be hinged by three rigid bodies including an upper arm, a front arm and a palm through an elbow joint and a wrist joint, and a coordinate system is defined; step two, a position vector of o1 in Fa is analyzed according to kinesiology, and a second-order differential form, shown in the specification, of P<o1><e> is obtained; step three, a position vector of o1 in Fb is analyzed according to kinesiology, and a second-order differential form, shown in the specification, of P<o1><e> is obtained; step four, a kinematic constraint relation, caused by ball joints, of P<o1><a> and P<o1><b> is obtained; step five, an equation set is solved with the least square method, and P<o1><a> and P<o1><b> are obtained; step six, the step two to the step five are executed again, and values of P<o2><b> and P<o2><c> are obtained; step seven, the length of the forearm is calculated. The method is applied to the field of limb measurement.

Description

Portable human synovial method for parameter estimation based on imu

Technical field

The present invention relates to human synovial method for parameter estimation.

Background technology

With scientific and technological development, human body real time kinematics capture systems are widely used in real life.In people It is important that the field locomotor capture systems such as machine interaction, cartoon making, medical rehabilitation, training and medical robot play it Effect.One accurate human skeleton model is analysis and reconstruct human motion is indispensable, and human skeleton parameter is The basis of skeleton pattern.Based on the reconstruct of one side human motion 3-dimensional model needs accurate human skeleton parameter.Another The indoor positioning algorithms based on imu for the aspect also must complete with reference to Forward kinematics on the premise of known human skeleton parameter Indoor positioning.Can additional to people be adapted to it with reference to human skeleton parameter on the basis of existing motion capture system simultaneously Ectoskeleton, helps its motion, can have the patient of obstacle using helping them daily routines can also be arranged on scholar to limbs Strengthen its heavy burden ability of marching with soldier.In human engineering field, the parameter of human skeleton as highly important parameter also by As workplace, equipment, the important references of furniture and dress designing, by being analyzed in conjunction with user to user's matrix parameter The correlation theorys such as experience finally determine the parameters such as the size of product thus improving product competitiveness.Because human synovial center of rotation Below skin, so measurement difficulty is very big, and the measuring method of human parameterss is generally comparatively laborious and cost is higher, institute With a kind of simple and effective human synovial measurement method of parameters of urgent needss.The present invention proposes a kind of portable people based on imu Body limbs length is the method for estimation of joint parameter.

Relation between somatometry parameter is constructed using multiple regression analysis on traditional sense.

Obtain human body limb length in statistics using statistical means, such as limbs are substantially estimated by Human Height Length.Somatometry parameter is estimated based on statistical data using adaptive fuzzy nervous system at present.

The measurement of human synovial parameter is the key link in human motion capture.Joint parameter measuring method is generally permissible It is divided into hand dipping, measured and three kinds of modes of photoelectric measurement using Medical Equipment.

Hand dipping mode needs to carry out under corresponding expert instructs, and carries out repeated measure to it and hardly result in phase Same result, not only contains systematic error and further comprises the incidental error being brought by operator in data.Skin and flesh Meat soft tissue will also result in and compares large effect for the degree of accuracy of result.

Measuring human synovial parameter using medical imaging technology is also a kind of joint parameter measuring method.Penetrated using gamma Line, ct, dual energy x-ray algoscopy and nmr imaging technique are carrying out joint parameter measurement efficiently and certainty of measurement High.But the cost of these technology is all that comparison is high, take also relatively long, not so convenient in daily life, and its In some rays also can health be caused must affect.

Photo-electric motion capture system measures human body by measuring the position of the labelling point being arranged on limbs and joint Limbs length.These labelling points must be based strictly on human anatomy and be laid.Substantial amounts of labelling point and constantly transmission Data leads to apply photo-electric capturing movement can expend long time and very complicated carrying out human synovial parameter estimation.

