CN108592950A - A kind of monocular camera and Inertial Measurement Unit are with respect to established angle scaling method - Google Patents
A kind of monocular camera and Inertial Measurement Unit are with respect to established angle scaling method Download PDFInfo
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
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- G—PHYSICS
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
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Abstract
The invention discloses a kind of monocular cameras and Inertial Measurement Unit with respect to established angle scaling method, belongs to field of sensor calibration, includes the following steps：Step 1：Rotation measuring component acquires calibration data；The measurement assembly includes monocular camera and Inertial Measurement Unit；Step 2：Relative attitude information is extracted from the image that monocular camera acquires；Step 3：Installation matrix is solved using nonlinear least square method.It can be avoided because of the calibrated error that absolute reference information measurement error band comes independent of the measurement to absolute reference information using method provided by the present invention；In addition data acquisition time is short in calibration process, and calibration result precision is high, can meet the spacial alignment demand of monocular camera and Inertial Measurement Unit combination configuration in practical applications.
Description
Technical field
The invention belongs to field of sensor calibration, more particularly to the measurement group of a kind of monocular camera and Inertial Measurement Unit
With respect to the scaling method of established angle, the equipment rotation mode being related in calibration process belongs in measuring coordinate system space both in part
Join scaling method outside multisensor.
Background technology
Sensor combinations based on monocular camera and Inertial Measurement Unit (Inertial Measurement Unit, IMU)
It is widely used in fields such as navigation, three-dimensional reconstructions, the IMU is made of three axis accelerometer and three-axis gyroscope.
IMU output bandwidths are big, good to high maneuver tracking, and computational accuracy is high in short-term, it is possible to provide dimensional information, but long-term calculate accumulates mistake
Difference is huge；Accumulated error is not present in the relative movement information obtained by the image information of monocular camera acquisition, and long-time stability are high,
But it is influenced by factors such as Feature Points Matchings, computational accuracy is general, and sample rate is low, and carrier can not carry out effective when doing high motor-driven
Exercise recovery, monocular camera can not provide scale.Two kinds of sensors measure characteristic on exist complementation, by they combine into
Row data fusion can greatly promote system performance.
The data fusion of multisensor first has to solve space-time alignment issues.For spacial alignment, seeking to will not
With under sensor measurement data unification to the same coordinate system, this just needs to seek the relative pose relationship between sensor.For
The combination of monocular camera and IMU, seeks to the opposite established angle for seeking monocular camera coordinate system and IMU carriers system and origin is flat
It moves.
For this problem, there are many scholars to be studied, but it is big be required for relying on absolute reference information come into
Row is weighed, such as introduces gravity measurement to find horizontal plane benchmark, or introducing target etc..When gravity can not be measured accurately or be needed
Want Fast Calibration can not preset target when, these methods will be no longer applicable in.
Invention content
The present invention is directed to by the connected measurement assembly being composed of both monocular camera and IMU, i.e. involved measurement group
Relative position and attitudes vibration between monocular camera and IMU is not present in part in use, or due to opposite position caused by vibrations
It sets and can be ignored with attitudes vibration.
The purpose of the present invention is to solve both IMU and monocular camera coordinate system spaces to mark with respect to established angle without support
The case where determining problem, but being also applied for target simultaneously proposes a kind of opposite established angle calibration side based on monocular camera and IMU
Method, this method, without rigid requirement, the absolute reference target standard of early period are can avoid when needing Fast Calibration for link, together to target
When evaded the calibrated error that the when of measuring inaccurate to absolute references such as target or gravitational vectors brings, be the quick of specific application
Calibration provides implementation.Simultaneously when there are absolute target, this method is equally applicable.
The monocular camera provided by the invention established angle scaling method opposite with IMU is a kind of nonlinear optimization calibration
Method specifically includes following steps：
Step 1：Rotation measuring component acquires calibration data；The measurement assembly includes monocular camera and IMU；
Step 2：Relative attitude information is extracted from the image that monocular camera acquires；
Step 3：Installation matrix is solved using nonlinear least square method, realizes monocular camera and IMU with respect to established angle
Calibration.
The advantage of the invention is that：
(1) equipment needed for is simple, and necessary equipment only includes the measurement assembly and mating of monocular camera and IMU compositions
Data acquisition device and calibrated and calculated platform；
(2) measurement of the scaling method proposed independent of absolute reference information, can save the early-stage preparations time, keep away simultaneously
The calibrated error that absolute reference information measurement error band comes is exempted from；
(3) under specific rotating condition, only very short data acquisition time is needed just to can be calibrated, and so-called specific
Rotation is actually easy to carry out；
(4) cost function used introduces the concept of Lie algebra, and the error term model about rotation perturbation is easy to linear
Change so that conventional Nonlinear Least Squares Method is applicable in；
(5) calibration result precision is high, can meet the spacial alignment of monocular camera and IMU combinations configuration in numerous applications
Demand.
Description of the drawings
Fig. 1 is monocular camera and Inertial Measurement Unit provided by the invention with respect to established angle scaling method flow chart；
The schematic diagram of rotary shaft alternation in rotary course and rotary course when Fig. 2 is monocular camera acquisition image；
Fig. 3 is that handheld camera specifically rotates schematic diagram.
