CN107680133A - A kind of mobile robot visual SLAM methods based on improvement closed loop detection algorithm - Google Patents

A kind of mobile robot visual SLAM methods based on improvement closed loop detection algorithm Download PDF

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CN107680133A
CN107680133A CN201710839954.5A CN201710839954A CN107680133A CN 107680133 A CN107680133 A CN 107680133A CN 201710839954 A CN201710839954 A CN 201710839954A CN 107680133 A CN107680133 A CN 107680133A
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胡章芳
鲍合章
罗元
孙林
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Chongqing University of Post and Telecommunications
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Abstract

The present invention is claimed a kind of based on the mobile robot visual SLAM methods for improving closed loop detection algorithm, including step：S1, Kinect is demarcated using Zhang Dingyou standardizations；S2, ORB feature extractions are carried out to the RGB image of acquisition, and characteristic matching is carried out using FLANN；S3, delete error hiding；Match point space coordinates is obtained, interframe pose conversion (R, t) is then estimated using PnP algorithms；S4, the pose conversion to be asked for PnP carry out structureless iteration optimization.S5, picture frame are pre-processed, and image is described by vision bag of words, and carry out images match with an improved similarity score matching process, so as to obtain candidate's closed loop；Filter out correct closed loop.S6, use and the figure optimization method of core is adjusted to boundling to be optimized to pose and road sign, pass through continuous iteration optimization and obtain more accurate camera pose and road sign.The present invention can obtain more accurate pose estimation and preferably three-dimensional reconstruction effect under environment indoors.

Description

Mobile robot vision SLAM method based on improved closed-loop detection algorithm
Technical Field
The invention belongs to the field of mobile robot navigation, and particularly relates to a synchronous positioning and map building method based on vision.
Background
Meanwhile, positioning and Mapping (SLAM) is a key technology for realizing complete autonomous movement of a robot, wherein a sensor carried by the robot is used for acquiring information of an environment where the robot is located, estimating the pose of the robot and constructing an environment map. Meanwhile, the visual SALM is also the key of the current VR technology, and has wide application prospect in the future virtual reality industry.
The visual sensor can acquire rich image information similar to human eye perception information, and the rich environment information provides more details for environment map construction, so that a better map construction effect can be realized. Great progress has been made in visual SLAM. In 2007, Klein et al proposed a PTAM that implemented the parallelization of trace and map building and was the first solution to use nonlinear optimization as the back-end; the Endres proposed an RGBD-SLAM based on a depth camera in 2014, which integrates the technologies of image characteristics, closed-loop detection, point cloud and the like, and realizes three-dimensional mapping of an indoor scene; in 2015, Raul Mur-Artal and the like are based on a PTAM framework, so that functions of map initialization and closed-loop detection are added, selection of key frames is optimized, and the like, and good effects are achieved in processing speed and map precision.
Although visual SLAM has achieved good processing speed and map accuracy over the past few years, there is still room for improvement because of its stringent requirements for processing speed and map accuracy. The mobile robot can carry out long-time running to bring accumulated errors, which can cause the problem of inconsistency of positioning and map building, and the introduction of closed-loop detection can reduce the accumulated errors. However, the traditional closed-loop detection algorithm has low closed-loop detection efficiency and low accuracy. Therefore, an improved closed-loop detection algorithm is introduced to improve the accuracy and efficiency of closed-loop detection. Meanwhile, in order to reduce system errors, a nonlinear optimization method is adopted to carry out local optimization on the front-end estimation pose, and then global optimization is carried out on the closed-loop information and the front-end estimation information. Therefore, the provided mobile robot vision synchronous positioning and map building method based on the improved closed-loop detection algorithm can meet the real-time requirement and can obtain more accurate pose estimation and three-dimensional reconstruction with better effect.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A mobile robot vision SLAM method based on an improved closed-loop detection algorithm and capable of estimating pose more accurately is provided. The technical scheme of the invention is as follows: a mobile robot vision SLAM method based on an improved closed-loop detection algorithm comprises the following steps:
s1, calibrating the Kinect by using a Zhang friend calibration method to obtain camera internal parameters;
s2, carrying out ORB feature extraction on the obtained RGB image, and carrying out feature matching by adopting a FLANN (fast approximate nearest neighbor) algorithm, wherein the feature matching comprises a correct matching result and a mismatching result;
s3, deleting the mismatching by using RANSAC (random sample consensus) according to the mismatching result of the step S2; acquiring spatial coordinates of matching points through a Kinect camera model, and estimating pose transformation (R, t) between frames by adopting a PnP (n-point perspective problem) algorithm;
s4, carrying out structureless iterative optimization on the pose transformation obtained by adopting the PnP algorithm in the step S3;
s5, preprocessing the image frames obtained in the step S2, describing the images through visual word bags, matching the images by using an improved similarity score matching method, and obtaining matching which is more consistent with the actual similarity between the images so as to obtain candidate closed loops;
and S6, optimizing the pose and the landmark by adopting a graph optimization method taking cluster adjustment BA as a core, and acquiring more accurate camera pose and landmark through continuous iterative optimization.
