Patent Publication Number: US-10775204-B2

Title: Encoder unit, angle measuring method, and robot

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to an encoder unit, an angle measuring method, and a robot. 
     2. Related Art 
     In the related art, an optical rotary encoder is known as a type of encoder. For example, JP-A-2007-178320 discloses a rotary encoder that includes a dial, a code pattern provided in the vicinity of a peripheral edge of the dial, and a pair of CCD linear sensors that read a code pattern at a symmetrical position. Here, the pair of CCD linear sensors reads the code pattern, obtained read angles are averaged, and thereby an error due to eccentricity of the dial is to be reduced. Further, when an eccentricity factor related to eccentricity of the dial is stored in advance, and a user measures an angle, an angle measurement value is corrected with the eccentricity factor such that an angle error due to the eccentricity with respect to a rotary shaft of the dial is to be eliminated. 
     A rotary encoder is used for measuring a rotation angle of an output shaft of a speed reducer such as a wave speed reducer. Here, the output shaft of the speed reducer has axial run-out (dynamic eccentricity) with rotation. Therefore, in this case, when, as described in a method disclosed in JP-A-2007-178320, an eccentricity factor obtained in advance in order to eliminate an angle error due to eccentricity is used, a problem arises in that it is not possible to sufficiently reduce an error due to eccentricity of a dial, which is caused by the axial run-out described above, and it is difficult to enhance detection accuracy. 
     SUMMARY 
     An encoder unit according to an application example of the invention includes: a speed reducer having an output shaft that rotates around a rotary shaft so as to output a drive force; and an encoder that measures a rotation angle of the output shaft. The encoder includes a rotary unit that moves rotationally around the rotary shaft along with rotational movement of the output shaft, a scale portion that is disposed on the rotary unit in a circumferential direction around the rotary shaft and has a first mark and a second mark, a first imaging element that images the first mark, a second imaging element that is disposed at a position symmetrical with the first imaging element with respect to the rotary shaft and images the second mark, a processor that performs a process of obtaining a rotation angle of the rotary unit based on imaging results imaged by the first imaging element and the second imaging element, and a storage unit that stores an instruction that is readable by the processor. The processor reads the instruction from the storage unit such that template matching with an image captured by the first imaging element is performed to obtain a first movement amount in the circumferential direction of the first mark, template matching with an image captured by the second imaging element is performed to obtain a second movement amount in the circumferential direction of the second mark, and a rotation angle is calculated and output by using the first movement amount and the second movement amount. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
         FIG. 1  is a side view illustrating a robot according to an embodiment of the invention. 
         FIG. 2  is a sectional view illustrating an encoder unit according to a first embodiment of the invention. 
         FIG. 3  is a block diagram illustrating an encoder of the encoder unit. 
         FIG. 4  is a view for illustrating a scale portion included in the encoder of the encoder unit. 
         FIG. 5  is a view for illustrating an image captured by a first imaging element or a second imaging element included in the encoder. 
         FIG. 6  is a view for illustrating template matching in a search region that is set in a captured image. 
         FIG. 7  is a view illustrating a deviated state by one pixel from a state of having the maximum similarity, when template matching is performed. 
         FIG. 8  is a view illustrating the state of having the maximum similarity, when the template matching is performed. 
         FIG. 9  is a view illustrating a deviated state by one pixel toward an opposite side with respect to the state illustrated in  FIG. 7  from the state of having the maximum similarity, when template matching is performed. 
         FIG. 10  is a view for illustrating a plurality of marks included in a scale portion. 
         FIG. 11  is a view illustrating a state in which, of the plurality of marks, one mark is detected through the template matching. 
         FIG. 12  is a view for illustrating prediction of a reference image that is used in the following template matching after the template matching (previous template matching). 
         FIG. 13  is a flowchart illustrating a method for determining a reference image that is used in the first template matching. 
         FIG. 14  is a flowchart illustrating a method for determining (a method for predicting) a reference image that is used in the following template matching. 
         FIG. 15  is a schematic diagram illustrating a relationship between run-out of a rotary shaft and a first movement amount and a second movement amount. 
         FIG. 16  is a schematic diagram illustrating a relationship between an effective visual field region and a movement locus of the scale portion. 
         FIG. 17  is a graph illustrating a relationship between a rotation angle and an error in angle measurement by using the first imaging element. 
         FIG. 18  is a graph illustrating a relationship between a rotation angle and an error in angle measurement by using the second imaging element. 
         FIG. 19  is a graph illustrating a relationship between a rotation angle and a measurement error in angle measurement by using the first imaging element and the second imaging element. 
         FIG. 20  is a graph illustrating a relationship between a positional deviation and a measurement error of the first imaging element and the second imaging element. 
         FIG. 21  is a schematic diagram illustrating a relationship between an effective visual field region and a movement locus of the scale portion in a second embodiment of the invention. 
         FIG. 22  is a diagram for illustrating a correction factor in the second embodiment of the invention. 
         FIG. 23  is a flowchart illustrating a flow of obtaining the correction factor in the second embodiment of the invention. 
         FIG. 24  is a perspective view illustrating a robot according to a third embodiment of the invention. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, an encoder unit, an angle measuring method, and a robot according to the invention will be described in detail on the basis of preferred embodiments illustrated in the accompanying drawings. 
     1. Robot 
       FIG. 1  is a side view illustrating a robot according to an embodiment of the invention. Hereinafter, for convenience of description, in  FIG. 1 , an upper side is referred to as “above”, and a lower side is referred to as “below”. In addition, in  FIG. 1 , a base side is referred to as a “proximal end side”, and an opposite side (end effector side) thereof is referred to as a “distal end side”. In addition, in  FIG. 1 , an up-down direction is referred to as a “vertical direction”, and a right-left direction is referred to as a “horizontal direction”. 
     A robot  100  illustrated in  FIG. 1  is a so-called horizontal articulated robot (SCARA robot), can be used in a manufacturing process or the like of manufacturing precision measuring equipment, and can perform gripping, transporting, or the like of the precision measuring equipment, a component, or the like. 
     As illustrated in  FIG. 1 , the robot  100  includes a base  110 , a first arm  120 , a second arm  130 , a work head  140 , an end effector  150 , and a wiring lay-out unit  160 . Hereinafter, portions of the robot  100  will be briefly described in order. 
     The base  110  is fixed to a floor (not illustrated) with a bolt, or the like. The first arm  120  is connected to a top portion of the base  110 . The first arm  120  is rotationally movable around a first axis J 1  in the vertical direction with respect to the base  110 . 
     Inside the base  110 , a motor  111  which is a first motor that generates a drive force for causing the first arm  120  to move rotationally and a speed reducer  112  which is a first speed reducer that reduces a speed of the drive force of the motor  111  are provided. An input shaft of the speed reducer  112  is connected to a rotary shaft of the motor  111 , and an output shaft of the speed reducer  112  is connected to the first arm  120 . Therefore, when the motor  111  is driven, and the drive force of the motor is transmitted to the first arm  120  via the speed reducer  112 , the first arm  120  moves rotationally in a horizontal plane around the first axis J 1  with respect to the base  110 . 
     In addition, an encoder  1  is provided in the base  110  and the first arm  120 , the encoder being a first encoder that measures a rotation angle of the output shaft of the speed reducer  112 , thereby, detecting a rotation state of the first arm  120  with respect to the base  110 . Here, the encoder  1  and the speed reducer  112  configure an encoder unit  10 . 
     The second arm  130  is connected to a distal portion of the first arm  120 . The second arm  130  is rotationally movable around a second axis J 2  in the vertical direction with respect to the first arm  120 . Although not illustrated, inside the second arm  130 , a second motor that generates a drive force for causing the second arm  130  to move rotationally and a second speed reducer that reduces a speed of the drive force of the second motor are provided. The drive force of the second motor is transmitted to the first arm  120  via the second speed reducer, and thereby the second arm  130  moves rotationally in the horizontal plane around the second axis J 2  with respect to the first arm  120 . In addition, although not illustrated, a second encoder is provided in the second motor and detects a rotation state of the second arm  130  with respect to the first arm  120 . 
     The work head  140  is disposed at a distal portion of the second arm  130 . The work head  140  has a spline shaft  141  that penetrates a spline nut and a ball screw nut (both not illustrated) which are disposed coaxially at the distal portion of the second arm  130 . The spline shaft  141  is rotationally movable around an axis of the spline shaft and is movable (liftable and lowerable) in the up-down direction with respect to the second arm  130 . 
     Although not illustrated, a rotation motor and a lifting/lowering motor are disposed inside the second arm  130 . When the drive force of the rotation motor is transmitted to the spline nut by a drive force transmitting mechanism not illustrated, and the spline nut rotates forward and reverse, the spline shaft  141  rotates forward and reverse around an axis J 3  in the vertical direction. In addition, although not illustrated, a third encoder is provided in the rotation motor and detects a rotation state of the spline shaft  141  with respect to the second arm  130 . 
