Patent Publication Number: US-2023143243-A1

Title: Attitude angle derivation device and attitude angle sensor

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2021-181568, filed on Nov. 8, 2021; the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to an attitude angle derivation device and an attitude angle sensor. 
     BACKGROUND 
     There is a sensor such as a gyro sensor or the like. The attitude (the attitude angle) of an object can be detected by the sensor. It is desirable to detect the attitude angle with high accuracy. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic view illustrating an attitude angle derivation device according to a first embodiment; 
         FIG.  2    is a schematic view illustrating an attitude angle derivation device according to the first embodiment; 
         FIG.  3    is a schematic view illustrating an attitude angle derivation device according to the first embodiment; 
         FIG.  4    is a schematic view illustrating an attitude angle derivation device according to the first embodiment; 
         FIGS.  5 A and  5 B  are schematic views illustrating a sensor according to the embodiment; 
         FIG.  6    is a schematic view illustrating the electronic device according to a third embodiment; and 
         FIGS.  7 A to  7 H  are schematic views illustrating applications of the electronic device. 
     
    
    
     DETAILED DESCRIPTION 
     According to one embodiment, an attitude angle derivation device includes an acquisition part, a storage, and a processor. The acquisition part is configured to acquire a rotation angle related to a first coordinate system. The rotation angle is obtained from an angle sensor located in an object. The storage is configured to store the rotation angle and an attitude angle. The attitude angle is related to a second coordinate system of the object. The processor is configured to acquire the rotation angle and the attitude angle, update the attitude angle based on a temporal change of the rotation angle derived from the rotation angle, and output the updated attitude angle. 
     According to one embodiment, an attitude angle sensor includes the attitude angle derivation device described above, and the angle sensor. 
     Various embodiments are described below with reference to the accompanying drawings. 
     The drawings are schematic and conceptual; and the relationships between the thickness and width of portions, the proportions of sizes among portions, etc., are not necessarily the same as the actual values. The dimensions and proportions may be illustrated differently among drawings, even for identical portions. 
     In the specification and drawings, components similar to those described previously or illustrated in an antecedent drawing are marked with like reference numerals, and a detailed description is omitted as appropriate. 
     First embodiment 
       FIG.  1    is a schematic view illustrating an attitude angle derivation device according to a first embodiment. 
     As shown in  FIG.  1   , the attitude angle derivation device  50  according to the embodiment includes an acquisition part  58 , storage  55 , and a processor  50 P. 
     The acquisition part  58  is configured to acquire an angle (a rotation angle DA 1 ) obtained from an angle sensor  110 . The acquisition part  58  is, for example, an interface circuit (I/F). 
     As described below, the angle sensor  110  is located in an object. The angle sensor  110  includes, for example, an integrating gyroscope (e.g., a Rate Integrating Gyroscope (RIG)). The angle sensor  110  may be a RIG. 
     The rotation angle DA 1  can be directly detected using the angle sensor  110 . In the gyroscope of a reference example, an angular velocity is detected. The angle can be detected by integrating the detected angular velocity. 
     According to the embodiment, an integrating gyroscope is applied to the angle sensor  110 . Thereby, for example, cumulative error of the integration does not occur. The angle sensor  110  is, for example, a three-axis angle sensor. 
     The angle (the rotation angle DA 1 ) that is obtained from the angle sensor  110  is related to a first coordinate system. For example, the first coordinate system is referenced to the position at which the angle sensor  110  is located. The first coordinate system is, for example, a sensor coordinate system or a body coordinate system. 
     The rotation angle DA 1  may include, for example, a first rotation angle A x  related to a first axis, a second rotation angle A y  related to a second axis, and a third rotation angle A z  related to a third axis. The second axis crosses the first axis. The third axis crosses a plane including the first and second axes. For example, the first axis is an X-axis. The second axis is a Y-axis. The third axis is a Z-axis. For example, the second axis is orthogonal to the first axis. The third axis is orthogonal to the first and second axes. 
     The first rotation angle A x  corresponds to the angle of the rotation around the first axis. The second rotation angle A y  corresponds to the angle of the rotation around the second axis. The third rotation angle A z  corresponds to the angle of the rotation around the third axis. 