Further, the ORB feature extraction step in step S2 is:
firstly, performing FAST corner extraction on an RGB image, and enabling ORB feature points to have invariance of scale and rotation by utilizing an image pyramid construction method and a gray centroid method;
thirdly, binary description is carried out on the image around the feature point extracted in the previous step through BRIEF.
Further, in step S3, the spatial coordinates of the matching points are obtained through a Kinect camera model, and the spatial coordinate solving method includes:
zo＝z
if the depth value corresponding to the pixel coordinate (u, v) in the image obtained by the Kinect is z, the space coordinate (x) can be obtained according to the Kinect camera modelo,yo,zo)。
Further, the step of optimizing the pose transformation obtained by PnP in step S4 is:
firstly, establishing an optimization problem by minimizing a reprojection error by taking a camera pose as an optimization variable;
then, the original PnP function is optimized by calling g2o with the PnP value as an initial value.
Further, the step S5 of detecting the candidate closed loop includes:
firstly, preprocessing an acquired image, acquiring an image similarity score by using the following similarity calculation function, and discarding a current frame when the score is greater than a set threshold value; if not, the current frame represents a new scene for participating in closed loop detection;
wherein, VlWeight vector, V, representing the image of the previous framecRepresents a weighting vector of the current frame, and the H value represents image similarity.
Next, describing the image by adopting a hierarchical K-means clustering algorithm; then adopting the following improved single-node score function to carry out image similarity score matching;
the repeated accumulation of similarity can be avoided by using a top-down similarity increment method, and the l-th layer similarity score increment is defined as:
defining the matching kernel as:
wherein, ηlIndicating the matching strength factor of the l-th layer.
Further, the function of the improved similarity score is defined as:
based on the new single-node similarity score function proposed by the above formula, the similarity score at the l-th layer is:
wherein,represents the score of image X on the ith node of the ith level of the tree,represents the score of image Y on the ith node of the l-th level of the tree.
Further, the optimizing the pose and the landmark by using the graph optimizing method with the cluster adjustment BA as the core specifically comprises the following steps: firstly, constructing a cost function of pose and whole road sign, namely an objective function, as follows:
e＝z-h(ξ,p)
ξ is a lie algebra corresponding to the camera pose (external parameters (R, t)), p is a three-dimensional coordinate point of the road sign, z is pixel coordinate data observed by Kinect, e is an observation error, z is an observation errorijShown in a seated position ξiWhere observation road sign pjGenerated pixel coordinate data;
this least squares method is then solved, defining the independent variables as all the variables to be optimized:
x＝[ξ1,...,ξm,p1,...,pn]
and continuously searching a descending direction △ x to find the optimal solution of the cost function according to the idea of nonlinear optimization, wherein when an increment is given to the independent variable, the objective function is changed into:
wherein, Fij、EijRespectively representing the partial derivative of the camera pose in the current state and the partial derivative of the position of the landmark point;
the following incremental equations are finally solved:
h △ x is g, g being a constant equivalent.