A kind of 3d based on the scanner of light image be developed for scan human body surface any through follow-up place Manage and to obtain the joint parameter of human body.This device all carried out experiment in anthropometric dummy and true man, and result degree of accuracy Very high.But the complexity of this system is difficult to imagine, thus for the personal joint parameter economy for measuring whole body and when Between cost be all suitable high.

With the decline of imu volume and price, certainty of measurement and reliability are constantly lifted, and are subject in field of motion capture Everybody favor.The problem carrying out the maximum of capturing movement presence using imu is exactly the side that imu can only measure human body limb Position, acceleration and angular speed, with its fine position that must go to follow the trail of human body limb or an open question.At present Some capturing movement equipment on the market are all mainly to go human synovial parameter is measured by the equipment that other extend out.

Inspired by robot motion model's bearing calibration, American scientist proposes a kind of people based on footprint template The method that body joint parameter is estimated.Footprint template refers to by both feet overlap thus drawing people with the footprint presetting in advance The method of the position of body end limbs.The joint angle in each joint is recorded by imu and then adds the position of known human foot, permissible Set up Forward kinematics equation, thus calculating the length of each limbs of human body.But in order to obtain more accurate joint angle, In advance sensor must be carried out initializing the cause not of uniform size corresponding footprint template of correction work and everyone foot Different, institute is less applicable in daily life in this way.

Content of the invention

The present invention is that have such problems as that precision is low, expensive, operation is not convenient and time-consuming to solve prior art, And the portable human synovial method for parameter estimation based on imu proposing.

Realized according to the following steps based on the portable human synovial method for parameter estimation of imu:

Step one: become to pass through elbow joint and carpal joint hinge by upper arm, forearm and three rigid bodies of palm equivalent for human arm Connect, and define coordinate system；

Step 2: o is passed through by kinesiology's analysis according to step one₁?Position vector, obtainSecond order Differential formWherein saidFor reference frame initial point e to elbow joint point of rotation o₁Position vector；

Step 3: o is passed through by kinesiology's analysis according to step one₁?Position vector, obtainSecond order Differential form

Step 4: obtained according to step 2 and step 3WithThe kinematical constraint relational expression being caused by ball-joint, its Described inRepresent and point to the relative of the elbow joint point of rotation from upper arm sensor coordinate system zero aPosition vector, Represent that the past arm sensor coordinate system zero b points to the relative of the elbow joint point of rotationPosition vector；

Step 5: system of linear equations is set up and with method of least square to solving equations according to step 4, obtainsWith

Step 6: according to o₂?Position vector and o₂?Position vector, re-execute step 2 to step 5, ObtainWithValue；Wherein saidRepresent that the past arm sensor coordinate system zero b points to carpal joint point of rotation o₂Phase RightPosition vector,Represent and point to the relative of the carpal joint point of rotation from palm sensor coordinate system zero cPosition Put vector；

Step 7: obtained according to step 5WithCalculate the length of forearm.

Invention effect:

(1) high precision, error is less than 0.5 centimetre with respect to traditional-handwork metering system, and measurement error is hand dipping 1/3rd.

(2) metering system is simple, takes short.Only imu sensor need to be dressed and do specific action and can be counted in real time by single-chip microcomputer Calculation obtains human synovial parameter.And by medical apparatus and instruments measure human synovial parameter method need human body is scanned and after Continuous analysis took as one week, comparatively speaking substantially reduced time of measuring and operation difficulty.

(3) good portability.Because being estimated to human synovial parameter using microsensor unit.So only needing to wear Wear imu can measure, device is compact portable can be applied in daily life.

(4) cheap.To carry out joint parameter measurement using medical apparatus and instruments, apparatus expense is more than 200,000 yuan, and adopts Carry out whole body human synovial parameter measurement to only need to spend 200 yuan with imu.

For the problems of the prior art, the present invention proposes one kind based on imu sensor but simple and effective human body closes Section measurement method of parameters.This method make use of the kinematical constraint of human synovial generation it is not necessary to understand any human dissection Sensor is carried out wearing and can measure obtaining human synovial parameter by the relevant knowledge learned.Complexity for the user Low.