Specific implementation mode
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.
In existing monocular camera and IMU measurement assemblies, the opposite established angle scaling method of the two is needed to absolute reference
Information measures, and these absolute reference information or needs are arranged in advance, or needs to carry out the measurement of degree of precision, before causing
Time phase is long, expense is big, and calibration result is easily influenced by absolute reference information measurement error.It is asked to solve above-mentioned technology
Topic, the present invention propose a kind of opposite established angle nonlinear optimization scaling method only relying on relative attitude measurement, give mark
Determine several rotation modes that process should be taken, and proposes nonlinear least square method and need the several of the cost function minimized
Kind form.
The present invention is a kind of monocular camera and IMU with respect to established angle scaling method, and the purpose is to solve the phase of monocular camera
Spin matrix (or " installation matrix ") of the machine coordinate system relative to the carrier system of IMU.
Due to being related to multiple coordinate systems, first make an explanation to each coordinate system symbol and definition：
(1) i systems：Inertial reference system；
(2) b systems：The connected carrier system with Inertial Measurement Unit (IMU), right-handed system, three axis directions be respectively it is right-under-it is preceding,
The measurement output of gyro is three axial projection's coordinate of b systems；Each instantaneous carrier system is also an inertial system；
(3) c systems：The camera coordinates system being connected with monocular camera, right-handed system, three axis directions be respectively it is right-under-it is preceding；Each
Instantaneous camera coordinates system is also an inertial system；
(4)c1System：The starting instantaneous (initial time is that the first frame image for demarcating acquires the moment) of nominal time section
Camera coordinates system, it is constant in its instantaneous direction of starting, therefore it is an inertial system.
The several points for additionally needing explanation have：The method of the present invention only demarcates relative rotational relationship, is not concerned with origin
Translation；The method of the present invention does not include the time synchronization strategy of data collecting system, it is believed that the time synchronization of different sensors is
Through what is completed；The present invention is to forming the monocular camera of measurement assembly and type selecting, the storage format of data of IMU etc. without hardness
It is specifically designed it is required that not being related to the software and hardware of measurement assembly, circuit etc., sample frequency etc. there are certain requirements；The present invention is not related to
The noise characteristic of each sensor itself is noted, therefore, it is considered that the measurement noise characteristic of gyroscope is that prior calibration is good, zero bias obtain
To effective compensation, the measurement noise in the short time influences integral operation little；This method only focuses on phase between monocular camera and IMU
Calibration to established angle, therefore, it is considered that the internal reference matrix of monocular camera is that prior calibration is good.
The monocular camera and IMU includes the following steps with respect to established angle scaling method, flow as shown in Figure 1：
Step 1：Rotation measuring component acquires calibration data；
The measurement assembly includes monocular camera and IMU；The calibration data of acquisition include the angle speed that gyroscope measures
The image of degree and monocular camera acquisition.Calibration is adopted with Calibration Field selection, measurement assembly rotating manner, data in data acquisition
Collect frequency and acquisition duration should be by following requirement：
(1) Calibration Field selects；
The precision in characteristic point orientation in the image of monocular camera acquisition, will influence the precision of vision measurement attitude algorithm.It is special
The precision of sign point is then determined by the distance of monocular camera resolution ratio, focal length and characteristic point corresponding actual point position to monocular camera
It is fixed.When being demarcated, monocular camera resolution ratio and focal length have all been fixed, therefore can only rely on the selection of Calibration Field to improve
Characteristic point measurement accuracy.
In the case where not considering marginal distortion, it is limited to monocular camera resolution ratio, the corresponding actual point position of characteristic point
Remoter away from monocular camera, azimuthal measurement precision is poorer.And when considering marginal distortion, even apart from closer characteristic point, such as
Fruit is located at the edge of image, and measurement accuracy also can be poor.The above-mentioned measurement characteristic for considering monocular camera, for indoor machine
The focal range (12mm-35mm) and pixel resolution (600 for the monocular camera that people, small drone and mobile phone etc. are often selected
Ten thousand dpi-2000, ten thousand dpi), following guidance program is proposed to Calibration Field selection：
The not notable and scene without mobile object of selection feature rich, easy to identify, illumination variation is demarcated, such as is selected
There is the street in many shops, before the not single building of architectural style, avoids selection texture-free, weak texture or repetition texture more
Scene.The distance of 90% or more the corresponding actual point position of characteristic point to monocular camera should be located at 10m between 20m, and
These corresponding actual points of characteristic point for being in suitable distance are distributed relatively uniform in visual field, and most of features is avoided to concentrate on
One pocket.
(2) measurement assembly rotating manner；
To realize the on-line proving of established angle, the rotation using measurement assembly is needed, by the short time (in one minute)
Vision measurement obtains the estimation of established angle with the otherness that inertia recursion resolves.In rotation process, to realize three-dimensional established angle
Estimation need to design specific scheme of rotation from the ornamental angle of established angle.