Wherein,
H＝JTJ+λI
j ═ F E, and matrices E and F represent the derivatives of the global objective function to the global variable.
The invention has the following advantages and beneficial effects:
the invention provides a mobile robot vision SLAM method based on an improved closed-loop detection algorithm, which uses ORB characteristics to improve the speed of characteristic extraction and matching and improve the real-time performance of a system; the closed loop detection accuracy is improved through an improved closed loop detection algorithm, the problem of perception ambiguity is avoided, and the system accumulated error is reduced; and errors caused by system noise and the like are reduced through local optimization of the pose and global optimization of the whole system data, so that more accurate pose estimation and a better three-dimensional reconstruction effect are obtained.
Drawings
Fig. 1 is a flow chart of the mobile robot vision SLAM method based on the improved closed-loop detection algorithm of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
as shown in fig. 1, the present invention provides a mobile robot vision SLAM method based on an improved closed-loop detection algorithm, which is characterized by comprising the following steps:
s1, calibrating the Kinect by using a Zhang-Daoyou calibration method; correcting the distortion of the camera and acquiring camera internal parameters; the Zhang DaoYong calibration method is a calibration method which can obtain the internal parameters of the camera by only using one printed checkerboard.
S2, performing ORB feature extraction on the RGB image by using opencv, wherein the obtained ORB features are good in robustness, short in time consumption and very suitable for real-time SLAM; the fast approximate nearest neighbor (FLANN) algorithm is suitable for the condition that the number of matching points is extremely large, and can effectively complete feature matching.
S3, for the mismatching situation, using random sample consensus (RANSAC) to delete the mismatching; acquiring spatial coordinates of the matching points through a Kinect camera model, and estimating pose transformation (R, t) between frames by adopting a PnP algorithm; the space coordinate solving method comprises the following steps:
zo＝z
if the depth value corresponding to the pixel coordinate (u, v) in the image obtained by the Kinect is z, the space coordinate (x) can be obtained according to the Kinect camera modelo,yo,zo)。
And S4, performing unstructured iterative optimization on the pose transformation obtained by the PnP in order to provide more stable and accurate pose estimation for the back-end global optimization. The method for optimizing the pose transformation obtained by PnP comprises the following steps:
firstly, establishing an optimization problem by minimizing a reprojection error by taking a camera pose as an optimization variable;
then, the original PnP function is optimized by calling g2o with the PnP value as an initial value.
S5, firstly, preprocessing the acquired image; obtaining an image similarity score by using the following similarity calculation function, and when the score is greater than a set threshold value, omitting the current frame; if not, the current frame represents a new scene for participating in closed loop detection; the threshold value in the preprocessing should be reasonably set according to the quality of the acquired image and the image acquisition rate, because the smaller the threshold value is, the more image frames are deleted, and the higher the accuracy rate of acquiring a new scene is. However, if the setting is too low, the closed loop cannot be detected even when the robot returns to the region that has been once reached, and therefore the threshold value should be set appropriately according to the situation.
Next, describing the image by adopting a hierarchical K-means clustering algorithm; the following modified single node scoring function was used for similarity score matching.
The function of the improved similarity score is defined as:
based on the new single-node similarity score function proposed by the above formula, the similarity score at the l-th layer is:
the repeated accumulation of similarity can be avoided by using a top-down similarity increment method, and the l-th layer similarity score increment is defined as:
defining the matching kernel as:
wherein, ηlIndicating the matching strength factor of the l-th layer.
Screening out a candidate closed loop by comparing the similarity score with a set threshold value; and screening out a correct closed loop from the candidate closed loops by utilizing the time continuity and the space consistency.