     One time is taken as a first time t. The rotation angle DA 1  includes the first rotation angle A x(t)  at the first time t, the second rotation angle A y(t)  at the first time t, and the third rotation angle A z(t)  at the first time t. The one time before the first time t is taken as a second time (t- 1 ). The first rotation angle A x  at the second time (t- 1 ) is taken as the first rotation angle A x(t-1) . The second rotation angle A y  at the second time (t- 1 ) is taken as the second rotation angle A y(t-1) . The third rotation angle A z  at the second time (t- 1 ) is taken as the third rotation angle A z(t-1) . The rotation angle DA 1  may include the first rotation angle A x(t-1) , the second rotation angle A y(t-1) , and the third rotation angle A z(t-1) . The rotation angle DA 1  is supplied from the angle sensor  110  to the acquisition part  58 . 
     For example, the storage  55  is configured to store the rotation angle DA 1  supplied from the acquisition part  58 . The storage  55  is configured to store an attitude angle DA 2  of the object in which the angle sensor  110  is located. The storage  55  is memory (or storage). The storage  55  may be buffer memory. The storage  55  is configured to store the rotation angle DA 1 . 
     The attitude angle DA 2  is related to a second coordinate system of the object. The second coordinate system may be different from the first coordinate system. In one example, the second coordinate system is, for example, an absolute coordinate system. For example, the second coordinate system may be referenced to the orientation of the acceleration due to gravity. The second coordinate system may be, for example, a spatial coordinate system or a reference coordinate system. The second coordinate system may be global coordinates. 
     The attitude angle DA 2  is, for example, a three-dimensional attitude angle. The attitude angle DA 2  includes, for example, a first attitude angle ϕ related to the first attitude axis, a second attitude angle θ related to the second attitude axis, and a third attitude angle ψ related to the third attitude axis. The second attitude axis crosses the first attitude axis. The third attitude axis crosses a plane including the first and second attitude axes. For example, the second attitude axis is orthogonal to the first attitude axis. The third attitude axis is orthogonal to the first and second attitude axes. The first to third attitude axes may be different from the first to third axes. 
     The first attitude angle ϕ corresponds to the angle of the rotation around the first attitude axis. The second attitude angle θ corresponds to the angle of the rotation around the second attitude axis. The third attitude angle ψ corresponds to the angle of the rotation around the third attitude axis. 
     The storage  55  may store the attitude angle DA 2  at the second time (t- 1 ). The attitude angle DA 2  includes the first attitude angle ϕ (t-1)  at the second time (t- 1 ), the second attitude angle θ (t-1)  at the second time (t- 1 ), and the third attitude angle ψ (t-1)  at the second time (t- 1 ). The attitude angle DA 2  may be supplied from the storage  55  to the processor  50 P. 
     The processor  50 P acquires the rotation angle DA 1  and the attitude angle DA 2 . For example, the rotation angle DA 1  that is supplied from the acquisition part  58  to the storage  55  is acquired from the storage  55  by the processor  50 P. For example, the processor  50 P acquires the attitude angle DA 2  from the storage  55 . The processor  50 P is configured to update the attitude angle DA 2  based on the temporal change of the rotation angle DA 1  derived from the rotation angle DA 1  and output an updated attitude angle DA 3 . 
     According to the embodiment, the attitude angle DA 3  is derived using the angle (the rotation angle DA 1 ) obtained from the angle sensor  110 . The attitude angle is not derived based on an angular velocity as in the reference example described above. Thereby, the error when integrating the angular velocity does not occur. According to the embodiment, the attitude angle can be derived (detected) with high accuracy. For example, the attitude angle can be quickly derived. 
     As described above, for example, the first rotation angle A x(t) , the second rotation angle A y(t) , the third rotation angle A z(t) , the first rotation angle A x(t-1) , the second rotation angle A y(t-1) , and the third rotation angle A z(t-1)  may be stored in the storage  55 . 
     The processor  50 P derives the first temporal change dA x(t) , the second temporal change dA y(t) , and the third temporal change dA z(t)  as the temporal change of the rotation angle DA 1 . 
     The first temporal change dA x(t) , the second temporal change dA y(t) , the third temporal change dA z(t) , the first rotation angle A x(t) , the second rotation angle A y(t) , the third rotation angle A z(t) , the first rotation angle A x(t-1) , the second rotation angle A y(t-1) , and the third rotation angle A z(t-1)  satisfy the following first formula. 
     