The core design principle of scheme of rotation is the rotation occurred around not dead axle, that is, carries out rotary shaft alternation or continuously change
Become rotary shaft to be directed toward, avoids measurement assembly rotary shaft in rotary course from being directed toward fixed or approximate fixed, the rotation of rotary shaft alternation
Schematic diagram as shown in Fig. 2, be shown in figure first around zcAxis rotates, further around xcAxis rotates, finally around ycThe rotary shaft of axis rotation
Alternation, but be not necessarily in real process according to this rotational order.The schematic diagram is it is emphasised that should allow three axis can
Rotary shaft should change in sensitivity to rotation and rotary course.To prevent, image from obscuring or successive frame lacks altogether simultaneously
Depending on characteristic point, during rotary shaft alternation angular velocity of rotation suggestion be no more than 20 °/s, should not be too large, if it is fuzzy existing image occur
As then needing reduction rotating speed to make image clearly.
Qualitatively provide angular velocity of rotation, such as following formula during a kind of rotary shaft alternation met the requirements：
WithThe projection of rotational angular velocity vector three axis of x, y, z under corresponding moment camera system is indicated respectively,
Unit be °/s.π is pi.It is 10s for the period, amplitude ax°/sine curve of s；For the period be 20s, amplitude is
ay°/sine curve of s；It is 20s for the period, amplitude az°/cosine curve of s；T is the time.ax、ayAnd azTake 0.5 °/s.
In the application scenarios of Fast Calibration, actual rotation process is often hand-held carries out, it is impossible to be carried out similar upper
The standard rotation stated.The effect for showing above-mentioned formula is to make qualitative description to the alternation concept of rotary shaft, and to rotating amplitude
Carry out substantially quantitative demonstration.Actual rotating speed can improve, and not obscured as long as principle is the image taken.
Provide a kind of hand-held scheme of rotation of the measurement assembly that actually can perform.It can according to the definition of camera coordinates system (c systems)
Know, X-axis (xc) right, Z axis (z is directed toward by camera photocentrec) be directed toward by camera photocentre before, Y-axis (yc) be directed toward down by camera photocentre.
First by camera alignment Calibration Field center (i.e. zcAxis is substantially aligned with Calibration Field center), while making its xcAxis substantially water
It is flat, ycAxis is pointed generally in plumb line direction.It is as shown in Figure 3 that subsequent handheld camera carries out specific scheme of rotation：Handheld camera into
Row is around yc(observation visual angle is along y for the left and right of axiscAxis direction) rotation, it first turns left, then turn right, eventually passes back to raw bits
It sets, rotation amplitude is no more than 30 ° to avoid Calibration Field completely not in the visual field.Then it carries out around xc(the observation visual angle up and down of axis
For along xcAxis is reversed) rotation, be first rotated up, rotate still further below, eventually pass back to home position, rotation amplitude be no more than 30 ° with
Avoid Calibration Field completely not in the visual field.Then around zcShaft rotation returns to home position in dynamic one week.
(3) data acquiring frequency and acquisition duration；
To ensure that integral accuracy, the data acquiring frequency of gyroscope are not lower than 100Hz.Simultaneously in view of inexpensive inertia
The measurement error of device is larger, and the integral of long period will be so that accumulated error be unacceptable, therefore data acquisition time is unsuitable
It is long, recommend valid data to acquire duration in 10s between 20s.
To keep the consecutive frame that monocular camera acquires image sensitive as possible to significantly rotation, while in shorter acquisition
Interior data volume is enough, and monocular camera picture-taken frequency is recommended in 1Hz between 5Hz.
Image to make monocular camera acquire does not obscure, and shutter speed suggestion is in 10ms or less.
Step 2：Relative attitude information is extracted from the image that monocular camera acquires；
This step will extract relative attitude information, including each image sampling moment in the image acquired from monocular camera
Relative attitude of the camera coordinates system relative to upper image sampling moment camera coordinates system, and each image sampling moment
Relative attitude of the camera coordinates system relative to calibration initial time camera coordinates system, is missed as cost function in optimization processing below
The reference data of poor item.
This method is used without calibration is relied on, as reference without absolute reference system, it is therefore desirable to which selected reference frame is made
To define the benchmark of posture.Such a inertial system is chosen to be used as with reference to coordinate system：It is static relative to inertial space, and sits
Mark the camera coordinates system (c of origin and first frame image capture moment in calibration data (i.e. starting is instantaneous)1System) origin weight
It closes, reference axis and c1The coordinate overlapping of axles of system, in the case where not causing to obscure, it is believed that instantaneous c1System is the reference frame,
Its symbol also takes c1。
(1) consecutive frame Feature Points Matching；
First carry out the Feature Points Matching of the image between consecutive frame.Slightly matched including single frames feature point extraction, characteristic point and
Characteristic point screening after matching etc..
There are many ripe image characteristic point extractions and characteristic point slightly matched method in the prior art, such as
Harris angle points (Harris Corner), SIFT (Scale Invariant Feature Transform), SURF
(Speeded Up Robust Features) and ORB (Oriented FAST and Rotated BRIEF) etc..For needs
The application of Fast Calibration, in the case where not losing precision, should choose arithmetic speed to improve the calculating speed of calibration as possible
Fast feature detection and description, ORB features is based on FAST (Features from Accelerated Segment
Test) feature is improved, and using BRIEF (Binary Robust Independent Elementary Features) two
System description, under the apparent scene of feature, precision and rapidity can be met the requirements.
