CN108789404A - A kind of serial manipulator kinematic calibration method of view-based access control model - Google Patents

Abstract

The invention provides a vision-based calibrating method for the kinematics parameters of serial robots. The optical axis of the camera is used as a virtual straight line constraint, and a kinematics error model based on the straight line constraint is established; a fixed point is selected as a feature point on a calibration plate fixed at the end of the robot. , use the image-based visual control method to control the movement of the manipulator, so that the feature points reach the optical axis of the camera; according to the joint angle data of the robot, use forward kinematics to calculate the nominal position of the feature points, and calculate the alignment error matrix; through iterative least squares The multiplication algorithm estimates the kinematic parameter error, and calculates the actual kinematic parameter according to the nominal kinematic parameter. The invention uses the optical axis of the camera as a virtual constraint, and can complete the calibration using only the joint angle data of the robot. It is low in cost, easy to operate, and does not require expensive high-precision measuring equipment. It is universal for calibrating series robots and can be widely used Improve the absolute positioning accuracy of the robotic arm in industrial, space, and underwater environments.

Description

A Vision-Based Calibration Method for Kinematics Parameters of Serial Robots

technical field

The invention relates to a vision-based calibrating method for kinematics parameters of serial robots, belonging to the field of robot calibrating.

Background technique

As robots are more and more used in tasks such as assembly, surgery, and collaboration, there are increasingly higher requirements for the positioning accuracy of the robot's end. At present, the position and attitude errors of the robot end cannot be directly measured, and are usually calculated indirectly by using kinematic models and joint angle data. Due to the influence of manufacturing tolerances, wear, transmission errors, installation position, environmental changes and other factors, there are deviations between the actual kinematic parameters in the robot model and their nominal values. If the nominal kinematic parameters are used to calculate the end pose of the robot, it will lead to The absolute localization accuracy of the end pose is reduced. In order to improve the absolute positioning accuracy of the robot, the kinematic parameters of the robot must be calibrated effectively, which is also one of the difficulties in the field of robotics research.

Usually, high-precision measuring equipment is used in the robot calibration algorithm to measure the actual pose of the robot end, but such measuring instruments are very expensive and the calibration process is very complicated, which requires high technical requirements for installation, debugging and measurement process. Vision-based calibration methods usually use the camera as a measurement tool to measure the actual end pose, and the camera field of view and camera parameter errors have a great impact on the calibration results of kinematic parameters. In order to avoid the use of high-precision measurement equipment, use a low-cost, easy-to-operate calibration method, and reduce the impact of measurement equipment on the calibration results, it is necessary to improve the absolute positioning accuracy of robots in various application scenarios.

The method involved in the invention solves the problem of low positioning accuracy at the end of the robot by defining the optical axis of the camera as a virtual straight line constraint for a typical six-degree-of-freedom industrial robot arm. The vision-based calibrating method of kinematic parameters of tandem manipulator has important reference significance for improving the absolute positioning accuracy of tandem manipulator, and can be directly applied to the calibration of kinematic parameters of tandem manipulator.

Contents of the invention

The purpose of the present invention is to provide a vision-based method for calibrating the kinematics parameters of serial robots in order to realize the calibration of the kinematics parameters of the robot based on the virtual constraints of the camera optical axis.

The object of the present invention is achieved like this: step is as follows:

Step 1: Use the camera optical axis as a virtual straight line constraint, and establish a kinematic error model based on the straight line constraint;

Step 2: Select a fixed point on the calibration plate fixed at the end of the robot as a feature point, and use an image-based visual control method to control the movement of the manipulator so that the feature point reaches the optical axis of the camera;

Step 3: According to the joint angle data of the robot, calculate the nominal position of the feature point based on the forward kinematics model, and calculate the position alignment error matrix;

Step 4: Estimate the error of the kinematic parameters by the iterative least squares algorithm, calculate the actual kinematic parameters according to the nominal kinematic parameters, and complete the calibration of the kinematic parameters of the tandem robot.