     On the other hand, when a drive force of the lifting/lowering motor is transmitted to the ball screw nut by a drive force transmitting mechanism not illustrated, and the ball screw nut rotates forward and reverse, the spline shaft  141  moves upward and downward. A fourth encoder is provided in the lifting/lowering motor and measures a movement amount of the spline shaft  141  with respect to the second arm  130 . 
     The end effector  150  is connected to a distal portion (bottom portion) of the spline shaft  141 . The end effector  150  is not particularly limited, and examples thereof include a unit that grips an object to be transported, and a unit that performs work on a workpiece. 
     A plurality of wirings that are connected to electronic components (for example, the second motor, the rotation motor, the lifting/lowering motor, the first to fourth encoders, or the like) disposed in the second arm  130  are laid out to the inside of the base  110  through the pipe-shaped wiring lay-out unit  160  that connects the second arm  130  and the base  110 . Further, the plurality of wirings are integrated inside the base  110 , thereby, together with a wiring that is connected to the motor  111  and the encoder  1 , being laid out to a control device (not illustrated) that is disposed outside the base  110  and controls the robot  100  collectively. 
     As described above, a configuration of the robot  100  is briefly described. As described above, the robot  100  includes the base  110 , which is a first member, the first arm  120 , which is a second member that moves rotationally with respect to the base  110 , and the encoder unit  10 . Here, the encoder unit  10  includes the speed reducer  112  that has an output shaft which rotates around a rotary shaft so as to output a drive force and the encoder  1  that measures the rotation angle of the output shaft of the speed reducer  112 . The speed reducer  112  is installed in the base  110  such that the output shaft of the speed reducer  112  is connected to the first arm  120 . According to the robot  100 , as will be described below, it is possible to measure the rotation angle of the first arm  120  with high accuracy and to perform drive control of the first arm  120  with high accuracy based on a detection result thereof. 
     Here, a rotary unit of the encoder  1  to be described below is the first arm  120  (second member). Consequently, it is possible to reduce the number of components. 
     2. Encoder Unit 
     First Embodiment 
     Hereinafter, the encoder unit  10  will be described in detail. Hereinafter, a case where the encoder unit  10  is installed in the robot  100  will be described as an example. 
       FIG. 2  is a sectional view illustrating the encoder unit according to a first embodiment of the invention.  FIG. 3  is a block diagram illustrating the encoder of the encoder unit.  FIG. 4  is a view for illustrating a scale portion included in the encoder of the encoder unit. In addition, in the drawings, for convenience of description, a scale of portions is appropriately changed, a scale in a configuration illustrated in the drawings is not necessarily equal to an actual scale, or portions are appropriately omitted in the drawing. 
     As illustrated in  FIG. 2 , the base  110  of the robot  100  described above includes a support member  114  that supports the motor  111  and the speed reducer  112  and houses the motor  111  and the speed reducer  112 . The first arm  120  is provided on the base  110  so as to be rotationally movable around the first axis J 1 . 
     The first arm  120  includes an arm main body portion  121  that extends in the horizontal direction and a shaft portion  122  that projects downward from the arm main body portion  121 , the arm main body portion and the shaft portion being connected to each other. The shaft portion  122  is supported on the base  110  via a bearing  115  so as to be rotationally movable around the first axis J 1  and is connected to the output shaft of the speed reducer  112 . In addition, the input shaft of the speed reducer  112  is connected to a rotary shaft  1111  of the motor  111 . The speed reducer  112  is not particularly limited, and examples thereof include a wave speed reducer, a planetary gear speed reducer, a cyclo-speed reducer, an RV speed reducer, or the like. 
     Here, the base  110  is a structure to which a load due to own weight of the base  110  or a mass of another member supported by the base  110  is applied. Similarly, the first arm  120  is a structure to which a load due to own weight of the first arm  120  or a mass of another member supported by the first arm  120  is applied. A configurational material of the base  110  and the first arm  120  is not particularly limited, and an example thereof includes a metal material. 
     In the embodiment, outer surfaces of the base  110  and the first arm  120  configure a part of an outer surface of the robot  100 . An exterior member such as a cover or an impact absorbing member may be installed on the outer surfaces of the base  110  and the first arm  120 . 
     In the base  110  and the first arm  120  which relatively move rotationally with respect to each other, the encoder  1  that detects rotation states thereof is provided therein. 
     The encoder  1  includes a scale portion  2  that is provided on the first arm  120 , a first detector  3   a  and a second detector  3   b  that are provided on the base  110  so as to detect the scale portion  2 , and a circuit section  4  that is electrically connected to the first detector  3   a  and the second detector  3   b . Here, the circuit section  4  includes a processor  5  and a storage unit  6 . 
     As illustrated in  FIG. 2 , the scale portion  2  is provided in a region that is opposite to the base  110  of the arm main body portion  121 , that is, a region that is on an underside of the arm main body portion  121  and surrounds the shaft portion  122 . As illustrated in  FIG. 4 , the scale portion  2  has an irregular pattern that is disposed around the first axis J 1  at a position different from the first axis J 1 . Here, the scale portion  2  is provided on a surface of the first arm  120 . Consequently, there is no need to provide a member for providing the scale portion  2  thereon separately from the base  110  and the first arm  120 . Therefore, it is possible to reduce the number of components. The scale portion  2  is not limited to being provided right on the surface of the first arm  120 , and may be provided on a sheet-shaped member adhered to the surface of the first arm  120  or may be provided on a plate-shaped member provided to move rotationally along with the first arm  120 . In other words, the member, on which the scale portion  2  is provided, may be a member that moves rotationally around the first axis J 1  along with the first arm  120  with respect to the base  110 . Accordingly, the member, on which the scale portion  2  is provided in the encoder  1 , can be referred to as a rotary unit. In addition, the second member described above is the first arm  120 , and thus the rotary unit is the first arm  120 . 
     As illustrated in  FIG. 4 , the scale portion  2  (irregular pattern) has a configuration in which a plurality of dots  20  (designs) are irregularly disposed. Here, “the irregular pattern” means that two or more patterns do not appear to be the same as each other (patterns that are not identifiable by the processor  5 ) in a size corresponding to a reference image TA to be described below in a predetermined region (for example, an effective visual field region RU or a search region RS to be described below) in a captured image G, when the scale portion  2  is caused to move rotationally over an angle range (in the embodiment, an angle range in which the first arm  120  is rotatable with respect to the base  110 ) around the first axis J 1 . Therefore, each of a plurality of parts of the scale portion  2 , which are disposed at different positions from each other, can be used as a mark  21  for position identification in a circumferential direction of the scape portion. In this manner, the scale portion  2  can be considered to have a plurality of marks  21  which are different from each other such that different positions are identifiable from each other in the circumferential direction thereof.  FIG. 4  illustrates a case where the plurality of marks  21  are arranged along a circumference with the first axis J 1  as the center. In addition, positions, a size, the number, or the like of the marks  21  illustrated in  FIG. 4  are an example and are not limited. In addition, contrary to  FIG. 2 , the scale portion  2  may be disposed on the base  110 , and the detectors  3   a  and  3   b  may be disposed on the side of the arm  120 . 
     It is preferable that the scale portion  2  (pattern) has a configuration in which unique pattern designs different from each other are designed into print drawing. In the example, dot-shaped black dots are disposed on a white background so as to form unique patterns. 
     In addition, since the patterns of the scale portion  2  are continually disposed around the first axis J 1 , constraints of positions in a rotational movement direction (circumferential direction) are reduced, and a degree of freedom increases, when the processor  5  generates a reference image (template) as will be described below. In addition, the patterns of the scale portion  2  are disposed even outside the effective visual field region RU in a Y-axis direction of the captured image G. Therefore, even when positioning of the scale portion  2  (pattern) with respect to the first arm  120  is not performed with high accuracy, it is possible to generate the reference image (template), and it is possible to estimate a corresponding rotation state. 
     The scale portion  2  may have a gradual change in shades in the circumferential direction. In other words, density (disposition density) of the plurality of dots  20  may change around the first axis J 1  (rotary shaft). In addition, a color of the dots  20  (design) of the scale portion  2  is not particularly limited, and may be any color; however, it is preferable that the color is different from a color of part other than the dots  20  of the scale portion  2 , and it is preferable to use black or a dark color. Consequently, it is possible to increase contrast of the captured images acquired by a first imaging element  31   a  and a second imaging element  31   b  to be described below. 
     In addition, a shape of the dots  20  (designs) of the scale portion  2  is a circle; but the shape is not limited thereto, and an ellipse, a quadrangle, an abnormal shape, or the like may be employed, for example. In addition, the patterns of the scale portion  2  are not limited to dot patterns (repetition of design) like the patterns configured of the plurality of dots  20  described above, and examples of the pattern may include a pattern configured of straight lines, a pattern configured of curves, a pattern configured of a combination of at least two types of dots, straight lines, and curves, a reverse pattern thereof, or the like. 