Individual features and description can be selected to be matched in practical operation according to demand：It needs to may be selected when Fast Calibration
Using ORB features；SIFT or SURF features can be used when needing degree of precision without considering calculating speed.As long as the former is suitable for
The scene for giving rough established angle as that can carry out fine estimation to installation matrix online in some application scenarios, but needs one
A rational initial value, for example, port University of Science and Technology monocular vision inertia odometer plan V SINS.The latter may be only available for disposably marking
It is fixed, but the application scenarios by not having special target, such as introduce the monocular vision ORBSLAM schemes of inertia measurement information.
Characteristic point screening after matching includes rejecting error hiding outlier and characteristic point distribution screening.For thick of characteristic point
With the error hiding outlier in result, rejected using RANSAC (Random Sample Consensus) algorithm of standard.
It rejects in the characteristic point after error hiding outlier, then carries out characteristic point distribution screening, to improve essential matrix computational accuracy, described
Stromal matrix be used for describe two field pictures acquisition the moment camera coordinates system between to pole restriction relation, it can reflect two interframe
Relative pose relationship.The mode that minimum range between characteristic point in restriction image can be used carries out characteristic point distribution screening so that sieve
Characteristic point after choosing is evenly distributed.Meanwhile the characteristic point after the completion of screening should not be close to image border, to reduce pattern distortion shadow
It rings, can be realized by limiting the ranks bound of characteristic point pixel coordinate.
(2) consecutive frame spin matrix calculates；
The essential matrix that adjacent two frame is calculated using the characteristic point after screening, can be used 8 methods or 5 methods are solved.
Then restore monocular camera relative motion from essential matrix.SVD decomposition is carried out to essential matrix, obtains multigroup rotation
Torque battle array R and multigroup unit translational movement v, and using characteristic point should before monocular camera this characteristic from multigroup R and multigroup v
In filter out correct R and v combination.Remember that the spin matrix between -1 frame of kth and kth frame is Rk-1,k, indicate that adjacent interframe rotation is closed
The Direct cosine matrix of system is spin matrix, i.e.,
(3) rotation per frame relative to initial frame is calculated；
To image characteristic point be carried out continuously aforesaid operations can be obtained all adjacent two field pictures camera coordinates systems of description it
Between attitudes vibration spin matrix R1,2、…、Rk-1,k。
Using above-mentioned adjacent two interframe spin matrix, each frame camera coordinates system can be calculated in addition to initial frame relative to first
The spin matrix of beginning frame camera coordinates system, the spin matrix (Direct cosine matrix) for calculating initial frame (the 1st frame) to kth frame calculate public
Formula is as follows：
In formula, Π indicates even to multiply symbol.
Step 3：Installation matrix is solved using nonlinear least square method, realizes monocular camera and IMU with respect to established angle
Calibration；
Next monocular camera is optimized using non-linear least square method relative to the installation matrix of IMU and is asked
Solution.The step include design cost function, nonlinear least square method optimization and it is excellent for different reference frame cost functions
Change the selection of result.
(1) cost function is designed；
The key for carrying out nonlinear optimization is to determine cost function.According to the choosing for the reference frame for considering relative attitude
It selects, the cost function used in the scaling method of proposition is divided into two kinds of fixed reference form and incremental form；In view of solving
It is manifold optimization problem to install matrix, can introduce Lie algebra and make further deformation to cost function.Therefore, cost function will have
Diversified forms, for each reference frame, can be selected its any one corresponding cost function and carry out in actual calculating
Optimization.
1. the cost function of fixed reference form designs；
As the instantaneous c of selection1System is reference frame, when relative attitude is considered with respect to the coordinate system always, cost
The form of function is known as fixed reference form.
The angular speed that all sampling instant gyroscopes measure in calibration process can pass through the c for being derived by the corresponding moment as follows
System is relative to instantaneous c1The angular speed of system：
WhereinThe angular speed that expression gyroscope measures, i.e. b systems are relative to the angular velocity of rotation of inertial system under b systems
Projection；Indicate c1It is projection of the angular velocity of rotation under b systems relative to inertial system；Indicate b systems relative to c1The rotation of system
Projection of the tarnsition velocity under b systems, due to c1System is inertial system, therefore this is always 0；Indicate c systems relative to c1System
Projection of the angular velocity of rotation under b systems；Angular velocity of rotation projection under b system of the b systems relative to c systems is indicated, due to IMU
It is connected always with monocular camera, therefore this is always 0；Indicate c systems relative to c1The angular velocity of rotation of system is under b systems
Projection.Instantaneous c is utilized in the derivation of above formula1System is fixed relative to inertial system, and IMU and monocular camera are connected to install and therefore appoint
The b systems at meaning moment are fixed relative to c systems.