The present invention also includes such structural features:

1. The establishment of the kinematic error model described in step 1 is specifically:

(1) Based on the improved DH method, the kinematics model of the tandem robot is established, and the transformation matrix from the robot base coordinates to the end effector is obtained;

(2) Establish the kinematics error model of the serial robot, and obtain the end pose error vector Error vector with kinematic parameters The linear relationship between , where ΔP _e and ΔR _e represent the tiny translation and rotation errors at the end of the robot, respectively;

(3) Taking the camera optical axis as a virtual straight line constraint, an error model based on the virtual straight line constraint is established, and the alignment error matrix E and the kinematic parameter error vector are obtained The relationship between.

2. The image-based visual control described in step 2 is specifically:

(1) Install a calibration board at the end of the robot, select a feature point on the calibration board, and the calibration board is completely in the field of view of the camera;

(2) The image-based visual control method consists of an image feature outer ring and a robot control inner ring. The expected image feature is that the feature point reaches the optical axis of the camera. According to the deviation between the expected image feature and the current image feature collected by the camera, The image coordinates are deviated by the end pose adjustment strategy Converted to the deviation at the end of the robot

(3) According to the end pose deviation of the robot Calculate the desired pose at the end, and control the robot to reach the desired pose through the robot control inner loop.

3. The calculation of the position alignment error matrix described in step 3 is as follows:

(1) After the feature point reaches the optical axis of the camera, record the joint angle of the robot at this time, and calculate the nominal position of the robot end based on the forward kinematics model

(2) Control the movement of the robot so that the feature points arrive at multiple positions on the optical axis in sequence, and calculate the nominal position of the end of the robot at each position;

(3) Select multiple optical axis vectors for measurement, the feature points move to multiple positions on each optical axis respectively, and calculate the position alignment error matrix E according to the nominal position of the end of the mechanical arm at each position:

E ^(i,j,k) ＝[μ _k ×](v ^(j,k) -v ^(i,k) )

Where: p is the number of points on each optical axis, q is the number of optical axes, μ _k is the vector of the optical axis, v ^(i,k) and v ^(j,k) are points and The distance to the constraint vector μ _k .

4. The kinematic parameter identification described in step 4 is specifically:

(1) According to the nominal position of the feature point at each position on the optical axis, use the least square method to fit the optical axis vector μ _k ;

(2) Based on the kinematic error model, use the iterative least square method to solve the kinematic parameter error and calculate the actual kinematic parameters

Compared with the prior art, the beneficial effect of the present invention is: the present invention uses the camera optical axis as a virtual linear constraint to calibrate the kinematic parameters of the series robot, and only uses the optical axis of the camera and the joint angle data of the mechanical arm to complete the calibration , without other expensive high-precision measuring instruments or specific calibration equipment, low cost and easy to operate. The established kinematic error model based on linear constraints is robust to low camera depth measurement accuracy. Except for the image coordinates of the center point of the camera optical axis, no other camera parameters need to be calibrated, which reduces the impact of camera parameter errors on kinematic parameters. impact on calibration results. It has important reference significance for improving the absolute positioning accuracy of serial manipulators, and can be directly applied to the calibration of kinematic parameters of serial manipulators in various fields.

Description of drawings

Fig. 1 is a schematic diagram of the position of feature points on the calibration plate of the present invention;

Fig. 2 is a schematic diagram of the image-based visual control method of the present invention;

Fig. 3 is the visual control block diagram based on image of the present invention;

Fig. 4 is a position diagram of the feature points of the present invention on the optical axis.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