     Further, as long as the pattern can be captured by the first imaging element  31   a  and the second imaging element  31   b  to be described below, the pattern of the scale portion  2  is not limited to the pattern formed with ink of dye, a pigment, or the like by using a printing device described above, and a pattern having an uneven shape, a pattern that is formed with natural objects, or the like may be employed. Examples of patterns having the uneven shape include an uneven pattern due to roughness or irregularity of a processed surface through etching, cutting, shot blast, sand blast, rasping, or the like, an uneven pattern due to fibers on a surface of paper, fabric (nonwoven fabric or woven fabric), or the like, an uneven pattern of a coated surface, or the like. In addition, an example of a pattern formed with a natural object includes a pattern with grains, or the like. In addition, when a coated film is formed with a transparent coating material mixed with black beads, it is possible to obtain coating film on which a plurality of black beads are irregularly disposed, and the plurality of beads of the coated film may be used in the scale portion  2  as the irregular pattern. 
     In addition, the marks  21  of the scale portion  2  are not limited to a design using the irregular pattern, and numbers may be used, characters such as Roman letters, Arabic letters, or Chinese characters may be used, or symbols, codes, emblems, a design, one-dimensional bar codes, QR codes (registered trademark), or the like may be used. 
     The first detector  3   a  (first camera) illustrated in  FIG. 2  includes the first imaging element  31   a , which is provided in the base  110 , and a first optical system  32   a , which is provided in an opening of the base  110 , and the first imaging element  31   a  images a part of the scale portion  2  in the circumferential direction (an imaging region RI 1  on the right side in  FIG. 4 ) via the first optical system  32   a . A light source that irradiates the imaging region RI 1  of the first imaging element  31   a  may be provided, as necessary. 
     Examples of the first imaging element  31   a  include a charge coupled device (CCD), a complementary metal oxide semiconductor (CMOS), or the like. The first imaging element  31   a  converts a captured image into an electric signal for each pixel and outputs the electric signal. The first imaging element  31   a  is applicable to both a two-dimensional imaging element (area image sensor) and a one-dimensional imaging element (line image sensor). It is desirable that the one-dimensional imaging element has a configuration in which pixels are arranged in a contact direction with a turning circle of the arm. In a case of using the two-dimensional imaging element, it is possible to acquire a two-dimensional image including a large amount of information, and it is easy to enhance detection accuracy of the mark  21  through template matching to be described below. As a result, it is possible to detect the rotation state of the first arm  120 . In a case of using the one-dimensional imaging element, an image acquisition cycle, that is, a frame rate, increases. Therefore, it is possible to increase detection frequency, and thus the element is advantageous during a high speed movement. 
     The first optical system  32   a  is an image forming optical system that is disposed between the scale portion  2  and the first imaging element  31   a . It is preferable that the first optical system  32   a  is telecentric at least on a side of an object (side of the scale portion  2 ). 
     Consequently, even when a distance between the scale portion  2  and the first imaging element  31   a  changes, it is possible to decrease a change in imaging magnification to the first imaging element  31   a  and, as a result, it is possible to decrease degradation of the detection accuracy of the encoder  1 . In particular, in a case where the first optical system  32   a  is telecentric on both sides, it is possible to decrease the change in imaging magnification to the first imaging element  31   a , even when a distance between a lens included in the first optical system  32   a  and the first imaging element  31   a  changes. Therefore, it is advantageous to easily assemble the first optical system  32   a.    
     Here, as illustrated in  FIG. 4 , the imaging region RI 1  of the first imaging element  31   a  is provided on the underside of the first arm  120  so as to overlap a part of the scale portion  2  in the circumferential direction. Consequently, the first imaging element  31   a  is capable of imaging the mark  21  in the imaging region RI 1 . Hence, the mark  21  positioned in the imaging region RI 1  is read, and thereby it is possible to know the rotation state of the first arm  120 . 
     On the other hand, the second detector  3   b  (second camera) is disposed at a position symmetrical with the first detector  3   a  with respect to the first axis J 1 . The second detector  3   b  is configured in a similar way to the first detector  3   a . In other words, the second detector  3   b  includes the second imaging element  31   b , which is provided in the base  110 , and a second optical system  32   b , which is provided in an opening of the base  110 , and the second imaging element  31   b  images a part of the scale portion  2  in the circumferential direction (an imaging region RI 2  on the left side in  FIG. 4 ) via the second optical system  32   b.    
     Here, it is preferable that the second imaging element  31   b  images the scale portion  2  in the same resolution as that of the first imaging element  31   a . Consequently, when the rotation angle is calculated by using a first movement amount and a second movement amount to be described below, calculation thereof is simplified. From such a viewpoint, it is preferable that the second imaging element  31   b  has the same size and the same number of pixels as those of the first imaging element  31   a , and it is preferable that the second optical system  32   b  has the same magnification as that of the first optical system  32   a.    
     The circuit section  4  illustrated in  FIGS. 2 and 3  includes the processor  5  such as a central processing unit (CPU), and a storage unit  6  (memory) such as a read only memory (ROM) or a random access memory (RAM). Here, the storage unit  6  stores an instruction that is readable by the processor  5 . Thus, the processor  5  appropriately reads and executes the instruction from the storage unit  6 , thereby, realizing various functions. For example, the circuit section  4  can be configured by using an application specific integrated circuit (ASIC) or a field-programmable gate array (FPGA). In this manner, the circuit section  4  becomes hardware by using the ASIC or the FPGA, and thereby it is possible to achieve a high processing speed and a reduction in size and cost of the circuit section  4 . At least a part of the circuit section  4  may be installed in the control device of the robot  100  described above. 
     The processor  5  estimates relative rotation states of the base  110  and the first arm  120  based on detection results of the first detector  3   a  and the second detector  3   b . Examples of the rotation state include a rotation angle, a rotation speed, a rotation direction, or the like. 
     In particular, the processor  5  performs template matching with captured images (captured image data) the first imaging element  31   a  and the second imaging element  31   b  by using the reference image (reference image data), thereby performing image recognition of the mark  21 , and estimates relative rotation states of the base  110  and the first arm  120  by using a recognition result thereof. In this manner, the processor estimates the rotation states by using both of the captured images acquired by the first imaging element  31   a  and the second imaging element  31   b , and thereby it is possible to decrease detection errors due to axial run-out (eccentricity) depending on rotation of the output shaft of the speed reducer  112 , and it is possible to more enhance the detection accuracy, compared with a case of estimating the rotation states by using any captured image acquired by the first imaging element  31   a  or the second imaging element  31   b . This will be described below in detail. 
     Here, the processor  5  is configured to be capable of more finely estimating the relative rotation angles of the base  110  and the first arm  120  (hereinafter, simply referred to as “the rotation angle of the first arm  120 ”) based on a position of the image of the mark  21  in the captured image acquired by the first imaging element  31   a  and the second imaging element  31   b . In addition, the processor  5  is configured to be capable of obtaining the rotation speed based on a time interval between detection of the mark  21  or estimating the rotation direction based on an order of types of marks  21  that are detected. The processor  5  outputs a signal depending on an estimation result described above, that is, a signal depending on the rotation states of the base  110  and the first arm  120 . For example, the signal is input to the control device (not illustrated) and is used in control of movement of the robot  100 . 
     In addition, the processor  5  has a function of cutting a part of the captured image acquired by the first imaging element  31   a  and the second imaging element  31   b  so as to generate a reference image (template). The reference image is generated before the relative rotation states of the base  110  and the first arm  120  are estimated, at a right time as necessary, or for each relative rotation angle of the base  110  and the first arm  120 . The generated reference image is stored in the storage unit  6 , in association with each relative rotation angle of the base  110  and the first arm  120 . The processor  5  performs the template matching by using the reference image (template) that is stored in the storage unit  6 . The template matching and the estimation of the rotation state using thereof will be described below in detail. 
     The storage unit  6  stores various items of information (data) that is readable by the processor  5 , in addition to the instruction (program) readable by the processor  5 . Specifically, the storage unit  6  stores the reference image described above (reference image data) together with information on a coordinate (coordinate of the reference pixel to be described below) in the captured image corresponding to the reference image, and image on the rotation angle of the first arm  120  (angle information), for each relative rotation state of the base  110  and the first arm  120 . The storage unit  6  may be a non-volatile memory or a volatile memory; however, the non-volatile memory is preferable, from a viewpoint of being capable of maintaining a state of storing information even when power is not supplied, and it is possible to achieve power saving. 
     Template Matching and Estimation of Rotation State by Using Template Matching 
     Hereinafter, the template matching and the estimation of the rotation state by using the template matching in the processor  5  will be described below in detail. Hereinafter, first, a case of estimating a rotation angle as the rotation state by using any captured image acquired by either the first imaging element  31   a  or the second imaging element  31   b  will be representatively described. A case of estimating a rotation angle as the rotation state by using both of the captured images acquired by the first imaging element  31   a  and the second imaging element  31   b  will be described below. 
     Acquisition of Reference Image 