       
      
       dA 
       x(t) 
       =A 
       x(t) 
       −A 
       x(t-1)  
      
     
     
       
      
       dA 
       y(t) 
       =A 
       y(t) 
       −A 
       y(t-1)  
      
     
         dA   z(t)   =A   z(t)   −A   z(t-1)    (1)
 
     The processor  50 P derives such a temporal change. 
     The processor  50 P updates the derived temporal change and the attitude angle DA 2  of the second time (t- 1 ) acquired from the storage  55 . For example, the processor  50 P derives the first attitude angle ϕ (t)  of the first time t from the sum of the first attitude angle ϕ (t-1)  at the second time (t- 1 ) and a function f 1 (dA x(t) , dA y(t) , dA z(t) ). For example, the processor  50 P derives the second attitude angle θ (t)  of the first time t from the sum of the second attitude angle θ (t-1)  at the second time (t- 1 ) and a function f 2 (dA x(t) , dA y(t) , dA z(t) ). For example, the processor  50 P derives the third attitude angle ψ (t)  of the first time t from the sum of the third attitude angle ψ (t-1)  at the second time (t- 1 ) and a function f 3 (dA x(t) , dA y(t) , dA z(t) ). 
     Thus, according to the embodiment, the temporal change of the rotation angle DA 1  is derived from the angle (the rotation angle DA 1 ) obtained from the angle sensor  110 . The attitude angle DA 2  is updated based on the temporal change of the derived rotation angle DA 1 ; and the updated attitude angle DA 3  is derived. The attitude angle DA 3  includes, for example, the first attitude angle φ (t) , the third attitude angle θ (t) , and the third attitude angle ψ (t) . 
     Several examples of the processor  50 P will now be described. 
       FIG.  2    is a schematic view illustrating an attitude angle derivation device according to the first embodiment. 
     In the attitude angle derivation device  50 A according to the embodiment as shown in  FIG.  2   , the processor  50 P may include a first calculation part  51 . The first calculation part  51  is configured to derive the temporal change of the rotation angle DA 1 . The first calculation part  51  performs the calculation of the first formula above. 
     The processor  50 P may further include a second calculation part  52 . The temporal change that is derived by the first calculation part  51  is supplied to the second calculation part  52 . The second calculation part  52  is configured to derive the change of the attitude angle based on the temporal change derived by the first calculation part  51  and the attitude angle DA 2  acquired from the storage  55 . 
     The change of the attitude angle includes, for example, the first attitude angle change dϕ (t) , the second attitude angle change dθ (t) , and the third attitude angle change dψ (t) . The first attitude angle change dϕ (t) , the second attitude angle change dθ (t) , and the third attitude angle change dψ (t)  satisfy the following second formula. 
         dϕ   (t) =( dA   y(t)  sin ϕ (t-1)   +dA   x(t)  cos ϕ (t-1) )tan θ t-1 )+ dA   x(t)  
 
         dθ   (t)   =dA   y(t)  cos ϕ (t-1)   −dA   x(t)  sin ϕ (t-1)  
 
         dψ   (t) =( dA   y(t)  sin ϕ+ dA   x(t)  cos ϕ)/cos θ (t-1)    (2)
 
     The processor  50 P may further include a third calculation part  53 . The change of the attitude angle derived by the second calculation part  52  is supplied to the third calculation part  53 . The third calculation part  53  is configured to derive the updated attitude angle DA 3  by adding the change of the attitude angle derived by the second calculation part  52  and the attitude angle DA 2  acquired from the storage  55 . 
     For example, the calculation of the following third formula is performed in the third calculation part  53 . 
       ϕ (t) =ϕ (t-1)   +dϕ   (t)  
 
       θ (t) =θ (t-1)   +dθ   (t)  
 
       ψ (t) =φ (t-1)   +dψ   (t)    (3)
 