Brief description

Fig. 1 is human arm schematic diagram；

Fig. 2 is upper arm parameter estimation schematic diagram；

Fig. 3 is to simplify human skeleton model figure；

Fig. 4 is parameter estimation algorithm schematic flow sheet；

Fig. 5 is the estimation difference figure to elbow joint position for the front arm sensor；

Fig. 6 is the estimation difference figure to wrist position for the front arm sensor.

Specific embodiment

Specific embodiment one: as shown in figure 4, included following based on the portable human synovial method for parameter estimation of imu Step:

Ignore the translational motion of human synovial, only consider its rotation.Generally human body can be regarded as by ginglymus and The hinged multi-rigid body structure of ball-joint.By wearing imu sensor assembly on each limbs, melt then in conjunction with sensor Hop algorithm can be obtained by direction, linear acceleration and the angular rate information of this limbs.Then it is calculated human synovial parameter Information.Simplify human skeleton model as shown in Figure 3.

Step one: become to pass through elbow joint and carpal joint hinge by upper arm, forearm and three rigid bodies of palm equivalent for human arm Connect, and define coordinate system；

Step 2: o is passed through by kinesiology's analysis according to step one₁?Position vector, obtainSecond order Differential formWherein saidFor reference frame initial point e to elbow joint point of rotation o₁Position vector；

Step 3: o is passed through by kinesiology's analysis according to step one₁?Position vector, obtainSecond order Differential form

Step 4: obtained according to step 2 and step 3WithThe kinematical constraint relational expression being caused by ball-joint, its Described inRepresent and point to the relative of the elbow joint point of rotation from upper arm sensor coordinate system zero aPosition vector, Represent that the past arm sensor coordinate system zero b points to the relative of the elbow joint point of rotationPosition vector；

Step 5: system of linear equations is set up and with method of least square to solving equations according to step 4, obtainsWith

Step 6: according to o₂?Position vector and o₂?Position vector, re-execute step 2 to step 5 (i.e. step 6 one is to step 6 four), obtainsWithValue；Wherein saidRepresent the past arm sensor coordinate system coordinate Initial point b points to carpal joint point of rotation o₂RelativelyPosition vector,Represent and point to from palm sensor coordinate system zero c The carpal joint point of rotation relativePosition vector；

Step 6 one: o is passed through by kinesiology's analysis₂?Position vector, obtainSecond-order differential formWherein saidFor reference frame initial point e to carpal joint point of rotation o₂Position vector；

Step 6 two: o is passed through by kinesiology's analysis₂?Position vector, obtainSecond-order differential form

Step 6 three: obtained according to step 6 one and step 6 twoWithClosed by the kinematical constraint that ball-joint causes It is formula, wherein saidRepresent that the past arm sensor coordinate system zero b points to the relative of the carpal joint point of rotationPosition Vector,Represent and point to the relative of the carpal joint point of rotation from palm sensor coordinate system zero cThe vector of position；

Step 6 four: system of linear equations is obtained and with method of least square to solving equations according to step 6 three, obtains With

Step 7: calculated according to step 5WithObtain the length of forearm.

In order to solve, precision in existing human synovial parameter measurement is low, place limits, Financial cost and time cost are higher And operation convenient the problems such as.The invention provides a kind of convenient, high-precision human synovial measurement method of parameters.By On each limbs of human body, imu sensor is installed, records its orientation, linear acceleration and angular rate information, propose in conjunction with the present invention Algorithm can record the parameter information of each limbs.