     In the encoder  1 , before the rotation state of the first arm  120  with respect to the base  110  is estimated by using the template matching, the reference image is acquired by using the template matching. The acquisition of the reference image may be performed only once before the first template matching; however, the acquisition may be performed appropriately as necessary thereafter. In this case, it is possible to update the reference image acquired by using the template matching to a newly acquired reference image. 
     When the reference image is acquired, the first arm  120  is caused to move rotationally around the first axis J 1  with respect to the base  110 , and the first imaging element  31   a  and the second imaging element  31   b  image the plurality of marks  21  for each mark  21 . The acquired captured images are trimmed, and thereby a reference image for each mark  21  is generated. The generated reference image is stored together with image coordinate information and angle information thereof in the storage unit  6 , in association with the information. Hereinafter, this will be described below in detail with reference to  FIG. 5 . 
       FIG. 5  is a view for illustrating an image (a captured image, that is, an imaging result) captured by the first imaging element or the second imaging element included in the encoder. 
     When the first arm  120  moves rotationally around the first axis J 1  with respect to the base  110 , for example, as illustrated in  FIG. 5 , a mark image  21 A, which is an image of the mark  21  that is imaged in the captured image G acquired by the first imaging element  31   a  or the second imaging element  31   b , moves along arcs C 1  and C 2  in the captured image G. Here, the arc C 1  is a locus drawn by a bottom of the mark image  21 A in  FIG. 5  along with the rotational movement of the first arm  120  with respect to the base  110 , and the arc C 2  is a locus drawn by a top of the mark image  21 A in  FIG. 5  along with the rotational movement of the first arm  120  with respect to the base  110 . In addition,  FIG. 5  illustrates a case where three marks  21  are included within an imaging region RI illustrated in  FIG. 4 . In this respect, the captured image G illustrated in  FIG. 5  includes a mark image  21 B that positions on one side of the mark image  21 A in the circumferential direction and a mark image  21 X that positions on the other side thereof, in addition to the mark image  21 A. The imaging region RI has the imaging regions RI 1  and RI 2  described above. 
     Here, the captured image G obtained by being captured by the first imaging element  31   a  or the second imaging element  31   b  has a shape corresponding to the imaging region RI and has a rectangular shape including two sides extending in the X-axis direction and two sides extending in the Y-axis direction. In addition, the two sides extending in the X-axis direction of the captured image G are disposed to follow the arcs C 1  and C 2  as much as possible. In addition, the captured image G has a plurality of pixels arranged into a matrix shape in the X-axis direction and the Y-axis direction. Here, a position of the pixel is represented by a pixel coordinate system (X, Y), in which “X” represents a position of the pixel in the X-axis direction, and “Y” represents a position of the pixel in the Y-axis direction. In addition, a desired region is cut from a region having a small aberration of a lens in a range of the captured image G so as to be set as the effective visual field region RU, and a pixel on an upper right end of the effective visual field region RU is set as an origin pixel (0, 0) of the image coordinate system (X, Y). 
     For example, in a case where the reference image TA corresponding to the mark image  21 A is generated, the first arm  120  is caused to appropriately move rotationally with respect to the base  110 , and the mark image  21 A is positioned at a predetermined position (on a center line LY set at the center in the X-axis direction in the drawing) in the effective visual field region RU. Here, a rotation angle θA0 of the first arm  120  with respect to the base  110  when the mark image  21 A is positioned at the corresponding position is acquired through measurement or the like in advance. 
     The captured image G is trimmed in a rectangular pixel range so as to be in a minimum necessary range including the mark image  21 A, and thereby the reference image TA (template for detecting the mark  21 ) is acquired. The acquired reference image TA is stored in the storage unit  6 . In this case, the reference image TA is stored together with angle information on the rotation angle θA0 described above and pixel information on a reference pixel coordinate (XA0, YA0), which is a pixel coordinate of a reference pixel (pixel at an upper left end in the drawing) in the pixel range of the reference image TA, in association therewith. In other words, the reference image TA, the angle information, and the pixel coordinate information are included in one template set which is used in the template matching. 
     Estimation of Rotation State by Using Template Matching 
     Next, the template matching by using the reference image TA generated as described above will be described with reference to  FIGS. 6 to 9 . 
       FIG. 6  is a view for illustrating the template matching in a search region that is set in a captured image.  FIG. 7  is a view illustrating a state of deviation by one pixel from a state of having the maximum similarity, when template matching is performed.  FIG. 8  is a view illustrating the state of having the maximum similarity, when the template matching is performed.  FIG. 9  is a view illustrating a state of deviation by one pixel toward an opposite side with respect to the state illustrated in  FIG. 7  from the state of having the maximum similarity, when template matching is performed. SAD, SSD, ZNCC, or the like is used as a technique of obtaining similarity. A value thereof is minimum in the SAD and the SSD, and the maximum similarity is obtained in the ZNCC when the value thereof is the maximum. 
     As illustrated in  FIG. 6 , when the mark image  21 A is present in the effective visual field region RU, the template matching with an image of the effective visual field region RU is performed by using the reference image TA. In the embodiment, the entire effective visual field region RU is set as the search region RS, the reference image TA overlaps the search region RS, and similarity of an overlap part between the search region RS and the reference image TA is calculated, while the reference image TA is deviated by one pixel with respect to the search region RS. Here, pixel coordinates of reference pixels of the reference image TA move by one pixel from a start coordinate PS (origin pixel P0) to an end pixel PE, and the similarity of the overlap part between the search region RS and the reference image TA with respect to pixels of the entire search region RS is calculated for each pixel coordinate of the reference pixels of the reference image TA. The calculated similarity is stored in the storage unit  6 , as similarity data of captured image data and reference image data in association with the pixel coordinate of the reference pixel of the reference image TA. 
     Next, among a plurality of similarities for each pixel coordinate stored in the storage unit  6 , a similarity having the maximum value is selected, and a pixel coordinate (XA1, YA1) of the reference image TA having the selected similarity is determined as a pixel coordinate of the mark image  21 A. In this manner, it is possible to detect the position of the mark image  21 A in the captured image G. 
     Here, in obtaining the pixel coordinate of the mark image  21 A, it is preferable to use a subpixel estimation method. As illustrated in  FIGS. 7 to 9 , in the vicinity of a position at which the maximum similarity is obtained, the reference image TA overlaps the mark image  21 A. The similarity in a state illustrated in  FIG. 8  is higher than that in states illustrated in  FIGS. 7 and 9  (state of a deviation by one pixel from the state illustrated in  FIG. 8 ) and becomes the maximum similarity. However, as illustrated in the state illustrated in  FIG. 8 , in a case where the reference image TA is deviated not to completely match and overlap the mark image  21 A, and the state illustrated in  FIG. 8  is determined as the pixel position of the mark image  21 A, the deviation becomes an error. The deviation is a pixel size BX at the maximum. In other words, in a case where the subpixel estimation method is not used, the pixel size BX has minimum resolution (accuracy). By comparison, in the subpixel estimation method, a coordinate of the maximum similarity and similarity values of eight coordinates adjacent thereto from a map of similarity obtained at intervals of a pixel size BX through the template matching are fitted on a parabolic surface, and thereby it is possible to perform complementation (approximation) between the similarities (between pixel pitches). Therefore, it is possible to obtain the pixel coordinate of the mark image  21 A with higher accuracy. 
     In this manner, the processor  5  sets the search region RS in the effective visual field region RU which is a part of a region of the captured image G and performs the template matching in the search region RS. Consequently, it is possible to decrease the number of pixels of the search region RS by using the template matching, and it is possible to shorten a computation time related to the template matching. Therefore, even in a case where an angular velocity of the first arm  120  around the first axis J 1  is high, it is possible to perform detection with high accuracy. In addition, even when the distortion or blurring on an outer circumferential part of the captured image G increases due to the aberration of the first optical system  32   a  or the second optical system  32   b  which is disposed between the first imaging element  31   a  or the second imaging element  31   b  and the mark  21 , it is possible to reduce degradation of detection accuracy by using the search region RS in which the distortion or the blurring is low. The reference image TA may be generated and the template matching may be performed by using the captured image G, and in this case, it is preferable to perform correction with consideration for the aberration, as necessary. 
     In the embodiment, since a distance between the imaging region RI and the first axis J 1  is sufficiently long, the arcs C 1  and C 2  can approximate to the straight line in the captured image G. Hence, a movement direction of the mark image  21 A in the captured image G can be considered to be coincident with the X-axis direction. 
     Then, the mark image  21 A illustrated in  FIG. 6  is disposed at a position deviated by the number of pixels (XA1−XA0) in the X-axis direction with respect to the reference image TA that is positioned in the reference pixel coordinate (XA0, YA0). Hence, when R represents a distance between the center of the imaging region RI and the first axis J 1 , and BX represents a width (a visual field size per one pixel of the imaging element  31 ) of a region on the imaging region RI in the X-axis direction, the width corresponding to one pixel of the imaging element  31 , it is possible to obtain a rotation angle θ of the first arm  120  with respect to the base  110  by using Expression (1). 
     