     Thus, the processor  50 P (e.g., the third calculation part  53 ) is configured to derive, as the updated attitude angle DA 3 , the first attitude angle ϕ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t. The first attitude angle ϕ (t) , the second attitude angle θ (t) , and the third attitude angle ψ (t)  satisfy the third formula above. The result of the calculation of the third formula corresponds to the attitude angle DA 3  to be derived. 
     According to the embodiment, the processor  50 P (e.g., the third calculation part  53 ) may supply the updated attitude angle DA 3  to the storage  55 . The storage  55  is configured to store the updated attitude angle DA 3 . The processing described above may be repeatedly performed. The attitude angle at any subsequent time may be derived using the updated attitude angle DA 3 . 
     Euler angles may be used in the embodiment as described above. Quaternions are applicable as the attitude angle in the embodiment as follows. 
     For example, the attitude angle DA 2  can be represented by a first quaternion value α, a second quaternion value β, a third quaternion value γ, and a fourth quaternion value δ. For example, the attitude angle DA 2  includes the first quaternion value α, the second quaternion value β, the third quaternion value γ, and the fourth quaternion value δ. 
       FIG.  3    is a schematic view illustrating an attitude angle derivation device according to the first embodiment. n the attitude angle derivation device  50 B according to the embodiment as shown in  FIG.  3   , the processor  50 P includes the first to third calculation parts  51  to  53 . A calculation similar to the calculation described above is performed in the first calculation part  51 . 
     The attitude angle DA 2  includes the first quaternion value α (t-1)  at the second time (t- 1 ), the second quaternion value β (t-1)  at the second time (t- 1 ), the third quaternion value γ (t-1)  at the second time (t- 1 ), and the fourth quaternion value δ (t-1)  at the second time (t- 1 ). These quaternion values are supplied to the processor  50 P (the second calculation part  52  and the third calculation part  53 ). 
     The processor  50 P (the second calculation part  52 ) derives the first quaternion value change dα (t) , the second quaternion value change dβ (t) , the third quaternion value change dγ (t) , and the fourth quaternion value change dδ (t)  as the change of the attitude angle DA 2 . 
     The first quaternion value change dα (t) , the second quaternion value change dβ (t) , the third quaternion value change dγ (t) , and the fourth quaternion value change dδ (t)  satisfy the following fourth formula. 
         dα   (t) =−0.5(β (t-1)   dA   x(t) +γ (t-1)   dA   y(t) +δ (t-1)   dA   z(t) )
 
         dβ   (t) =−0.5(α (t-1)   dA   x(t) −δ (t-1)   dA   y(t) +γ (t-1)   dA   z(t) )
 
         dγ   (t) =−0.5(δ d   (t-1)   dA   x(t) +α (t-1)   dA   y(t) +β (t-1)   dA   z(t) )
 
         dδ   (t) =−0.5(γ (t-1)   dA   x(t) −β (t-1)   dA   y(t) +α (t-1)   dA   z(t) )   (4)
 
     For example, the second calculation part  52  performs the calculation of the fourth formula above by using the temporal change of the rotation angle (the first temporal change dA x(t) , the second temporal change dA y(t) , and the third temporal change dA z(t) ) and the attitude angle DA 2  acquired from the storage  55 . 
     The processor  50 P (the third calculation part  53 ) derives the first quaternion value α (t)  at the first time t, the second quaternion value β (t)  at the first time t, the third quaternion value γ (t)  at the first time t, and the fourth quaternion value δ (t)  at the first time t as the updated attitude angle DA 3 . 
     The first quaternion value α (t)  at the first time t, the second quaternion value β (t)  at the first time t, the third quaternion value γ (t)  at the first time t, and the fourth quaternion value δ (t)  at the first time t satisfy the following fifth formula. 
       α (t) =α (t-1)   +dα   (t)  
 
       β (t) =β (t-1)   +dβ   (t)  
 
       γ (t) =γ (t-1)   +dγ   (t)  
 
       δ (t) =δ (t-1)   +dδ   (t)    (5)
 
     The calculation of the fifth formula above is performed in the third calculation part  53 ; and the first quaternion value α (t) , the second quaternion value β (t) , the third quaternion value γ (t) , and the fourth quaternion value δ (t)  are derived as the updated attitude angle DA 3 . 
     The quaternion values may be transformed into Euler angles as described below. 
       FIG.  4    is a schematic view illustrating an attitude angle derivation device according to the first embodiment. 
     In the attitude angle derivation device  50 C according to the embodiment as shown in  FIG.  4   , the processor  50 P includes a fourth calculation part  54 . Otherwise, the configuration of the attitude angle derivation device  50 C may be similar to that of the attitude angle derivation device  50 B. 
     In the attitude angle derivation device  50 C, the processor  50 P (the fourth calculation part  54 ) derives, as the updated attitude angle DA 3 , the first attitude angle ϕ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t based on the first quaternion value α (t)  at the first time t, the second quaternion value β (t)  at the first time t, the third quaternion value γ (t)  at the first time t, and the fourth quaternion value δ (t)  at the first time t. 
     The first attitude angle δ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t satisfy the following sixth formula. 
     