Matrix is installedIt is defined as the Direct cosine matrix to c systems by b systems.The specific rotation mode of the installation matrix is described
Can self-defining, using such as giving a definition in the present invention：B systems and c systems are all made of right-handed system before bottom right, three fix error angle difference
For azimuthal error angle ψ, pitch error angle θ and roll error angle γ, then can be missed by three installations by coordinate system between b systems and c systems
The rotation successively of declinate describes and constructs installation matrix, has the rotation mode by b systems to c systems to be：First around ybAxis rotates ψ, then
Around xbAxis rotates θ, finally around zbAxis rotates γ.Then it can obtainExpression formula it is as follows：
According to above formula, an installation matrix can be calculated in any given one group of fix error angle ψ, θ and γ.Setting one
A installation Matrix Estimation valueThe camera coordinates system that corresponding moment monocular camera can be then carried out using gyro to measure is relatively initial
The resolving of the relative attitude of frame camera coordinates system：
WhereinIndicate c1It is the estimated value to the Direct cosine matrix of c systems；Indicate c systems relative to c1The rotation angle of system
The estimated value of projection of the speed under c systems；Indicate installation Matrix Estimation value；Indicate c systems relative to c1The rotation angle speed of system
The projection under b systems is spent, it is equal to the angular speed that gyroscope measures known to Such analysis Indicate angular speedTo time integral, rotating vector will be obtained；∧ operators indicate to be negated symmetrical matrix by vector；Exp () refers to for matrix
Number mapping, converts antisymmetric matrix to the element of SO (3) (three-dimensional proper orthogonal group).
Matrix is then installedIt can be obtained by enabling following cost function minimums, reality can optional one when calculating：
Wherein, k=1 ..., n indicates that each sampling instant of monocular camera, n indicate sampling sum；Representing matrixTransposition, i.e.,Function eulr () indicates to seek Eulerian angles by Direct cosine matrix；Logm maps log () and indicates
Direct cosine matrix in SO (3) (three-dimensional proper orthogonal group) is transformed intoIn (three-dimensional proper orthogonal group corresponding Lie algebra)
Rotating vector antisymmetric matrix；∨ operators indicate to seek rotating vector by antisymmetric matrix；Function qtn () is indicated by direction cosines
Battle array seeks unit quaternion；Indicate quaternary number multiplication；||·||2Two norm of matrix is sought in expression；I indicates unit matrix.
In practical calculating, according to the selection of referential, however, it is determined that use the cost function of fixed reference form, and rotate not
It will appear unusual influence calculation accuracy, then selecting one in aforementioned four cost function optimizes.
The physical significance of above-mentioned cost function is to be compared with the angular speed that gyroscope measures to project to camera coordinates system product
It branches away, the image that the posture and monocular camera relative to initial camera coordinate system acquire is calculated relative to initial phase
The posture of machine coordinate system.The Direct cosine matrix of each sampling instant, expression is Current camera coordinate system relative to initial camera
The direction cosine matrix of system；The Eulerian angles of each sampling instant, expression is Current camera coordinate system relative to initial camera system
Eulerian angles；The physical significance of each sampling instant rotating vector, expression is Current camera coordinate system relative to initial camera
The direction of the rotation of system, the vector is the direction of rotary shaft, and the size of modulus value indicates the angle of rotation；Each sampling instant
Quaternary number is rotated, expression is that Current camera coordinate system rotates quaternary number (i.e. unit four relative to the normalization of initial camera system
First number).In brief, what each error term investigated at this time is that the camera coordinates system of certain frame shooting time is shot relative to first frame
The posture of the camera coordinates system at moment.
2. the cost function of incremental form designs；
When each error term in cost function only considers the relative attitude variation of adjacent two frame, incremental form can be designed
Cost function.Unified reference frame is not present at this time, when selecting former frame shooting in adjacent two frame in each error term
Reference of the camera coordinates system at quarter as measurement relative attitude.
Between monocular camera acquires in calibration process -1 frame image of kth and kth frame image, the angular speed that gyroscope measures can
By being derived by the c systems at corresponding moment as follows relative to instantaneous ck-1The angular speed of system：
WhereinThe angular speed that expression gyroscope measures, i.e. b systems are relative to the angular velocity of rotation of inertial system under b systems
Projection；Indicate b systems relative to instantaneous ck-1Projection of the angular velocity of rotation of system under b systems,Indicate instantaneous ck-1
It is projection of the angular velocity of rotation under b systems relative to inertial system, due to arbitrarily instantaneous ck-1System is inertial system, therefore this
It is always 0；Indicate c systems relative to instantaneous ck-1Projection of the angular velocity of rotation of system under b systems；Indicate that b systems are opposite
In projection of the angular velocity of rotation under b systems of c systems, since IMU and monocular camera are connected always, this is always 0；
Indicate c systems relative to instantaneous ck-1Projection of the angular velocity of rotation of system under b systems.Instantaneous c is utilized in the derivation of above formulak-1System
It is fixed relative to inertial system, and arbitrary instantaneous b systems are fixed relative to c systems.