       
         
           
             
               
                 
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     In Expression (1), (XA1−XA0)×BX corresponds to a distance between an actual position corresponding to the reference pixel coordinate (XA0, YA0) of the reference image TA and an actual position corresponding to the pixel coordinate (XA1, YA1) of the reference image TA having the maximum value of similarity described above. In addition, 2πR corresponds to a length of locus (a length of a circumference) of the mark  21  when the first arm  120  rotates by 360° with respect to the base  110 . As described above, θA0 represents a rotation angle of the first arm  120  with respect to the base  110  when the mark image  21 A is positioned at a predetermined position. In addition, the rotation angle θ is an angle of the first arm  120  that moves rotationally from the reference state (0°) with respect to the base  110 . 
     The template matching and the calculation of rotation angle θ by using the template matching described above are similarly performed with another mark  21 . Here, at least one mark  21  is imaged without a defect in the effective visual field region RU at any rotation angle θ, and a reference image corresponding to each of the marks  21  is registered such that it is possible to perform the template matching. Consequently, it is possible to prevent an angle region, in which it is not possible to perform the template matching, from appearing. 
     In  FIG. 5  described above, the marks  21  and the effective visual field region RU are configured such that one mark  21  is imaged without a defect in the effective visual field region RU at any rotation angle θ; however, it is preferable that the marks  21  and the effective visual field region RU are configured such that a plurality of marks  21  are imaged without a defect in the effective visual field region RU at any rotation angle θ. In this case, the template matching is performed by using two or more reference images corresponding to two or more marks  21  which are adjacent to each other such that it is possible to perform the template matching with the plurality of marks  21  imaged in the effective visual field region RU at any rotation angle θ. In this case, the two or more reference images may partially overlap each other. 
     In other words, it is preferable that the imaging element  31  images at least two entire marks  21  of the plurality of marks  21 , which are targets of the template matching. Consequently, even when it is not possible to accurately read one mark  21  of two marks  21  imaged by the imaging element  31  due to a stain or the like, it is possible to read and detect the other mark  21 . Therefore, it is advantageous to easily secure highly accurate detection. In this manner, it is preferable that the processor  5  performs the template matching by using a plurality of reference images with respect to the search region RS at the same time. Consequently, it is possible to enhance the detection accuracy. 
     Determination of Reference Image 
       FIG. 10  is a view for illustrating the plurality of marks provided on the scale portion.  FIG. 11  is a view illustrating a state in which, of the plurality of marks, one mark is detected through the template matching.  FIG. 12  is a view for illustrating prediction of the reference image that is used in the following template matching after the template matching (previous template matching).  FIG. 10  illustrates the pattern of the scale portion  2 ; however, in  FIGS. 11 and 12 , for convenience of description, the pattern of the scale portion  2  is omitted. 
     As illustrated in  FIG. 10 , the plurality of marks  21  arranged on the scale portion  2  in the rotation direction thereof are set.  FIG. 10  illustrates a state in which five marks  21   i −2 to  21   i+ 2 from i−2-th to i+2-th marks are imaged in the captured image G. i represents a number assigned to the marks  21  in an arrangement order and is an integer from 1 to n when n marks  21  are set on the scale portion  2  (n is an integer of 3 or higher). 
     As illustrated in  FIG. 11 , the search region RS described above is set in the captured image G. The search region RS is set, in which one mark  21  is always imaged without a defect. In the drawing, the mark  21   i  is imaged in the search region RS, and the processor  5  performs the template matching as described above by using the reference image corresponding to the mark  21   i  (hereinafter, also referred to as a “reference image i”) so as to detect a position of the mark  21   i  by performing. The processor  5  estimates the rotation state as described above on the basis of the detected position. 
     Here, when the scale portion  2  rotates, the marks  21   i  moves along with the rotation of the scale portion in the rotation direction of the scale portion  2  (the right-left direction in  FIG. 11 ) in the search region RS. In this case, while the reference image i is acquired along with movement of the mark  21   i , the processor  5  performs the template matching (hereinafter, also referred to as the “previous template matching”) so as to sequentially detect the position of the mark  21   i.    
     It is possible to detect the position of the mark  21   i  when the mark  21   i  is imaged in the search region RS. When the mark  21   i  is not imaged in the search region RS along with the rotation of the scale portion  2 , the mark  21   i −1 or  21   i+ 1 adjacent to the mark  21   i  is imaged in the search region RS. Hence, when the mark  21   i  is not imaged in the search region RS, the processor  5  performs the template matching (hereinafter, also referred to as the “following template matching”) by using a reference image corresponding to the mark  21   i −1 (hereinafter, also referred to as a “reference image i−1”) or a reference image corresponding to the mark  21   i+ 1 (hereinafter, also referred to as a “reference image i+1”) so as to detect a position of the mark  21   i −1 or the mark  21   i+ 1. 
     Here, the processor  5  predicts the reference image that is used in the following template matching based on a result (detected position of the mark  21   i ) of the previous template matching. To be more specific, a first region R 1  (first detection region) is set to be adjacent to the search region RS on one side (right side in  FIG. 11 ) thereof in a movement direction of the mark  21   i , and a second region R 2  (second detection region) is set to be adjacent to the search region on the other side (left side in  FIG. 11 ) thereof. In a case where the mark  21   i  reaches the second region R 2  as illustrated in  FIG. 12 , that is, in a case where a left end of the mark  21   i  in the drawing is out of the search region RS, the processor  5  predicts that a reference image that is used in the following template matching is the reference image corresponding to the mark  21   i+ 1. On the other hand, although not illustrated, in a case where the mark  21   i  reaches the first region R 1 , that is, in a case where a right end of the mark  21   i  is out of the search region RS, the processor  5  predicts that a reference image that is used in the following template matching is the reference image corresponding to the mark  21   i −1. 
     The reference image that is used in the following template matching is described as described above, and thereby it is possible to early detect the position of the mark  21   i+ 1 or the mark  21   i −1 in the following template matching. Therefore, it is possible to reduce an occurrence of a blank state in which the position of the mark  21  is not detected, and thus it is possible to improve the detection accuracy. 
     By comparison, in a case where the reference image that is used in the following template matching as described above is not predicted, and the mark  21   i  is not imaged in the search region RS, it is necessary to perform the template matching by using all of the reference images corresponding to the n marks  21  sequentially and select a reference image having the maximum similarity. Therefore, a large amount computation is likely to be performed for the template matching in the processor  5 . As a result, a period of time of a blank state in which the position of the mark  21  is prolonged, and thus there is a possibility that the detection accuracy will be degraded. 
     In  FIGS. 11 and 12 , the first region R 1  and the second region R 2  do not overlap each other in the search region RS; however, when the previous mark  21  reaches the first region R 1  or the second region R 2 , the next mark  21  may be imaged without a defect in the search region RS, and the first region R 1  and the second region R 2  may be set to overlap each other in at least a part thereof in the search region RS. 
     Hereinafter, a flow of determination of the reference image in the processor  5  will be described with reference to  FIGS. 13 and 14 . 
       FIG. 13  is a flowchart illustrating a method for determining the reference image that is used in the first template matching.  FIG. 14  is a flowchart illustrating a method for determining (a method for predicting) the reference image that is used in the following template matching. 