       
         
           
             
               
                 
                                    
                   
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                   6 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ? 
             
             indicates text missing or illegible when filed 
           
         
       
     
     For example, the calculation of the sixth formula above is performed by the fourth calculation part  54 . Thereby, the quaternion values are transformed into Euler angles. 
     According to the embodiment, for example, a digital arithmetic device is applicable as the processor  50 P. According to the embodiment, at least a part of the processor  50 P may include an analog circuit. According to the embodiment, the configuration of the processor  50 P is arbitrary. 
     According to the embodiment, the updated attitude angle DA 3  may be output via the acquisition part  58  (e.g., an interface). The acquisition part  58  may function as an output part. 
     Second Embodiment 
     An attitude angle sensor  210  according to a second embodiment (see  FIGS.  1  to  4   ) includes the angle sensor  110  and the attitude angle derivation device (the attitude angle derivation devices  50  to  50 C, etc.) according to the embodiment. According to the attitude angle sensor  210  according to the embodiment, an attitude angle sensor that can detect an attitude angle with high accuracy can be provided. 
     An example of the angle sensor  110  will now be described. 
       FIGS.  5 A and  58    are schematic views illustrating a sensor according to the embodiment. 
       FIG.  5 A  is a plan view.  FIG.  58    is a line A 1 -A 2  cross-sectional view of  FIG.  5 A . As shown in  FIGS.  5 A and  5 B , the angle sensor  110  according to the embodiment includes a base body  60 , a structure body  60 A, and a control device  70 . The angle sensor  110  is located in an object  90 . For example, the angle sensor  110  is fixed to the object  90 . 
     The base body  60  includes a first surface  60 F. The structure body  60 A is, for example, a RIG. 
     The structure body  60 A includes a movable member  10 . The movable member  10  can vibrate. The vibration of the movable member  10  includes a first component and a second component. The first component is along a first direction D 1 . The second component is along a second direction D 2 . The first direction D 1  is along the first surface  60 F. The second direction D 2  crosses the first direction D 1  and is along the first surface  60 F. 
     The first surface  60 F is taken as an X 1 -Y 1  plane. One direction in the X 1 -Y 1  plane is taken as an X 1 -axis direction. A direction perpendicular to the X 1 -axis direction along the X 1 -Y 1  plane is taken as a Y 1 -axis direction. A direction perpendicular to the X 1 -axis direction and the Y 1 -axis direction is taken as a Z 1 -axis direction. The first direction D 1  is, for example, the X 1 -axis direction. The second direction D 2  is, for example, the Y 1 -axis direction. 
     The control device  70  is configured to output a rotation angle Av 1  of the movable member  10  obtained based on the first and second components. 
     For example, the control device  70  detects the amplitude of the first component and the amplitude of the second component of the vibration of the movable member  10 . The ratio of these amplitudes corresponds to the rotation angle Av 1 . 
     As shown in  FIGS.  5 A and  5 B , the structure body  60 A includes, for example, a fixed part  1 OF and a connection part  10 S. The fixed part  1 OF is fixed to the base body  60 . The connection part  10 S is supported by the fixed part  10 F. The connection part  10 S is connected with the movable member  10 . In the example, the movable member  10  is located around the fixed part  1 OF in the X 1 -Y 1  plane. The movable member  10  is ring-shaped. The movable member  10  is supported by the multiple connection parts  10 S. A gap g 1  is provided between the movable member  10  and the base body  60 . For example, the connection part  10 S has a bent shape. For example, the connection part  10 S may have a meandering shape. The connection part  10 S is, for example, a spring structure body. The connection part  10 S is deformable. 
     For example, the movable member  10  and the connection part  10 S are conductive. 
     As shown in  FIGS.  5 A and  5 B , for example, the structure body  60 A includes a first counter electrode member  20 M. In the example, multiple first counter electrode members  20 M are included. The vibration of the movable member  10  may be controlled by the multiple first counter electrode members  20 M. The vibration of the movable member  10  may be controlled by a voltage (e.g., a voltage including an AC component) applied to the first counter electrode member  20 M. For example, the voltage is applied between the first counter electrode member  20 M and the movable member  10 . 