Specific embodiment two: present embodiment from unlike specific embodiment one: defined in described step one sit Mark system particularly as follows:

To represent upper arm, forearm and palm with a, b, c respectively, as shown in figure 1, defining o₁、o₂For elbow joint and carpal Center of rotation；Imu sensor is separately mounted on upper arm, forearm and palm with any direction, in upper arm, forearm and palm Upper arm sensor coordinate system is set up respectively on imu sensorForearm sensor coordinate systemWith palm sensor coordinate systemA, b, c are the initial point of its corresponding coordinate system,For fixing reference frame.Imu sensor can be separately mounted to The optional position of arm, forearm and palm.

Other steps and parameter are identical with specific embodiment one.

Specific embodiment three: present embodiment from unlike specific embodiment one or two: described step 2 obtainsSecond-order differential formParticularly as follows:

Obtained by kinesiology's analysis:

${\stackrel{\&centerdot;\&centerdot;}{p}}_{o_1}^e=r_{ea}(a_a^a+({\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a\left)p_{o_1}^a\right)---\left(1\right)$

Wherein r_eaForWithRelative rotation matrices,For upper arm sensor coordinate origin under its coordinate system Linear acceleration；

The vector product of expression normal vector:

${\widehat{\mathrm{\&omega;}}}_{ea}^a=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_z^a& {\mathrm{\&omega;}}_y^a\\ {\mathrm{\&omega;}}_z^a& 0& -{\mathrm{\&omega;}}_x^a\\ -{\mathrm{\&omega;}}_y^a& {\mathrm{\&omega;}}_x^a& 0\end{array}\right]$

The angular velocity that respectively upper arm sensor records component in the x, y, z-directions；Wherein x, y, z It is to be determined by imu sensor internal gyroscope installation site.

Approximately tried to achieve by its three rank:

${\stackrel{\&centerdot;}{\mathrm{\&omega;}}}_{ea}^a\left(k\right)\&ap;\frac{{\mathrm{\&omega;}}_{ea}^a(k-2\mathrm{\&delta;}t)-8{\mathrm{\&omega;}}_{ea}^a(k-\mathrm{\&delta;}t)+8{\mathrm{\&omega;}}_{ea}^a(k-\mathrm{\&delta;}t)-{\mathrm{\&omega;}}_{ea}^a(k-2\mathrm{\&delta;}t)}{12\mathrm{\&delta;}t}$

The large arm sensor coordinate system that expression k moment measurement obtains is with respect to the angular acceleration of reference frame. In formula, (k-2 △ t) and (k- △ t) represents the moment of measurement.△ t is the time difference between measurement twice, should ensure that △ t here relatively Little.

Other steps and parameter are identical with specific embodiment one or two.

Specific embodiment four: unlike one of present embodiment and specific embodiment one to three: described step 3 In obtainSecond-order differential formParticularly as follows:

${\stackrel{\&centerdot;\&centerdot;}{p}}_{o_1}^e=r_{eb}(a_b^b+({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b\left)p_{o_1}^b\right)---\left(2\right)$

Wherein r_ebForWithRelative rotation matrices,For forearm sensor coordinate system initial point under its coordinate system Linear acceleration；

The vector product of expression normal vector:

${\widehat{\mathrm{\&omega;}}}_{eb}^b=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_z^b& {\mathrm{\&omega;}}_y^b\\ {\mathrm{\&omega;}}_z^b& 0& -{\mathrm{\&omega;}}_x^b\\ -{\mathrm{\&omega;}}_y^b& {\mathrm{\&omega;}}_x^b& 0\end{array}\right]$

The angular velocity that respectively upper arm sensor records component in the x, y, z-directions；

Approximately tried to achieve by its three rank:

${\stackrel{\&centerdot;}{\mathrm{\&omega;}}}_{eb}^b\left(k\right)\&ap;\frac{{\mathrm{\&omega;}}_{eb}^b(k-2\mathrm{\&delta;}t)-8{\mathrm{\&omega;}}_{eb}^b(k-\mathrm{\&delta;}t)+8{\mathrm{\&omega;}}_{eb}^b(k-\mathrm{\&delta;}t)-{\mathrm{\&omega;}}_{eb}^b(k-2\mathrm{\&delta;}t)}{12\mathrm{\&delta;}t}.$

One of other steps and parameter and specific embodiment one to three are identical.