One installation Matrix Estimation value of settingThe consecutive frame figure of monocular camera acquisition can be then carried out using gyro to measure
As the resolving of relative attitude between camera coordinates system：
WhereinIndicate instantaneous ck-1It is to instantaneous ckThe estimated value of the Direct cosine matrix of system；Indicate c systems phase
For instantaneous ck-1The estimated value of projection of the angular velocity of rotation of system under c systems；Indicate installation Matrix Estimation value；Table
Show c systems relative to instantaneous ck-1It is projection of the angular velocity of rotation under b systems, it is measured equal to gyroscope known to Such analysis
Value Indicate angular speedTo time integral, rotating vector will be obtained.
Matrix is then installedFollowing cost function minimums can be enabled to obtain, reality can optional one when calculating：
In practical calculating, according to the selection of referential, however, it is determined that use the cost function of incremental form, and rotation will not go out
Existing unusual influence calculation accuracy then selects one in aforementioned four cost function and optimizes.
The physical significance of above-mentioned cost function is to project to camera coordinates system to the angular speed using gyro to measure to integrate out
The each camera sampling instant come is calculated relative to the image that the posture increment and monocular camera of last camera sampling instant acquire
The consecutive frame posture increment gone out is compared.The Direct cosine matrix of each sampling instant, expression is Current camera coordinate system phase
For the direction cosine matrix of previous frame camera coordinates system；The Eulerian angles of each sampling instant, expression is Current camera coordinate
It is the Eulerian angles relative to previous frame camera coordinates system；The physical significance of each sampling instant rotating vector, expression is current
The direction of rotation of the camera coordinates system relative to previous frame camera coordinates system, the vector is the direction of rotary shaft, and modulus value is big
The small angle for indicating rotation；The rotation quaternary number of each sampling instant, expression is Current camera coordinate system relative to previous frame
The normalization rotation quaternary number (i.e. unit quaternion) of camera coordinates system.
3. introducing the cost function design of Lie algebra；
In conclusion cost function either general type or incremental form, the mathematical expression mode of posture all include
Direct cosine matrix, four elements of Eulerian angles, rotating vector and normalization etc..It, can be according in calibration process when actually calculating
The size of rotational steps considers from convenience of nonsingularity, the intuitive of expression and calculating etc., selects suitable generation
Valence function.
It solves and makes cost function minimumThis problem can realize by non-linear least square method, and common non-
It is required for solving Jocobian matrixes in linear least square method.It is noted that installation matrixBelong to SO (3), to addition
It does not close, is not easy to seek Jocobian matrixes, therefore introduce Lie algebra in cost function, be converted in solution procedure
For(3) the solution of rotating vector on, the optimization problem being converted into manifold are replaced in cost function with following formula
Wherein exp () maps for matrix exponetial, converts antisymmetric matrix to the element of (3) SO；θbcIndicate installation matrix
Corresponding rotating vector；∧ operators indicate to be negated symmetrical matrix by vector.The cost of above-mentioned fixed reference form and incremental form
The form variation of function is as follows, and reality can optional one when calculating：
Indicate the angular speed that t moment gyroscope measures.
It is practical to calculate, according to the selection of referential, a fixed reference form and incremental form are first selected respectively
Cost function (if in view of rotation is likely to occur unusual influence calculation accuracy, selects the cost function of representation of Lie algebra), i.e.,
2, which are selected, in above-mentioned eight cost functions optimizes (F11(θbc)~F14(θbc) in selection one；F21(θbc)~F24(θbc)
Middle selection one).
(2) nonlinear least square method optimizes；
Installation matrix is acquired by minimizing one of above-mentioned cost functionIt is a unconfined non-linear least square
Problem solves the problems, such as that the common algorithm includes single order (steepest decline) and the literary Burger-of second order gradient method, gauss-newton method, row
Ma Kuiertefa etc..Wherein row text Burger-Ma Kuiertefa is with its higher robustness in non-linear least square problem solving
In be widely adopted.This method carries out nonlinear optimization using the literary Burger-Ma Kuiertefa of row.
Optimize above-mentioned corresponding cost function Fjq(θbc) (j=1,2, q=1,2,3,4) obtain installation matrix process use
Mathematical formulae is described as follows：
(3) for the selection of different reference frame cost function optimum results
Cost function for different reference frames are respectively adopted optimize as a result, need to select, determine a kind of generation
The result of valence function optimization is final installation matrix.If using a fixed reference form cost function and an incremental form
The Direct cosine matrix that cost function acquires is respectivelyWithThe specific method is as follows：
It will using logm mapping log () and ∨ operatorsWithIt is respectively converted into corresponding established angle
Rotating vectorWith
It asksWithThe absolute value of the difference of modulus value：
Wherein norm () is vectorial modulo operator；Abs () is that signed magnitude arithmetic(al) is asked to accord with；Δ σ is that two rotations are sweared
The absolute value of the difference of modulus value is measured, unit uses degree (°).
When Δ σ is less than certain threshold value (such as taking 0.01 °), it is believed that estimated using the cost function of different reference frames
As a result it approaches,WithIn take any one.
When Δ σ is more than or equal to threshold value, then the estimated result of two kinds of reference frame cost functions is substituted into the two of selection respectively
In a cost function, by taking the cost function for introducing Lie algebra as an example, i.e., seek respectivelyWith
With(m and n appoint in 1~4 takes a value).If judgingAndThen recognize
Estimated result for fixed reference system form cost function is good, and final matrix of installing takesIf judging
AndThen think that the estimated result of incremental form cost function is good, final matrix of installing takes
Then think that this calibration gathered data or other intermediate process errors that resolve are larger when other situations, as a result not adopts, need
It re-scales.