S6, first, in order to optimize the pose and landmark points calculated by the visual odometer, an overall cost function (also called an objective function) is constructed as follows:
e＝z-h(ξ,p)
ξ is a lie algebra corresponding to the camera pose (external parameters (R, t)), p is a three-dimensional coordinate point of the road sign, z is pixel coordinate data observed by Kinect, e is an observation error, z is an observation errorijShown in a seated position ξiWhere observation road sign pjThe generated pixel coordinate data.
This least squares method is then solved, defining the independent variables as all the variables to be optimized:
x＝[ξ1,...,ξm,p1,...,pn]
and continuously searching a descending direction △ x to find the optimal solution of the cost function according to the idea of nonlinear optimization, wherein when an increment is given to the independent variable, the objective function is changed into:
wherein, Fij、EijRespectively representing the partial derivative of the camera pose in the current state and the partial derivative of the road mark position.
The following incremental equations are finally solved:
H△x＝g
wherein,
H＝JTJ+λI
J＝[F E]
and finally, obtaining a convergence value x meeting the state variable of the target equation through multiple iterations, and obtaining the optimized pose and the optimized landmark.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (7)

1. A mobile robot vision SLAM method based on an improved closed-loop detection algorithm is characterized by comprising the following steps:
s1, calibrating the Kinect by using a Zhang friend calibration method to obtain camera internal parameters;
s2, carrying out ORB feature extraction on the obtained RGB image, and carrying out feature matching by adopting a FLANN fast approximate nearest neighbor algorithm, wherein the feature matching comprises a correct matching result and a wrong matching result;
s3, aiming at the mismatching result in the step S2, the random sample consensus is utilized to delete the mismatching; acquiring spatial coordinates of matching points through a Kinect camera model, and estimating interframe pose transformation (R, t) by adopting an n-point perspective problem algorithm PnP;
s4, carrying out structureless iterative optimization on the pose transformation obtained by adopting the PnP algorithm in the step S3;
s5, preprocessing the image frames obtained in the step S2, describing the images through visual word bags, matching the images by using an improved similarity score matching method, and obtaining matching which is more consistent with the actual similarity between the images so as to obtain candidate closed loops;
and S6, optimizing the pose and the landmark by adopting a graph optimization method taking cluster adjustment BA as a core, and acquiring more accurate camera pose and landmark through continuous iterative optimization.
2. The mobile robot vision-synchronized positioning and mapping method of claim 1, wherein the ORB feature extraction step in step S2 is:
firstly, performing FAST corner extraction on an RGB image, and enabling ORB feature points to have invariance of scale and rotation by utilizing an image pyramid construction method and a gray centroid method;
thirdly, binary description is carried out on the image around the feature point extracted in the previous step through BRIEF.
3. The method for visual synchronous positioning and mapping of a mobile robot as claimed in claim 2, wherein the spatial coordinates of the matching points are obtained through a Kinect camera model in step S3, and the spatial coordinate solving method comprises:
<mrow> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>=</mo> <mfrac> <mi>z</mi> <msub> <mi>f</mi> <mi>x</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mi>c</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>=</mo> <mfrac> <mi>z</mi> <msub> <mi>f</mi> <mi>y</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mi>v</mi> <mo>-</mo> <msub> <mi>c</mi> <mi>y</mi> </msub> <mo>)</mo> </mrow> </mrow>
zo＝z
if the depth value corresponding to the pixel coordinate (u, v) in the image obtained by the Kinect is z, the space coordinate (x) can be obtained according to the Kinect camera modelo,yo,zo)。
4. The mobile robot vision SLAM method based on the improved closed-loop detection algorithm of claim 3, wherein the step of optimizing the pose transformation found by PnP in step S4 comprises:
firstly, establishing an optimization problem by minimizing a reprojection error by taking a camera pose as an optimization variable;
then, the original PnP function is optimized by calling g2o with the PnP value as an initial value.