     First, as illustrated in  FIG. 13 , in the first template matching, i is set to 1 (Step S 31 ). A search in the search region RS is performed by using the reference image i (i=1 at first), and the maximum similarity Ci is stored to correspond to a number i in the storage unit  6  (Step S 32 ). Then, whether or not the number i is equal to N is determined (Step S 33 ). In a case where i is equal to N (NO in Step S 33 ), i+1 is set as i (Step S 34 ), and the process proceeds to Step S 32  described above. Consequently, the maximum similarities Ci (C 1  to CN) from the reference image i (i=1) to the reference image i (i=N) are stored to correspond to the numbers i (1 to N) in the storage unit  6 . 
     In a case where the number i is equal to N (YES in Step S 33 ), a number i of the maximum similarity Ci of the maximum similarities Ci (C 1  to CN) from the reference image i (i=1) to the reference image i (i=N) is obtained from information stored in the storage unit  6  (Step S 35 ), and the reference image i is determined (Step S 36 ). 
     As described above, the processor  5  obtains the maximum similarity Ci of the captured image G with each of the reference images by using the N (three or more) reference images sequentially with respect to the captured image G and selects at least one reference image from the N (three or more) reference images based on the maximum similarity Ci. Consequently, it is possible to determine the reference image i that is used in the template matching in an initial state (before starting the template matching). After the reference image i is determined, the mark  21   i  that is imaged in the search region RS is determined, and thus a reference image is predicted in the following flow. 
     First, as illustrated in  FIG. 14 , the position of the mark  21   i  is detected through the template matching performed by using the reference image i (Step S 11 ). Then, an angle A, which is a rotation angle of the scale portion  2 , is computed, based on the detected position of the mark (Step S 12 ). The angle A, which is a result of the computation, is output (Step S 13 ). 
     Next, whether or not the reference image i acquired along with the movement of the mark  21   i  reaches the second region R 2  is determined (Step S 14 ). In a case where the reference image i reaches the second region R 2  (YES in Step S 14 ), i+1 is set as i (Step S 15 ). In other words, in this case, a reference image that is used in the following template matching is predicted to be the reference image i+1 corresponding to the mark  21   i+ 1. Then, whether or not an end instruction is issued is determined (Step S 18 ). In a case where the end instruction is not issued (NO in Step S 18 ), the process proceeds to Step S 11  described above, and the following template matching using the reference image i+1 is performed. 
     On the other hand, in a case where the reference image i acquired along with the movement of the mark  21   i  does not reach the second region R 2  (NO in Step S 14 ), whether or not the reference image i acquired along with the movement of the mark  21   i  reaches the first region R 1  is determined (Step S 16 ). In a case where the reference image i reaches the first region R 1  (YES in Step S 16 ), i−1 is set as i (Step S 17 ). In other words, in this case, a reference image that is used in the following template matching is predicted to be the reference image i−1 corresponding to the mark  21   i −1. Then, whether or not the end instruction is issued is determined (Step S 18 ). In a case where the end instruction is not issued (NO in Step S 18 ), the process proceeds to Step S 11  described above, and the following template matching using the reference image i−1 is performed. 
     In addition, in a case where the reference image i acquired along with the movement of the mark  21   i  does not reach the first region R 1  or the second region R 2  (NO in Step S 14  and NO in Step S 16 ), Steps S 11  to S 13  described above are repeated until the reference image i reaches the first region R 1  or the second region R 2  or the end instruction is issued. 
     Measurement Error Due to Axial Run-Out and Reduction Thereof 
       FIG. 15  is a schematic diagram illustrating a relationship between run-out of a rotary shaft and a first movement amount and a second movement amount.  FIG. 16  is a schematic diagram illustrating a relationship between the effective visual field region and a movement locus of the scale portion.  FIG. 17  is a graph illustrating a relationship between a rotation angle and an error in angle measurement by using the first imaging element.  FIG. 18  is a graph illustrating a relationship between a rotation angle and an error in angle measurement by using the second imaging element.  FIG. 19  is a graph illustrating a relationship between a rotation angle and a measurement error in angle measurement by using the first imaging element and the second imaging element.  FIG. 20  is a graph illustrating a relationship between a positional deviation and a measurement error of the first imaging element and the second imaging element. 
     As described above, the processor  5  estimates the rotation states by using both of the captured images acquired by the first imaging element  31   a  and the second imaging element  31   b , and thereby the measurement error due to axial run-out along with the rotation of the output shaft of the speed reducer  112  is decreased. Hereinafter, a principle thereof will be described. Hereinafter, for convenience of description, the first detector  3   a  and the second detector  3   b  are disposed with respect to each other such that a tangential line to the arc C at an intersection point between the center line LY and the arc C as the locus of the mark  21  is parallel to the X axis. In addition, as illustrated in  FIGS. 15 and 16 , a direction in which the mark  21  that moves in the effective visual field region RU faces is defined as a forward direction of the X axis, and a direction in which the mark  21  that moves in the effective visual field region RU moves away from the first axis J 1  is defined as a forward direction of the Y axis. In addition, it is preferable that the effective visual field region RU is a region in which an aberration or an image distortion of the lens is low. 
     The mark  21  is imaged at the center of the effective visual field region RU of the first imaging element  31   a  and the second imaging element  31   b  at a time point 0. Then, at a time point t, as illustrated in  FIG. 15 , when the scale portion  2  rotates around the first axis J 1  at the rotation angle θ clockwise and the first axis J 1  translates, a translation vector is represented by (Dx, Dy) in a coordinate system of the first imaging element  31   a  and is represented by (−Dx, −Dy) in a coordinate system of the second imaging element  31   b . In other words, the translation vectors in the coordinate systems of the first imaging element  31   a  and the second imaging element  31   b  are opposite to each other. 
     Here, when the template matching is performed with respect to the effective visual field regions RU of both the first imaging element  31   a  and the second imaging element  31   b , movement vectors Va and Vb of the reference image are obtained. The movement vectors Va and Vb are resultant vectors of the translation vectors described above and the original movement vectors V in a case where translation of the first axis J 1  does not occur. Hence, when the movement vectors Va and Vb are added to be divided by 2, it is possible to offset the translation vector and obtain the original movement vector (Lx, Ly). The movement vector Va is a first movement amount of a first mark  21   a  imaged by the first imaging element  31   a . In addition, the movement vector Vb is a second movement amount of a second mark  21   b  imaged by the second imaging element  31   b.    
     In addition, since the arc C has a sufficiently large radius, the arc C in the effective visual field region RU can approximate to a straight line having only an X-axis-direction component. Therefore, when an X-axis-direction component Lx of the original movement vector is found, it is possible to obtain the rotation angle θ by using a relational expression of θ=arcsin (Lx/R). 
     In the relational expression, R represents the radius of the arc C. At the time point 0, when a distance between the first axis J 1  and the first imaging element  31   a  is represented by RA, and a distance between the first axis J 1  and the second imaging element  31   b  is represented by RB (RA and RB are not illustrated), an average of the distances RA and RB has a relationship of (RA+RB)/2=R and t and is constant at the time points 0. Hence, when the radius R is accurately measured in advance, it is possible to obtain the rotation angle θ through the above-described method without an influence of the translation of the first axis J 1 . In addition, when the rotation angle θ is minute, it is possible to obtain an approximate relationship of sin θ ≈θ [radian], and it is possible to obtain the rotation angle θ through simply computation of a relational expression of θ=Lx/R. In a case where it is possible to tolerate an error, which occurs by approximating the arc C to the straight line having only the X-axis-direction component, to 1 arcsec ( 1/3600 degrees), the relational expression can is applied within a range in which θ is 0.041 rad (2.3 degrees) or smaller. 
     In this manner, it is possible to calculate the rotation angle θ by using the movement vector Va (first movement amount) obtained by performing template matching with the captured image G acquired by the first imaging element  31   a  and the movement vector Vb (second movement amount) obtained by performing the template matching with the captured image G acquired by the second imaging element  31   b.    