     The vibration state changes when the vibrating movable member  10  is rotated by an external force, etc. It is considered that the change of the vibration state is due to, for example, an action of a Coriolis force. For example, the movable member  10  vibrates via a spring mechanism (e.g., the connection part  10 S). A Coriolis force due to an angular velocity S) of rotation acts on the movable member  10  vibrating in the first direction D 1 . Thereby, a component of a vibration along the second direction D 2  is generated in the movable member  10 . The control device  70  detects the amplitude of the vibration along the second direction D 2 . On the other hand, a Coriolis force due to the angular velocity S) of rotation acts on the movable member  10  vibrating in the second direction D 2 . Thereby, a component of a vibration along the first direction D 1  is generated in the movable member  10 . The control device  70  detects the amplitude of the vibration along the first direction D 1 . For example, the rotation angle corresponds to tan −1 (−A 2 /A 1 ), where “A 1 ” is the amplitude of the first component of the first direction D 1 , and “A 2 ” is the amplitude of the second component of the second direction D 2 . 
     The rotation angle (e.g., the rotation angle Av 1 ) is obtained by such an angle sensor  110 . The rotation angle DA 1  illustrated in  FIG.  1   , etc., is obtained by determining the rotation angle for the different multiple axes. 
     According to the embodiment, for example, instead of using the angular velocity, the rotation angle (the angle) is input as-is to the attitude angle derivation device. The attitude angle can be derived thereby. For example, in a reference example that uses the angular velocity, high-frequency noise or drift due to the integral error is easily generated. According to the embodiment, the drift or high-frequency noise is suppressed, and the attitude angle can be detected with high accuracy. According to the embodiment, temporal information is unnecessary to derive the attitude angle. Thereby, the attitude angle can be detected with high accuracy even by irregular sampling. 
     Third Embodiment 
     A third embodiment relates to an electronic device. The electronic device may be, for example, at least a part of the object 
       FIG.  6    is a schematic view illustrating the electronic device according to the third embodiment. 
     As shown in  FIG.  6   , the electronic device  310  according to the embodiment includes a circuit controller  170  and a sensor according to an embodiment. In the example of  FIG.  6   , the attitude angle sensor  210  (and the angle sensor  110 ) are illustrated as the sensor. The circuit controller  170  is configured to control a circuit  180  based on a signal S 1  obtained from the sensor. The circuit  180  is, for example, a control circuit of a drive device  185 , etc. According to the embodiment, the circuit  180  for controlling the drive device  185 , etc., can be controlled with high accuracy based on a highly-accurate detection result. 
       FIGS.  7 A to  7 H  are schematic views illustrating applications of the electronic device. 
     As shown in  FIG.  7 A , the electronic device  310  may be at least a part of a robot. As shown in  FIG.  7 B , the electronic device  310  may be at least a part of a machining robot provided in a manufacturing plant, etc. As shown in  FIG.  7 C , the electronic device  310  may be at least a part of an automatic guided vehicle inside a plant, etc. As shown in  FIG.  7 D , the electronic device  310  may be at least a part of a drone (an unmanned aircraft). As shown in  FIG.  7 E , the electronic device  310  may be at least a part of an airplane. As shown in  FIG.  7 F , the electronic device  310  may be at least a part of a ship. As shown in  FIG.  7 G , the electronic device  310  may be at least a part of a submarine. As shown in  FIG.  7 H , the electronic device  310  may be at least a part of an automobile. The electronic device  310  may include, for example, at least one of a robot or a mobile body. 
     Embodiments may include the following configurations (e.g., technological proposals). 
     Configuration 1 
     An attitude angle derivation device, comprising: 
     an acquisition part configured to acquire a rotation angle related to a first coordinate system, the rotation angle being obtained from an angle sensor located in an object; 
     a storage configured to store the rotation angle and an attitude angle, the attitude angle being related to a second coordinate system of the object; and 
     a processor configured to acquire the rotation angle and the attitude angle, update the attitude angle based on a temporal change of the rotation angle derived from the rotation angle, and output the updated attitude angle. 
     Configuration 2 
     The attitude angle derivation device according to Configuration 1, wherein 
     the angle sensor includes an integrating gyroscope. 
     Configuration 3 
     The attitude angle derivation device according to Configuration 1 or 2, wherein 
     the angle sensor includes a movable member, 
     the movable member can vibrate, 
     the vibration of the movable member includes:
         a first component along a first direction; and   a second component along a second direction crossing the first direction, and       