Specific embodiment five: unlike one of present embodiment and specific embodiment one to four: described step 4 Obtained according to step 2 and step 3WithThe kinematical constraint relational expression that caused by ball-joint particularly as follows:

Simultaneous formula (1) and formula (2) obtain constraint equation:

$r_{ea}(a_a^a+({\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a\left)p_{o_1}^a\right)=r_{eb}(a_b^b+({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b\left)p_{o_1}^b\right)---\left(3\right)$

After arrangement:

$({\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a)p_{o_1}^a-r_{ab}({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b)p_{o_1}^b=r_{ab}{a}_b^b-a_a^a---\left(4\right)$

Whereinr_abForWithRelative rotation matrices, angular speedAnd linear acceleration Directly record from imu sensor, r_ea、r_ebCarry out data fusion by the data that imu sensor records to obtain.Formula (4) Describe with regard toWithThe kinematical constraint being caused by ball-joint.

One of other steps and parameter and specific embodiment one to four are identical.

Specific embodiment six: unlike one of present embodiment and specific embodiment one to five: described according to step Rapid five obtain system of linear equations and with method of least square to solving equations, obtainWithDetailed process be:

Formula (4) is reduced to:

$a_{o_1}{x}_{o_1}=b_{o_1}---\left(5\right)$

Wherein

$a_{o_1}=\&lsqb;\begin{array}{cc}{\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a& r_{ab}({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b)\end{array}\&rsqb;$

$x_{o_1}=\&lsqb;\begin{array}{cc}{p}_{o_1}^a& p_{o_1}^b\end{array}\&rsqb;$

$b_{o_1}=r_{ab}{a}_b^b-a_a^a$

System of linear equations is obtained by multiple measurement:

${\tilde{a}}_{o_1}{x}_{o_1}={\tilde{b}}_{o_1}---\left(6\right)$

Assume the n group data that we collect,Record from sensor, ThenThe data being obtained by sensor is through being calculated；

IfColumn vector be nonlinear correlation, then position vectorObtained by Least Square Method；

From linear least square, when equation (6) is overdetermined equation (equation number is more than unknown number number), side Journey does not solve, and now choosesMake its residual sum of squares (RSS) functionValue minimum；

$\widehat{x_{o_1}}=\arg min\left(s\right(x_{o_1}\left)\right)$

RightTwo ends take differential to seek its minima；

${{\tilde{a}}_{o_1}}^t{\tilde{a}}_{o_1}\widehat{x_{o_1}}={{\tilde{a}}_{o_1}}^t{\tilde{b}}_{o_1}$

IfFor nonsingular matrix, thenThere is a unique solution:

$\widehat{x_{o_1}}={\left({{\tilde{a}}_{o_1}}^t{\tilde{a}}_{o_1}\right)}^{-1}{{\tilde{a}}_{o_1}}^t{\tilde{b}}_{o_1}---\left(7\right)$

This algorithm can carry out offline computing using the data of all collections using method of least square as from the foregoing, when The data of collection is more, then finally estimate that the human parameterss obtaining also can be more accurate.

One of other steps and parameter and specific embodiment one to five are identical.

Specific embodiment seven: unlike one of present embodiment and specific embodiment one to six: described step 7 In obtain forearm the detailed process of length be:

As shown in Fig. 2Lower o₁O relatively₂Position vector:

$p_{o_1}^{o_2}=p_{o_1}^b-p_{o_2}^b---\left(8\right)$

So the length of forearm isMould:

$l_b=\left|p_{o_1}^{o_2}\right|---\left(9\right).$

One of other steps and parameter and specific embodiment one to six are identical.