     In a case where the rotation angle θ is calculated by using only the movement vector Va (first movement amount), an angle error (hereinafter, also referred to as a “first angle error”) that changes with time as illustrated in  FIG. 17  due to dynamic eccentricity (axial run-out) of the first axis J 1  along with the rotation of the output axis of the speed reducer  112  occurs. On the other hand, in a case where the rotation angle θ is calculated by using only the movement vector Vb (second movement amount), an angle error (hereinafter, also referred to as a “second angle error”) that changes with time as illustrated in  FIG. 18  due to dynamic eccentricity of the first axis J 1  along with the rotation of the output axis of the speed reducer  112  occurs. 
     Here, when one of the first angle error and the second angle error increases on the plus side, the other angle error increases on the minus side. Hence, as described above, when the rotation angle θ is calculated by using the movement vector Va (first movement amount) and the movement vector Vb (second movement amount), the first angle error and the second angle error are offset or reduced as by each other, and the angle error is small as illustrated in  FIG. 19 . 
     In order to reduce the angle error, as illustrated in  FIG. 15 , an angle β formed between a straight line La that connects the first axis J 1  and the first imaging element  31   a  and a straight line Lb that connects the first axis J 1  and the second imaging element  31   b  is most preferably 180 degrees, when viewed in a direction parallel to the first axis J 1  (rotary shaft); however, it is possible to tolerate an angular deviation within a range of ±6 degrees with respect to 180 degrees (hereinafter, also simply referred to as the “angular deviation”). Hereinafter, a reason thereof will be described. 
     An eccentricity amount of the dynamic rotary shaft along with the rotation of the output shaft in a common speed reducer (for example, a wave speed reducer) is about ±20 μm. In such a case, an angle error due to the dynamic eccentricity increases as the angular deviation increases, as illustrated in  FIG. 20 . Here, in a case where a total tolerable accuracy error is 1 arcsec, it is preferable to suppress the angle error due to the eccentricity to about 0.5 arcsec. Then, as found from  FIG. 20 , it is preferable that the angular deviation is 6 degrees or smaller. 
     In this manner, the angle β formed between the straight line La that connects the first axis J 1  and the first imaging element  31   a  and the straight line Lb that connects the first axis J 1  and the second imaging element  31   b  is preferably in a range from 174 degrees to 186 degrees, when viewed in a direction parallel to the first axis J 1  (rotary shaft). Consequently, it is possible to suppress the accuracy error to 1 arcsec or smaller. More preferably, the angular deviation is 4 degrees or smaller, and thereby it is possible to suppress the angle error due to the eccentricity to 0.2 arcsec or smaller. 
     As described above, the encoder unit  10  includes the speed reducer  112  that has the output shaft which rotates around the first axis J 1  (rotary shaft) so as to output the drive force and the encoder  1  that measures the rotation angle of the output shaft of the speed reducer  112 . The encoder  1  includes the first arm  120  as the rotary unit, which rotates around the first axis J 1  along with the rotation of the output shaft of the speed reducer  112 , the scale portion  2  that is disposed on the first arm  120  in the circumferential direction around the first axis J 1  and has the first mark  21   a  and the second mark  21   b , the first imaging element  31   a  that images the first mark  21   a , the second imaging element  31   b  that is disposed at the position symmetrical with the first imaging element  31   a  with respect to the first axis J 1  and images the second mark  21   b , the processor  5  that performs the process of obtaining the rotation angle of the first arm  120  based on the imaging results imaged by the first imaging element  31   a  and the second imaging element  31   b , and a storage unit  6  that stores the instruction that is readable by the processor  5 . The processor  5  reads the instruction from the storage unit  6  such that the template matching with the image captured by the first imaging element  31   a  is performed to obtain the movement vector Va (first movement amount) in the circumferential direction of the first mark  21   a  around the first axis J 1 , the template matching with the image captured by the second imaging element  31   b  is performed to obtain the movement vector Vb (second movement amount) in the circumferential direction of the second mark  21   b  around the first axis J 1 , and the rotation angle θ is calculated and output by using the movement vector Va and the movement vector Vb. 
     According to the encoder unit  10 , it is possible to reduce the error by the eccentricity of the scale portion  2  due to the axial run-out of the output shaft of the speed reducer  112 , and thus it is possible to enhance the measurement accuracy. 
     Here, it is preferable that the processor  5  performs the template matching by using a reference image (first reference image corresponding to the first mark  21   a ) in association with information on the angle, when obtaining the movement vector Va (first movement amount). Consequently, it is possible to measure the rotation angle of the first arm  120 , as an absolute angle. Similarly, it is preferable that the processor  5  performs the template matching by using a reference image (second reference image corresponding to the second mark  21   b ) in association with information on the angle, when obtaining the movement vector Vb (second movement amount). 
     In addition, in the angle measuring method of the embodiment, the rotation angle of the output shaft of the speed reducer  112  is measured by using the encoder  1  that includes the first arm  120  as the rotary unit, which rotates around the first axis J 1  along with the rotation of the output shaft of the speed reducer  112  that has the output shaft which rotates around the first axis J 1  (rotary shaft) so as to output the drive force, the scale portion  2  that is disposed on the first arm  120  in the circumferential direction around the first axis J 1  and has the first mark  21   a  and the second mark  21   b , the first imaging element  31   a  that images the first mark  21   a , and the second imaging element  31   b  that is disposed at the position symmetrical with the first imaging element  31   a  with respect to the first axis J 1  and images the second mark  21   b . Here, the angle measuring method includes a step of performing the template matching with the image captured by the first imaging element  31   a  and obtaining the movement vector Va (first movement amount) in the circumferential direction of the first mark  21   a  around the first axis J 1 , a step of performing the template matching with the image captured by the second imaging element  31   b  and obtaining the movement vector Vb (second movement amount) in the circumferential direction of the second mark  21   b  around the first axis J 1 , and a step of calculating and outputting the rotation angle of the first arm  120  by using the movement vector Va and the movement vector Vb. 
     According to the angle measuring method, it is possible to reduce the error by the eccentricity of the scale portion  2  due to the axial run-out of the output shaft of the speed reducer  112 , and thus it is possible to enhance the measurement accuracy. 
     Second Embodiment 
       FIG. 21  is a schematic diagram illustrating a relationship between an effective visual field region and a movement locus of the scale portion in a second embodiment of the invention.  FIG. 22  is a diagram for illustrating a correction factor in the second embodiment of the invention.  FIG. 23  is a flowchart illustrating a flow of obtaining the correction factor in the second embodiment of the invention. 
     Hereinafter, the second embodiment is described by focusing on differences from the embodiment described above, and the same description is omitted. 
     The embodiment is the same as the first embodiment described above except that the correction factor of an inclination of the imaging region is used when the rotation angle is calculated. 
     In the first embodiment described above, a case where the tangential line to the arc C at the intersection point between the center line LY and the arc C as the locus of the mark  21  is parallel to the X axis is described. However, an effort needs to be put for adjusting a posture of the effective visual field region RU with high accuracy. Hereinafter, a problem and a correction method of the problem of the case where the tangential line to the arc C at the intersection point between the center line LY and the arc C as the locus of the mark  21  is not parallel to the X axis are described. 
     When η represents an inclined angle of the X axis with respect to the tangential line of the arc C at the intersection point between the center line LY and the arc C as the locus of the mark  21 , and (Dx′, Dy′) represents translation components that are observed by the first imaging element  31   a  and the second imaging element  31   b  when the first axis J 1  is translated by the translation components (Dx, Dy), similarly to the description of the first embodiment above described, the following relationship is satisfied. 
     