5. The visual SLAM method for mobile robots based on improved closed loop detection algorithm as claimed in claim 4 wherein the step S5 detection steps of candidate closed loop are:
firstly, preprocessing an acquired image, acquiring an image similarity score by using the following similarity calculation function, and discarding a current frame when the score is greater than a set threshold value; if not, the current frame represents a new scene for participating in closed loop detection;
<mrow> <mi>H</mi> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>V</mi> <mi>l</mi> </msub> <mo>,</mo> <msub> <mi>V</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>V</mi> <mi>l</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>V</mi> <mi>c</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> <mo>,</mo> </mrow>
wherein, VlWeight vector, V, representing the image of the previous framecRepresenting a weighting vector of the current frame, and an H value representing image similarity;
next, describing the image by adopting a hierarchical K-means clustering algorithm; then adopting the following improved single-node score function to carry out image similarity score matching;
the repeated accumulation of similarity can be avoided by using a top-down similarity increment method, and the l-th layer similarity score increment is defined as:
<mrow> <msup> <mi>&amp;Delta;S</mi> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>-</mo> <msup> <mi>S</mi> <mrow> <mi>l</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>1</mn> <mo>&amp;le;</mo> <mi>l</mi> <mo>&lt;</mo> <mi>d</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>S</mi> <mi>d</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>l</mi> <mo>=</mo> <mi>d</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
defining the matching kernel as:
<mrow> <mi>K</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>d</mi> </munderover> <msub> <mi>&amp;eta;</mi> <mi>l</mi> </msub> <msup> <mi>&amp;Delta;S</mi> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </mrow>
wherein, ηlIndicating the matching strength factor of the l-th layer.
6. The visual SLAM method for mobile robots based on an improved closed loop detection algorithm as claimed in claim 5 wherein the function of the improved similarity score is defined as:
<mrow> <msubsup> <mi>S</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>min</mi> <mo>{</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>,</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>}</mo> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mo>|</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mfrac> </mrow>
based on the new single-node similarity score function proposed by the above formula, the similarity score at the l-th layer is:
<mrow> <msup> <mi>S</mi> <mi>l</mi> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msup> <mi>k</mi> <mi>l</mi> </msup> </munderover> <msubsup> <mi>S</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msup> <mi>k</mi> <mi>l</mi> </msup> </munderover> <mi>min</mi> <mo>{</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>,</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>}</mo> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msup> <mi>k</mi> <mi>l</mi> </msup> </munderover> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mo>|</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>&amp;omega;</mi> <mi>i</mi> <mi>l</mi> </msubsup> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mfrac> </mrow>
wherein,represents the score of image X on the ith node of the ith level of the tree,representing image Y in treeThe score on the ith node of the ith layer of (1).
7. The mobile robot vision SLAM method based on the improved closed-loop detection algorithm as claimed in claim 5 or 6, wherein the optimization of pose and road sign by using a graph optimization method with cluster adjustment BA as core specifically comprises: firstly, constructing a cost function of pose and whole road sign, namely an objective function, as follows:
<mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>e</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>z</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mi>h</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow>
e＝z-h(ξ,p)
ξ is a lie algebra corresponding to the camera pose (external parameters (R, t)), p is a three-dimensional coordinate point of the road sign, z is pixel coordinate data observed by Kinect, e is an observation error, z is an observation errorijShown in a seated position ξiWhere observation road sign pjGenerated pixel coordinate data;
this least squares method is then solved, defining the independent variables as all the variables to be optimized:
x＝[ξ1,...,ξm,p1,...,pn]
and continuously searching a descending direction △ x to find the optimal solution of the cost function according to the idea of nonlinear optimization, wherein when an increment is given to the independent variable, the objective function is changed into:
<mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>|</mo> <mo>|</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>x</mi> <mo>)</mo> </mrow> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>&amp;ap;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>e</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>&amp;Delta;&amp;xi;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>&amp;Delta;p</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow>
wherein, Fij、EijRespectively representing the partial derivative of the camera pose in the current state and the partial derivative of the position of the landmark point;
the following incremental equations are finally solved:
h △ x is g, g being a constant equivalent.
Wherein,
H＝JTJ+λI
j ═ F E, and matrices E and F represent the derivatives of the global objective function to the global variable.
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Application publication date: 20180209