Claims (5)
1. a kind of monocular camera and Inertial Measurement Unit are with respect to established angle scaling method, which is characterized in that specifically include step：
Step 1：Rotation measuring component acquires calibration data；The measurement assembly includes monocular camera and inertia measurement list
Member；The calibration data of acquisition include the image of the angular speed that gyroscope measures and monocular camera acquisition；
Step 2：Relative attitude information is extracted from the image that monocular camera acquires；
Step 3：Installation matrix is solved using nonlinear least square method, realizes monocular camera and the opposite peace of Inertial Measurement Unit
Fill the calibration at angle.
2. monocular camera as described in claim 1 and Inertial Measurement Unit are with respect to established angle scaling method, which is characterized in that step
Rotation measuring component described in rapid one, it is the camera coordinates system being connected with monocular camera to define c systems first, according to determining for c systems
Justice, xcAxis is perpendicularly oriented to the right side, z with monocular camera optical centercBefore axis overlaps direction with monocular camera optical center, ycAxis and monocular camera light
The heart is perpendicularly oriented to down, by monocular camera alignment Calibration Field center, makes xcAxis is horizontal, ycAxis is directed toward plumb line direction, holds single
Mesh camera is carried out around ycThe left-right rotation of axis, first turns left, then turns right, and eventually passes back to home position, and rotational angle is small
In 30 °；Then it carries out around xcRotating upwardly and downwardly for axis, is first rotated up, and rotates still further below, eventually passes back to home position, rotates width
Degree is less than 30 °；Then around zcShaft rotation returns to home position in dynamic one week.
3. monocular camera as described in claim 1 and Inertial Measurement Unit are with respect to established angle scaling method, which is characterized in that institute
The frequency acquisition for stating the angular speed of gyroscope measurement is not less than 100Hz, and data acquire duration in 10s between 20s；The monocular
The frequency acquisition of the image of camera acquisition is in 1Hz between 5Hz, and shutter speed is in 10ms or less.
4. monocular camera as described in claim 1 and Inertial Measurement Unit are with respect to established angle scaling method, which is characterized in that institute
It states step 2 and extracts relative attitude information from the image that monocular camera acquires, include the camera coordinates at each image sampling moment
It is the relative attitude relative to upper image sampling moment camera coordinates system, and the camera coordinates at each image sampling moment
It is the relative attitude relative to calibration initial time camera coordinates system；
Define c1System is the instantaneous camera coordinates system of the starting of nominal time section, constant in its instantaneous direction of starting, therefore it is one
A inertial system；For selected reference frame as the benchmark for defining posture, the reference frame is static relative to inertial space, and
Coordinate origin is overlapped with calibration with the origin for originating instantaneous camera coordinates system in data, the starting of reference axis and nominal time section
The coordinate overlapping of axles of instantaneous camera coordinates system；
(1) consecutive frame Feature Points Matching include single frames feature point extraction, characteristic point slightly match and matching characteristic point screening；
The matching characteristic point screening includes rejecting error hiding outlier and characteristic point distribution screening, rejects error hiding outlier and uses
RANSAC algorithms, characteristic point distribution screening is between limiting characteristic point by the way of minimum range；
(2) consecutive frame spin matrix calculates；
The essential matrix that adjacent two frame is calculated using the characteristic point after screening, decomposes essential matrix, obtains multigroup rotation
Matrix R and multigroup unit translational movement v remembers that the spin matrix between -1 frame of kth and kth frame is Rk-1,k；
(3) rotation per frame relative to initial frame is calculated；
The spin matrix calculation formula of initial frame to kth frame is as follows：
5. monocular camera as described in claim 1 and Inertial Measurement Unit are with respect to established angle scaling method, which is characterized in that institute
Step 3 is stated using nonlinear least square method solution installation matrix to optimize including design cost function, nonlinear least square method
With the selection for different reference frame cost function optimum results；
(1) cost function is designed；
1. the cost function of fixed reference form designs；
It is inertial reference system to define i systems, and the camera coordinates system for selecting the starting of nominal time section instantaneous is reference frame, calibration
The angular speed that all sampling instant gyroscopes measure in the process by being derived by c systems relative to c as follows1The angular speed of system：
WhereinIndicate the angular speed that gyroscope measures, i.e. angular velocity of rotation projection under b system of the b systems relative to inertial system；Indicate c1It is projection of the angular velocity of rotation under b systems relative to inertial system；Indicate b systems relative to c1The rotation angle of system
Projection of the speed under b systems, due to c1System is inertial system；Indicate c systems relative to c1Throwing of the angular velocity of rotation of system under b systems
Shadow；Indicate angular velocity of rotation projection under b system of the b systems relative to c systems；Indicate c systems relative to c1The rotation angle of system