The invention provides a vision-based calibrating method for kinematics parameters of serial robots. Aiming at the problem that the absolute positioning accuracy of robots is relatively low, and the positioning accuracy of robots is required to be higher and higher in more and more application fields, a calibration method for robot kinematic parameters is proposed; in addition, for the current robot kinematic parameter calibration The method requires expensive high-precision measuring instruments or specific calibration equipment, and the calibration results are affected by the measuring instruments. A vision-based kinematic parameter calibration method is designed. First, the camera optical axis is used as a virtual linear constraint, and on the basis of using the improved DH method to establish the kinematics model of the robot, a kinematics error model based on the linear constraint is established; then, a fixed calibration plate is selected on the end of the robot. Points are used as feature points, and the image-based visual control method is used to control the movement of the manipulator, so that the feature points reach the optical axis of the camera, select multiple optical axes, and make the feature points sequentially reach multiple optical axes on each optical axis. Position, record the joint angle of the robot at each position; finally, according to the joint angle data of the robot, use forward kinematics to calculate the nominal position of the feature point, calculate the alignment error matrix, and estimate it by iterative least squares algorithm based on the kinematic error model Kinematic parameter error, calculate the actual kinematic parameters according to the nominal kinematic parameters. The invention uses the optical axis of the camera as a virtual constraint, and can complete the calibration using only the joint angle data of the robot. It has the characteristics of low cost and easy operation, does not require expensive high-precision measuring equipment, and has versatility for calibrating series robots. It is widely used in industrial, space, and underwater environments to improve the absolute positioning accuracy of robotic arms.

The present invention adopts following technical scheme:

A vision-based calibrating method for kinematics parameters of serial robots includes establishment of a kinematics error model, image-based vision control, position alignment error matrix calculation, and kinematics parameter identification. in:

Step 1: Use the camera optical axis as a virtual straight line constraint, and establish a kinematic error model based on the straight line constraint;

Step 2: Select a fixed point on the calibration plate fixed at the end of the robot as a feature point, and use an image-based visual control method to control the movement of the manipulator so that the feature point reaches the optical axis of the camera;

Step 3: According to the joint angle data of the robot, use forward kinematics to calculate the nominal position of the feature point, and calculate the position alignment error matrix;

Step 4: Estimate the error of the kinematic parameters by the iterative least squares algorithm, calculate the actual kinematic parameters according to the nominal kinematic parameters, and complete the calibration of the kinematic parameters of the tandem robot.

The establishment of the kinematic error model in step 1 is specifically:

(1) Based on the improved DH method, the kinematics model of the tandem robot is established, and the transformation matrix from the robot base coordinates to the end effector is obtained;

(2) Establish the kinematics error model of the serial robot, and obtain the end pose error vector Error vector with kinematic parameters The linear relationship between , where ΔP _e and ΔR _e represent the tiny translation and rotation errors at the end of the robot, respectively;

(3) Taking the camera optical axis as a virtual straight line constraint, an error model based on the virtual straight line constraint is established, and the alignment error matrix E and the kinematic parameter error vector are obtained The relationship between.

The image-based visual control in step 2 is specifically:

(1) Install a calibration board at the end of the robot, select a feature point on the calibration board, and the calibration board is completely in the field of view of the camera;

(2) The image-based visual control method consists of an image feature outer ring and a robot control inner ring. The expected image feature is that the feature point reaches the optical axis of the camera. According to the deviation between the expected image feature and the current image feature collected by the camera, The image coordinates are deviated by the end pose adjustment strategy Converted to the deviation at the end of the robot

(3) According to the end pose deviation of the robot Calculate the desired pose at the end, and control the robot to reach the desired pose through the robot control inner loop.

The calculation of the position alignment error matrix in step 3 is as follows:

(1) After the feature point reaches the optical axis of the camera, record the joint angle of the robot at this time;

(2) Control the movement of the robot so that the feature points reach multiple positions on the optical axis in sequence, and calculate the nominal position of the end of the robot at each position according to the joint angle

(3) Select multiple optical axis vectors for measurement, and move the feature points to multiple positions on each optical axis, and calculate the alignment error matrix E according to the nominal position of the end of the mechanical arm at each position:

E(i,j,k)＝[μ _k ×](v ^(j,k) -v ^(i,k) )

Among them, p is the number of points on each optical axis, q is the number of optical axes, μ _k is the optical axis vector, v ^(i,k) and v ^(j,k) are points and The distance to the constraint vector μ _k .