Embodiment one:

In order to obtain human parameterss data, need by sensor, the motion of each limbs of human body and attitude information to be carried out Collection, sensor uses the acceleration of 3 axis accelerometers, 3 axle gyroscopes and each limbs of 3 axle magnetometer measures human bodies, angular speed And Geomagnetism Information.The data obtaining at the skeleton being placed in below skin by sensor in theory is the most accurate, but due to peace Sensor can only be placed in motion and the attitude letter that human skin approximately to obtain skeleton by the limitation of dress mode Breath.In view of the impact of human body soft tissue, there is a relative motion with skeleton in skin, measurement can have certain error. Research shows that laying of sensor should reduce the impact that soft tissue brings as far as possible.Consider mentioned above principle, in person upright's both arms When naturally drooping, the sensor of large arm is placed in the tendon position of triceps brachii and elbow joint junction, little arm sensor is laid In forearm back, the sensor of palm is placed in the back of the hand center.

Keep upright above the waist after placing sensor, large arm does the different speed change circumference fortune of many all radiuses around shoulder joint Dynamic, forearm and palm do the motion of any direction and speed simultaneously.Sensor records multigroup acceleration of large arm, forearm and palm Degree, angular speed and Geomagnetism Information, combine Geomagnetism Information after carrying out low-pass filtering to angular speed and acceleration and adopt Kalman to filter Ripple algorithm estimates the spin matrix r of sensor_ea、r_eb、r_ec, obtain angular acceleration in conjunction with angular speed using three rank approximation methods InformationThen chosen in the data obtaining, finally obtained joint with the kinematical equation of formula (1.1) ConstraintRight It obtains the vector with respect to carpal joint and elbow joint for the zero of sensor b using Least Square Method after being arranged CoordinateWithThen it is calculated the vector that carpal joint is with respect to elbow joint center of rotationOnly need to be to its modulus, you can Obtain the length of human body forearm.Finally by the attitude and the movable information that record each limbs of human body using imu sensor, in conjunction with Kinematical constraint presented herein, by constraint equation and least-squares estimation obtain sensor with respect to the joint point of rotation to Amount, obtains the length between two adjacent segment points of rotation by the combination of multiple equations, using simple and convenient and high precision side Method is very ingenious to solve the problems, such as that the hidden human body limb linear measure longimetry causing of the human synovial point of rotation is difficult.

Using the inventive method, the large arm of one subjects and forearm are measured, obtain forearm sensor coordinate system Initial point b to elbow joint point of rotation o₁With carpal joint point of rotation o₂Position vector then pass through using medical apparatus and instruments to subjects Carry out joint parameter measurement and to carry out error analyses as benchmark.Fig. 5 and Fig. 6 is respectively position vectorWith? Error between the component of three axial directions and benchmark is with sample frequency change curve.The measurement result of upper arm and forearm and mistake Difference is as shown in table 1:

Table 1

Claims (7)

1. the portable human synovial method for parameter estimation based on imu is it is characterised in that described human synovial method for parameter estimation Comprise the following steps:

Step one: equivalent for human arm become by upper arm, forearm and three rigid bodies of palm by elbow joint and carpal joint hinged and Become, and define coordinate system；

Step 2: o is passed through by kinesiology's analysis according to step one₁?Position vector, obtainSecond-order differential FormWherein saidFor reference frame initial point e to elbow joint point of rotation o₁Position vector；

Step 3: o is passed through by kinesiology's analysis according to step one₁?Position vector, obtainSecond-order differential Form

Step 4: obtainWithThe kinematical constraint relational expression being caused by ball-joint, wherein saidRepresent from upper arm sensing Device coordinate system zero a points to the relative of the elbow joint point of rotationPosition vector,Represent the past arm sensor coordinate system Zero b points to the relative of the elbow joint point of rotationPosition vector；

Step 5: system of linear equations is set up and with method of least square to solving equations according to step 4, obtainsWith

Step 6: according to o₂?Position vector and o₂?Position vector, re-execute step 2 to step 5, obtainWithValue；Wherein saidRepresent that the past arm sensor coordinate system zero b points to carpal joint point of rotation o₂RelativelyPosition vector,Represent and point to the relative of the carpal joint point of rotation from palm sensor coordinate system zero cPosition Put vector；

Step 7: obtained according to step 5WithCalculate the length of forearm.