       
         
           
             
               
                 
                   
                     Dx 
                     = 
                     
                       
                         
                           
                             Dx 
                             2 
                           
                           + 
                           
                             Dy 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               arctan 
                               ⁡ 
                               
                                 ( 
                                 
                                   Dy 
                                   Dx 
                                 
                                 ) 
                               
                             
                             - 
                             η 
                           
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     Dy 
                     = 
                     
                       
                         
                           
                             Dx 
                             2 
                           
                           + 
                           
                             Dy 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             
                               arctan 
                               ⁡ 
                               
                                 ( 
                                 
                                   Dy 
                                   Dx 
                                 
                                 ) 
                               
                             
                             - 
                             η 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     As known from the expression, in a case where the inclined angle η is different in the first imaging element  31   a  and the second imaging element  31   b  from each other, it is not possible to make the translation vector to zero by only adding the movement vectors Va and Vb and dividing an added value by 2 unlike the above description of the first embodiment. Then, correction factor α of the inclined angle η of each of the first imaging element  31   a  and the second imaging element  31   b  is obtained in advance, and the correction factor α is used when the rotation angle θ is calculated. As illustrated in  FIG. 22 , when two coordinates on a line parallel to the tangential line to the arc C at the intersection point between the center line LY and the arc C as the locus of the mark  21  are (x1, y1) and (x2, y2), h=x1−x2, and v=y1−y2, the correction factor α satisfies a relationship of √(h 2 +v 2 )/h. Hereinafter, an example of a flow of obtaining the correction factor α will be described with reference to  FIG. 23 . 
     First, the center of the effective visual field region RU is the origin, an image having a pixel size, which is positioned at the origin, is generated and saved as a temporary template (Step S 41 ). Next, the scale portion  2  is rotated normally by a predetermined angle a (for example, 1 degree) (Step S 42 ), and then the template matching is performed by using the temporary template so as to obtain the maximum correlation coordinate (x1, y1) (Step S 43 ). Next, the scale portion  2  is rotated reversely by the angle a (Step S 44 ) and further rotated reversely by the angle z (Step S 45 ), and then, similarly, the template matching is performed by using the temporary template so as to obtain the maximum correlation coordinate (x2, y2) (Step S 46 ). The pixel movement amounts h and v are obtained from two obtained coordinates (x1, y1) and (x2, y2) (Step S 47 ), and the correction factor α is obtained from the pixel movement amounts h and v (Step S 48 ). 
     As described above, the correction factor α is obtained. The correction factor α is a factor for converting the coordinate system that is inclined by η into a coordinate system in which η=0. The correction factor α is multiplied to a movement amount Dx′ observed on the coordinate system that is inclined by η, and thereby it is possible to obtain a real movement amount Dx on the coordinate system in which η=0. In other words, Dx=Dx′xα. Such conversion is performed for each of the first imaging element  31   a  and the second imaging element  31   b , and thereby it is possible to consider η=0 in the effective visual field regions RU of both elements. After the conversion, similarly to the first embodiment described above, the rotation angle θ is obtained. 
     As described above, the first imaging element  31   a  has the plurality of pixels arranged in a matrix shape in directions along the X axis and the Y axis which are orthogonal to each other. The storage unit  6  stores angular deviation information which is information on an angular deviation from each of a direction (Y-axis direction), in which the first imaging element  31   a  and the second imaging element  31   b  are aligned, and the direction along the X axis. The processor  5  calculates the rotation angle of the first arm  120  by using the angular deviation information. Consequently, it is possible to enhance the measurement accuracy regardless of the posture of the first imaging element  31   a . The same is true of the second imaging element  31   b.    
     The angular deviation information is not particularly limited; however, in the embodiment, the processor  5  uses the correction factor α as the angular deviation information. Here, when any position of the scale portion  2  is moved from the first position (x1, y1) to a second position (x2, y2) different from the first position in the captured image G of the first imaging element  31   a, h  represents a distance between the first position and the second position in the direction along the X axis, v represents a distance between the first position and the second position in the direction along the Y axis, and α represents the correction factor, a relationship of α=√/(h 2 +v 2 )/h is satisfied. Consequently, it is possible to easily acquire the correction factor α as the angular deviation information. 
     In addition, the angle measuring method of the embodiment further includes a step of obtaining the correction factor α and storing the correction factor in the storage unit  6  before the first movement amount and the second movement amount are obtained, in addition to the steps of the first embodiment described above. In the step of calculating and outputting the rotation angle θ, the rotation angle θ is calculated by using the correction factor α. Consequently, it is possible to enhance the measurement accuracy regardless of the posture of the first imaging element. 
     Also in the second embodiment described above, it is possible to achieve the same effects as those in the first embodiment described above. 
     Third Embodiment 
       FIG. 24  is a perspective view illustrating a robot according to a third embodiment of the invention. 
     Hereinafter, a side of the base  210  of a robot  100 C is referred to as a “proximal end side”, and a side of the end effector is referred to as a “distal end side”. 
     Hereinafter, the third embodiment is described by focusing on differences from the embodiments described above, and the same description is omitted. 
     The robot  100 C illustrated in  FIG. 24  is a vertical articulated (six-axis) robot. The robot  100 C includes the base  210  and a robotic arm  200 , and the robotic arm  200  includes a first arm  220 , a second arm  230 , a third arm  240 , a fourth arm  250 , a fifth arm  260 , and a sixth arm  270 . The arms are connected in this order from the proximal end side toward the distal end side. Although not illustrated, the end effector such as a hand, which grips is precision measuring equipment, a component, or the like, is detachably attached in a distal portion of the sixth arm  270 . In addition, although not illustrated, the robot  100 C includes a robot control device (control unit) such as a personal computer (PC) that controls motion of the members of the robot  100 C. 
     Here, The base  210  is fixed to a floor, a wall, a ceiling, or the like, for example. The first arm  220  is rotationally movable around a first rotation axis O 1  with respect to the base  210 . The second arm  230  is rotatably movable around a second rotation axis O 2  orthogonal to the first rotation axis O 1 , with respect to the first arm  220 . The third arm  240  is rotatably movable around a third rotation axis O 3  that is parallel to the second rotation axis O 2 , with respect to the second arm  230 . The fourth arm  250  is rotatably movable around a fourth rotation axis O 4  orthogonal to the third rotation axis O 3 , with respect to the third arm  240 . The fifth arm  260  is rotatably movable around a fifth rotation axis O 5  orthogonal to the fourth rotation axis O 4 , with respect to the fourth arm  250 . The sixth arm  270  is rotatably movable around a sixth rotation axis O 6  orthogonal to the fifth rotation axis O 5 , with respect to the fifth arm  260 . In the first rotation axis to the sixth rotation axis O 6 , “to be orthogonal” includes a case where an angle formed between two axes is within a range from 90° to ±5°, and “to be parallel” includes a case where one of the two axes is inclined with respect to the other axis in a range of ±5°. 
     In addition, as a drive source the drives the first arm  220  with respect to the base  210 , a motor (not illustrated) and the encoder unit  10  are provided. For example, the measurement result of the encoder  1  included in the encoder unit  10  is input to the robot control device (not illustrated) and is used for drive control of the drive source that rotates the first arm  220  with respect to the base  210 . In addition, although not illustrated, a motor and an encoder unit are also provided in another joint unit, and it is possible to use the encoder unit  10  as the encoder unit. 
     As described above, the robot  100 C includes the base  210 , which is the first member, the first arm  220 , which is the second member that moves rotationally with respect to the base  210 , and the encoder unit  10 . Here, the encoder unit  10  includes the speed reducer  112  that has the output shaft which rotates around the rotary shaft so as to output a drive force and the encoder  1  that measures the rotation angle of the output shaft of the speed reducer  112 . The output shaft of the speed reducer  112  is connected to the first arm  220 . According to the robot  100 C, it is possible to measure the rotation angle of the first arm  220  with high accuracy and to perform drive control of the first arm  220  with high accuracy based on a detection result thereof. 
     In the above description, a case where the encoder detects the rotation state of the first arm  220  with respect to the base  210  is described; however, it is also possible to dispose another joint unit such that the encoder measures a rotation state of another arm. In this case, an arm on one side of the joint unit may be set as the first member, and the arm on the other side of the joint unit may be set as the second member. 
     As described above, the encoder unit, the angle measuring method, and the robot according to the invention are described on the basis of the preferred embodiments in the figures; however, the invention is not limited thereto, and it is possible to replace the configurations of the members with any configurations having the same functions. In addition, another configurational component may be attached. In addition, combinations of the two or more embodiments described above may be combined. 
     In addition, the encoder according to the invention can be applied to any type of absolute type and incremental type. 
     In addition, in the embodiments described above, a case where the base of the robot is a “base unit (first member), and the first arm is the “rotary unit (second member) is described as an example; however, the invention is not limited thereto, and one of any two members which relatively move rotationally can be the “base unit”, and the other can be the “rotary unit”. In other words, an installation position of the encoder is not limited to the joint unit between the base and the first arm and may be a joint unit between any two arms that relatively moves rotationally. In addition, the installation position of the encoder is not limited to the joint unit provided in the robot. 
     In addition, in the embodiments described above, the one robotic arm is provided; however, the number of the robotic arms is not limited to one, and two or more arms may be provided. In other words, the robot according to the invention may be a multi-arm robot such as a double-arm robot, for example. 
     In addition, in the embodiments described above, the robot arm has two or six arms; however, the number of arms is not limited thereto, and the robot may have one arm or may have three or more, five or more, or seven or more arms. 
     In addition, in the embodiments described above, an installation position of the robot according to the invention is not limited to the floor and may be a ceiling surface or a side wall surface or a moving object such as an automatic guided vehicle. In addition, the robot according to the invention is not limited to a robot that is fixed to be installed in a structure such as a building and may be a legged walking (mobile) robot having a leg unit, for example. 
     The entire disclosure of Japanese Patent Application No. 2018-025438, filed Feb. 15, 2018 is expressly incorporated by reference herein.