The identification of kinematic parameters in step 4 is as follows:

(1) According to the nominal position of the feature point at each position on the optical axis, use the least square method to fit the optical axis vector μ _k ;

(2) Based on the kinematic error model, use the iterative least square method to solve the kinematic parameter error and calculate the actual kinematic parameters

A specific embodiment of the present invention is provided below in conjunction with specific numerical values:

(1) Establish a kinematic error model

Define the connecting rod parameter vector as: vector of parameters for the link approximately parallel to the previous joint axis Parameter vectors for other linkages Among them, a _i , d _i , α _i , θ _i , and β _i are the kinematic parameters of the i-th (i=1,2,3,4,5,6) connecting rod, which are respectively the length of the connecting rod and the length of the connecting rod Offset, Link Angle, Joint Angle, and Link Angle Parallel to Joint Axis.

Assume that the actual kinematic parameter vector of the robot is Its nominal value is Kinematic parameter error vector Based on the improved DH model, the robot kinematics error model can be obtained:

Among them, ΔP _e and ΔR _e represent the tiny translation and rotation errors of the robot end, respectively, and are the error Jacobian matrices with respect to position and attitude, respectively.

Define the k-th optical axis constraint vector as μ _k , let the i-th actual position of the feature point on the optical axis be P _e ^(i,k) , and the corresponding joint angle of the robot be θ _e ^(i,k) . The nominal position of the feature point calculated according to the nominal parameters of kinematics is The difference between the nominal position and the actual position of the feature point is:

Among them, ⁰ R ₆ ′ is the nominal attitude transformation matrix from the base to the end of the manipulator.

See Figure 1, is the coordinate origin of the camera, and is the actual position of the feature point on the optical axis vector μ _k , and is the corresponding nominal position, P _e ^(i,k) and Respectively expressed as:

Among them, s ^{(i, k)} is the point P _e ^{(i, k)} to the origin of the camera coordinates vertical distance of ; s′ ^(i,k) is the point to the origin of the camera coordinates The vertical distance of , v ^(i,k) is the point The distance to the constraint vector μ _k .

Define the operator [μ _k ×] as: Obviously [μ _k ×]μ _k =0. The difference between the nominal position and the actual position of the feature point is obtained by transformation:

Substitute two different positions P _e ^(i,k) and P _e ^(j,k) on the virtual constraint into the equation respectively, and make difference between the two equations to get:

Define E ^(i,j,k) as the alignment error, is the relative alignment error Jacobian matrix:

E ^(i,j,k) ＝[μ _k ×](v ^(j,k) -v ^(i,k) )

get Select q optical axes for measurement, move the feature points to p positions on each optical axis respectively, and construct the position alignment error matrix E and regression matrix Φ:

Get the solution kinematic parameter error vector The kinematic error model for :

(2) Image-based visual control

Referring to Figure 2, the feature point on the calibration plate at the end of the robot is F _p , the distance between the current position of the feature point P _f and the optical axis μ _k is d, the image coordinates of the feature point are (u _f , v _f ), and the center point of the optical axis The image coordinates of are (u ₀ , v ₀ ), the purpose of visual control is to make P _f move to the position point P′ _f on the optical axis, at this time d→0, u _f →u ₀ , v _f →v ₀ .