Projection of the speed under b systems, the b systems are the carrier system being connected with Inertial Measurement Unit, and right-handed system, three axis directions are respectively
Right-under-preceding, the measurement output as angular speed of gyro is in three axial projection's coordinate of b systems；Each instantaneous carrier system is also one
Inertial system；
Matrix is installedIt is defined as the Direct cosine matrix to c systems by b systems, three fix error angles are respectively azimuthal error angle ψ, bow
Error angle θ and roll error angle γ are faced upward, by elder generation around ybAxis rotates ψ, further around xbAxis rotates θ, finally around zbAxis rotates γ,'s
Expression formula is as follows：
One installation Matrix Estimation value of setting
Indicate c1It is the estimated value to the Direct cosine matrix of c systems；Indicate c systems relative to c1The angular velocity of rotation of system is in c systems
Under projection estimated value；Indicate installation Matrix Estimation value；Indicate c systems relative to c1The angular velocity of rotation of system is under b systems
Projection,The angular speed measured equal to gyroscopeIndicate angular speedTo time integral, incite somebody to action
To rotating vector；∧ operators indicate to be negated symmetrical matrix by rotating vector；Exp () maps for matrix exponetial, by antisymmetric matrix
It is converted into the element of three-dimensional proper orthogonal group SO (3)；
Matrix is installedIt is obtained by following any cost functions：
Wherein, k=1 ..., n indicates that each sampling instant of monocular camera, n indicate sampling sum；Indicate spin matrixTransposition；Function eulr () indicates to seek Eulerian angles by Direct cosine matrix；Logm maps log () expressions will be three-dimensional
Direct cosine matrix in proper orthogonal group SO (3) is transformed into the rotating vector antisymmetric matrix in so (3)；∨ operators are indicated by anti-
Symmetrical matrix seeks rotating vector；∧ operators indicate to be negated symmetrical matrix by rotating vector；Function qtn () is indicated by Direct cosine matrix
Seek quaternary number；Indicate quaternary number multiplication；||·||2Two norm of matrix is sought in expression；I indicates unit matrix,
2. the cost function of incremental form designs；
Between monocular camera acquires in calibration process -1 frame image of kth and kth frame image, the angular speed that gyroscope measures is by pushing away
Lead to obtain c systems relative to instantaneous ck-1The angular speed of system：
WhereinIndicate the angular speed that gyroscope measures, i.e. angular velocity of rotation projection under b system of the b systems relative to inertial system；Indicate instantaneous ck-1It is projection of the angular velocity of rotation under b systems relative to inertial system；Indicate b systems relative to wink
When ck-1Projection of the angular velocity of rotation of system under b systems, due to arbitrary instantaneous ck-1System is inertial system；Indicate c systems phase
For instantaneous ck-1Projection of the angular velocity of rotation of system under b systems；Indicate b systems relative to c systems angular velocity of rotation in b systems
Under projection,Indicate c systems relative to instantaneous ck-1Projection of the angular velocity of rotation of system under b systems；
One installation Matrix Estimation value of setting
Indicate instantaneous ck-1It is to instantaneous ckThe estimated value of the Direct cosine matrix of system；Indicate c systems relative to instantaneous
Ck-1The estimated value of projection of the angular velocity of rotation of system under c systems；Indicate installation Matrix Estimation value；Indicate c systems phase
For instantaneous ck-1Projection of the angular velocity of rotation of system under b systems；Indicate angular speedTime is accumulated
Point, rotating vector will be obtained；
Matrix is installedIt is obtained by following any cost functions：
3. introducing the cost function design of Lie algebra；
It is enabled in cost function
Wherein exp () maps for matrix exponetial, converts antisymmetric matrix to the element of three-dimensional proper orthogonal group SO (3)；θbcTable
Show installation rotating vector；∧ operators indicate to be negated symmetrical matrix by rotating vector, and the form variation of above-mentioned cost function is as follows,
Indicate the angular speed that t moment gyroscope measurement obtains；
(2) nonlinear least square method optimizes；
Optimize above-mentioned corresponding cost function Fjq(θbc) obtain installation matrix process it is as follows：
Wherein, j=1,2, q=1,2,3,4；
(3) for the selection of different reference frame cost function optimum results；
Determine that a kind of result of cost function optimization is final installation matrix, if using a fixed reference form cost function
The Direct cosine matrix acquired with an incremental form cost function is respectivelyWithThe specific method is as follows：
It will using logm mapping log () and ∨ operatorsWithIt is respectively converted into corresponding established angle rotation
VectorWith
It asksWithThe absolute value of the difference of modulus value：
Wherein norm () is vectorial modulo operator；Abs () is that signed magnitude arithmetic(al) is asked to accord with；
When Δ σ is less than threshold value, it is believed that it is close using the cost function estimated result of different reference frames,With
In take any one；
When Δ σ is more than or equal to threshold value, then the estimated result of two kinds of reference frame cost functions is substituted into the two of selection respectively
In a cost function, by taking the cost function for introducing Lie algebra as an example, i.e., seek respectivelyWith
WithM and n appoints in 1~4 takes a value；If judgingAndThen recognize
Estimated result for fixed reference system form cost function is good, and final matrix of installing takesIf judging
AndThen think that the estimated result of incremental form cost function is good, final matrix of installing takes
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