2. the portable human synovial method for parameter estimation based on imu according to claim 1 is it is characterised in that described Coordinate system defined in step one particularly as follows:

To represent upper arm, forearm and palm with a, b, c respectively, to define o₁、o₂For elbow joint and carpal center of rotation；By imu Sensor is separately mounted on upper arm, forearm and palm, sets up upper arm respectively and pass on upper arm, forearm and palm imu sensor Sensor coordinate systemForearm sensor coordinate systemWith palm sensor coordinate systemA, b, c are the former of its corresponding coordinate system Point,For fixing reference frame.

3. the portable human synovial method for parameter estimation based on imu according to claim 2 is it is characterised in that described Step 2 obtainsSecond-order differential formParticularly as follows:

Obtained by kinesiology's analysis:

${\stackrel{\&centerdot;\&centerdot;}{p}}_{o_1}^e=r_{ea}(a_a^a+({\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a\left)p_{o_1}^a\right)---\left(1\right)$

Wherein r_eaForWithRelative rotation matrices,Linear under its coordinate system for upper arm sensor coordinate origin Acceleration；

The vector product of expression normal vector:

${\widehat{\mathrm{\&omega;}}}_{ea}^a=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_z^a& {\mathrm{\&omega;}}_y^a\\ {\mathrm{\&omega;}}_z^a& 0& -{\mathrm{\&omega;}}_x^a\\ -{\mathrm{\&omega;}}_y^a& {\mathrm{\&omega;}}_x^a& 0\end{array}\right]$

The angular velocity that respectively upper arm sensor records component in the x, y, z-directions；

Approximately tried to achieve by its three rank:

${\stackrel{\&centerdot;}{\mathrm{\&omega;}}}_{ea}^a\left(k\right)\&ap;\frac{{\mathrm{\&omega;}}_{ea}^a(k-2\mathrm{\&delta;}t)-8{\mathrm{\&omega;}}_{ea}^a(k-\mathrm{\&delta;}t)+8{\mathrm{\&omega;}}_{ea}^a(k-\mathrm{\&delta;}t)-{\mathrm{\&omega;}}_{ea}^a(k-2\mathrm{\&delta;}t)}{12\mathrm{\&delta;}t}$

WhereinThe large arm sensor coordinate system that expression k moment measurement obtains is with respect to the angular acceleration of reference frame, △ T is the time difference between measurement twice.

4. the portable human synovial method for parameter estimation based on imu according to claim 3 is it is characterised in that described Obtain in step 3Second-order differential formParticularly as follows:

${\stackrel{\&centerdot;\&centerdot;}{p}}_{o_1}^e=r_{eb}(a_b^b+({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b\left)p_{o_1}^b\right)---\left(2\right)$

Wherein r_ebForWithRelative rotation matrices,Linear under its coordinate system for forearm sensor coordinate system initial point Acceleration；

The vector product of expression normal vector:

${\widehat{\mathrm{\&omega;}}}_{eb}^b=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_z^b& {\mathrm{\&omega;}}_y^b\\ {\mathrm{\&omega;}}_z^b& 0& -{\mathrm{\&omega;}}_x^b\\ -{\mathrm{\&omega;}}_y^b& {\mathrm{\&omega;}}_x^b& 0\end{array}\right]$

The angular velocity that respectively upper arm sensor records component in the x, y, z-directions；

Approximately tried to achieve by its three rank:

${\stackrel{\&centerdot;}{\mathrm{\&omega;}}}_{eb}^b\left(k\right)\&ap;\frac{{\mathrm{\&omega;}}_{eb}^b(k-2\mathrm{\&delta;}t)-8{\mathrm{\&omega;}}_{eb}^b(k-\mathrm{\&delta;}t)+8{\mathrm{\&omega;}}_{eb}^b(k-\mathrm{\&delta;}t)-{\mathrm{\&omega;}}_{eb}^b(k-2\mathrm{\&delta;}t)}{12\mathrm{\&delta;}t}.$

5. the portable human synovial method for parameter estimation based on imu according to claim 4 is it is characterised in that described Step 4 obtains according to step 2 and step 3WithThe kinematical constraint relational expression that caused by ball-joint particularly as follows:

Simultaneous formula (1) and formula (2) obtain constraint equation:

$r_{ea}(a_a^a+({\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a\left)p_{o_1}^a\right)=r_{eb}(a_b^b+({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b\left)p_{o_1}^b\right)---\left(3\right)$

After arrangement:

$({\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a)p_{o_1}^a-r_{ab}({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b)p_{o_1}^b=r_{ab}{a}_b^b-a_a^a---\left(4\right)$

Whereinr_abForWithRelative rotation matrices, angular speedAnd linear acceleration From Imu sensor directly records, r_ea、r_ebCarry out data fusion by the data that imu sensor records to obtain.

6. the portable human synovial method for parameter estimation based on imu according to claim 5 is it is characterised in that described System of linear equations is obtained and with method of least square to solving equations according to step 5, obtainsWithDetailed process be:

Formula (4) is reduced to:

$a_{o_1}{x}_{o_1}=b_{o_1}---\left(5\right)$

Wherein

$a_{o_1}=\&lsqb;\begin{array}{cc}{\widehat{\mathrm{\&omega;}}}_{ea}^a{\widehat{\mathrm{\&omega;}}}_{ea}^a\widehat{+}{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{ea}^a& r_{ab}({\widehat{\mathrm{\&omega;}}}_{eb}^b{\widehat{\mathrm{\&omega;}}}_{eb}^b+{\widehat{\stackrel{\&centerdot;}{\mathrm{\&omega;}}}}_{eb}^b)\end{array}\&rsqb;$

$x_{o_1}=\left[\begin{array}{cc}{p}_{o_1}^a& p_{o_1}^b\end{array}\right]$

$b_{o_1}=r_{ab}{a}_b^b-a_a^a$

System of linear equations is obtained by multiple measurement:

${\tilde{a}}_{o_1}{x}_{o_1}={\tilde{b}}_{o_1}---\left(6\right)$

Record from sensor, then The data being obtained by imu sensor is through being calculated；

IfColumn vector be nonlinear correlation, then position vectorObtained by Least Square Method；

From linear least square, when equation (6) is overdetermined equation, equation does not solve, and now choosesMake its residual error Sum of squares functionValue minimum；

$\widehat{x_{o_1}}=\arg min\left(s\right(x_{o_1}\left)\right)$

RightTwo ends take differential to seek its minima；

${{\tilde{a}}_{o_1}}^t{\tilde{a}}_{o_1}\widehat{x_{o_1}}={{\tilde{a}}_{o_1}}^t{\tilde{b}}_{o_1}$

IfFor nonsingular matrix, thenThere is a unique solution:

$\widehat{x_{o_1}}={\left({{\tilde{a}}_{o_1}}^t{\tilde{a}}_{o_1}\right)}^{-1}{{\tilde{a}}_{o_1}}^t{\tilde{b}}_{o_1}---\left(7\right).$

7. the portable human synovial method for parameter estimation based on imu according to claim 6 is it is characterised in that described The detailed process obtaining the length of forearm in step 7 is:

?Lower o₁O relatively₂Position vector:

$p_{o_1}^{o_2}=p_{o_1}^b-p_{o_2}^b---\left(8\right)$

So the length of forearm isMould:

$l_b=\left|p_{o_1}^{o_2}\right|---\left(9\right).$