Referring to Fig. 3, the image-based visual control block diagram is composed of the image feature outer loop and the robot position control inner loop. The control goal is to make the image coordinates (u _f , v _f ) of the feature points and the image coordinates (u ₀ ,v ₀ ) coincide, the current image collected by the camera is used as visual feedback, the deviation between the current actual coordinates of the feature points in the image coordinates and the expected coordinates is (u _f -u ₀ ,v _f -v ₀ ), adjusted according to the end pose The strategy converts the image coordinate deviation into the deviation of the end of the manipulator in the base coordinate system, and realizes the transformation from the image space deviation to the Cartesian space deviation. In the inner loop of robot control, the expected pose is calculated according to the feedback of the end pose deviation of the robot, the expected joint angle is calculated according to inverse kinematics, and the joint position controller of the robot is used to control the robot to move to the desired position and attitude. Among them, in the terminal pose adjustment strategy, the conversion matrix from image deviation to Cartesian space deviation is:

in, is the deviation between the actual position and the expected position of the feature point in the base coordinate system, is the rotation matrix from the camera coordinate system to the robot base coordinate system, is the position deviation of the feature point in the camera coordinate system, which can be calculated according to the camera model, (u ₀ , v ₀ ) can be obtained through camera calibration, and k _x , _ky are constant coefficients.

In the position control inner loop, due to kinematic parameter errors, the manipulator cannot be moved to the desired position according to inverse kinematics. It is necessary to control the manipulator to move in small increments, so that the feature point gradually approaches the optical axis until the feature point The distance from the optical axis reaches the acceptable error range. Assuming k is a normal number less than 1, the actual movement increment at the end of the mechanical arm is:

(3) Position alignment error matrix calculation

Referring to Figure 4, the feature points arrive at multiple positions on the optical axis μ _k in turn, record the joint angle θ of the robot at each position, and calculate the nominal position of the feature points in the base coordinate system based on the forward kinematics model of the robot is the element in the transformation matrix ⁰ T _n from the base coordinate system of the robot to the end coordinate system, where:

Among them, n is the number of connecting rods of the robot, ^i-1 T _i is the transformation matrix between the i-1 coordinate system and the i coordinate system, for the connecting rod whose joint axis is approximately parallel to the previous joint axis:

The transformation matrix ^i-1 T _i of other connecting rods is:

Select multiple optical axis vectors, and the feature points arrive at multiple position points on each optical axis in turn, according to the calculated nominal position of the feature point at each position Compute the position alignment error matrix E.

(4) Identification of kinematic parameters

According to the calculated nominal position of the feature point on an optical axis The optical axis vector μ _k in the error model is obtained by fitting with the least square method. Assuming that the nominal value coordinates of position i (i≤s) on the kth optical axis are (x _i , y _i , z _i ), the straight line equation of optical axis k is:

Among them, the parameters x ₀ , y ₀ , m, n are:

According to the regression matrix Φ and the measurement matrix E calculated above, the error vector of the kinematic parameters is estimated using the iterative least squares method based on the error model Estimated value at iteration t for:

Among them, Φ(t) and E(t) are updated for each iteration respectively The post-calculated regression matrix and measurement matrix, λ(t) is the penalty factor:

Wherein, h is usually a constant between 2 and 10, and λ(0) is a constant between 0.001 and 0.1.

According to the estimated kinematic parameter error of the tandem robot Calculation of actual kinematic parameters

In summary, the present invention belongs to the field of robot calibration, and relates to a vision-based calibrating method for kinematic parameters of series robots. The invention includes: using the optical axis of the camera as a virtual straight line constraint, establishing a kinematics error model based on the straight line constraint; selecting a fixed point on a calibration plate fixed at the end of the robot as a feature point, and using an image-based visual control method to control the movement of the mechanical arm , so that the feature point reaches the optical axis of the camera; according to the joint angle data of the robot, the nominal position of the feature point is calculated using forward kinematics, and the alignment error matrix is calculated; the kinematic parameter error is estimated by the iterative least squares algorithm, and according to the nominal motion kinematic parameters to calculate the actual kinematic parameters. The invention uses the optical axis of the camera as a virtual constraint, and can complete the calibration using only the joint angle data of the robot. It has the characteristics of low cost and easy operation, does not require expensive high-precision measuring equipment, and has versatility for calibrating series robots. It is widely used in industrial, space, and underwater environments to improve the absolute positioning accuracy of robotic arms.

Claims (5)

1. A serial robot kinematic parameter calibration method based on vision is characterized in that: the method comprises the following steps:

the method comprises the following steps: taking an optical axis of a camera as virtual straight line constraint, and establishing a kinematic error model based on the straight line constraint;

step two: selecting a fixed point on a calibration plate fixed at the tail end of the robot as a characteristic point, and controlling the movement of the mechanical arm by using an image-based visual control method to enable the characteristic point to reach the optical axis of the camera;

step three: calculating the nominal position of the characteristic point based on a positive kinematic model according to the joint angle data of the robot, and calculating a position alignment error matrix;

step four: and estimating the kinematic parameter error by an iterative least square algorithm, and calculating the actual kinematic parameter according to the nominal kinematic parameter to finish the kinematic parameter calibration of the serial robot.

2. The vision-based serial robot kinematic parameter calibration method according to claim 1, characterized in that: the establishing of the kinematic error model in the first step is specifically as follows:

(1) establishing a kinematic model of the serial robot based on an improved DH method to obtain a transformation matrix from a robot base coordinate to an end effector;

(2) establishing a kinematic error model of the serial robot to obtain a terminal pose error vectorAnd kinematic parameter error vectorA linear relationship therebetween, wherein Δ P_eAnd Δ R_eRespectively representing small translation and rotation errors of the tail end of the robot;

(3) using the optical axis of the camera as virtual straight line constraint, establishing an error model based on the virtual straight line constraint to obtain an alignment error matrix E and a kinematic parameter error vectorThe relationship between them.

3. The vision-based serial robot kinematic parameter calibration method according to claim 2, characterized in that: the visual control based on the image in the second step is specifically as follows:

(1) a calibration plate is arranged at the tail end of the robot, a point location characteristic point on the calibration plate is selected, and the calibration plate is completely positioned in the visual field of the camera;

(2) the vision control method based on the image is composed of an image characteristic outer ring and a robot control inner ring, an expected image characteristic is that a characteristic point arrives on an optical axis of a camera, and according to deviation of the expected image characteristic and current image characteristic acquired by the camera, image coordinate deviation is carried out through a terminal pose adjusting strategyInto deviations of the robot ends

(3) According to the terminal pose deviation of the robotAnd calculating the expected pose of the tail end, and controlling the robot to reach the expected pose through the inner ring controlled by the robot.

4. The vision-based serial robot kinematic parameter calibration method according to claim 3, characterized in that: the position alignment error matrix calculation in the third step is specifically as follows:

(1) after the characteristic points reach the optical axis of the camera, the joint angle of the robot at the moment is recorded, and the nominal position of the tail end of the robot is calculated based on the positive kinematics model

(2) Controlling the robot to move, enabling the characteristic points to sequentially reach a plurality of positions on the optical axis, and calculating the nominal position of the tail end of the robot at each position;

(3) selecting a plurality of optical axis vectors for measurement, respectively moving the characteristic points to a plurality of position points on each optical axis, and calculating a position alignment error matrix E according to the nominal position of the tail end of the mechanical arm at each position:

E^(i,j,k)＝[μ_k×](v^(j,k)-v^(i,k))

wherein: p is the number of position points on each optical axis, q is the number of optical axes, mu_kIs an optical axial quantity, v^(i,k)And v^(j,k)Are respectively a pointAndto the constraint vector mu_kThe distance of (c).

5. The vision-based serial robot kinematic parameter calibration method according to claim 4, characterized in that: the kinematic parameter identification in the step four is specifically as follows:

(1) fitting the optical axis vector mu by using a least square method according to the nominal position of the characteristic point at each position on the optical axis_k；

(2) Solving kinematic parameter errors by using an iterative least square method based on a kinematic error modelAnd calculating the actual kinematic parameters