     the angle sensor is configured to output, as the rotation angle, a rotation angle of the movable member obtained based on the first and second components. 
     Configuration 4 
     The attitude angle derivation device according to any one of Configurations 1 to 3, wherein. 
     the processor includes a first calculation part, and 
     the first calculation part is configured to derive the temporal change of the rotation angle. 
     Configuration 5 
     The attitude angle derivation device according to Configuration 4, wherein 
     the processor further includes a second calculation part, and 
     the second calculation part is configured to derive a change of the attitude angle based on the temporal change derived by the first calculation part and based on the attitude angle acquired from the storage. 
     Configuration 6 
     The attitude angle derivation device according to Configuration 5, wherein 
     the processor further includes a third calculation part, and 
     the third calculation part is configured to derive the updated attitude angle by adding:
         the change of the attitude angle derived by the second calculation part; and   the attitude angle acquired from the storage.       

     Configuration 7 
     The attitude angle derivation device according to any one of Configurations 1 to 6, wherein 
     the processor supplies the updated attitude angle to the storage, and 
     the storage is configured to store the updated attitude angle. 
     Configuration 8 
     The attitude angle derivation device according to any one of Configurations 1 to 7, wherein 
     the rotation angle includes a first rotation angle related to a first axis, a second rotation angle related to a second axis, and a third rotation angle related to a third axis, 
     the second axis crosses the first axis, and 
     the third axis crosses a plane including the first and second axes. 
     Configuration 9 
     The attitude angle derivation device according to Configuration 8, wherein 
     the second axis is orthogonal to the first axis, and 
     the third axis is orthogonal to the first and second axes. 
     Configuration 10 
     The attitude angle derivation device according to Configuration 9, wherein 
     the rotation angle includes the first rotation angle A x(t)  at a first time t, the second rotation angle A y(t)  at the first time t, and the third rotation angle A z(t)  at the first time t, 
     the processor derives a first temporal change dA x(t) , a second temporal change dA y(t) , and a third temporal change dA z(t)  as the temporal change of the rotation angle, and 
     the first temporal change dA x(t) , the second temporal change dA y(t) , the third temporal change dA z(t) , the first rotation angle A x(t) , the second rotation angle A y(t) , the third rotation angle A z(t) , the first rotation angle A x(t-1)  at a second time (t- 1 ) before the first time t, the second rotation angle A y(t-1)  at the second time (t- 1 ), and the third rotation angle A z(t-1)  at the second time (t- 1 ) satisfy 
     
       
      
       dA 
       x(t) 
       =A 
       x(t) 
       −A 
       x(t-1)  
      
     
     
       
      
       dA 
       y(t) 
       =A 
       y(t) 
       −A 
       y(t-1)  
      
     
         dA   z(t)   =A   z(t)   −A   z(t-1)    (1)
 
     Configuration 11 
     The attitude angle derivation device according to Configuration 10, wherein 
     the attitude angle includes:
         a first attitude angle related to a first attitude axis;   a second attitude angle related to a second attitude axis; and   a third attitude angle related to a third attitude axis, the second attitude axis crosses the first attitude axis, and the third attitude axis crosses a plane including the first and second attitude axes.       

     Configuration 12 
     The attitude angle derivation device according to Configuration 11, wherein 
     the second attitude axis is orthogonal to the first attitude axis, and 
     the third attitude axis is orthogonal to the first and second attitude axes. 
     Configuration 13 
     The attitude angle derivation device according to Configuration 12, wherein 
     the attitude angle includes the first attitude angle ϕ (t-1)  at the second time (t- 1 ), the second attitude angle θ (t-1)  at the second time (t- 1 ), and the third attitude angle ψ (t-1)  at the second time (t- 1 ), 
     the processor derives a first attitude angle change dϕ (t) , a second attitude angle change dθ (t) , and a third attitude angle change dψ (t)  as a change of the attitude angle, and 
     the first attitude angle change dϕ (t) , the second attitude angle change dθ (t) , and the third attitude angle change dΨ (t)  satisfy 
         dϕ   (t) =( dA   y(t)  sin ϕ (t-1)   +dA   x(t)  cos ϕ (t-1) )tan θ t-1 )+ dA   x(t)  
 
         dθ   (t)   =dA   y(t)  cos ϕ (t-1)   −dA   x(t)  sin ϕ (t-1)  
 
         dψ   (t) =( dA   y(t)  sin ϕ+ dA   x(t)  cos ϕ)/cos θ (t-1)    (2)
 
     Configuration 14 
     The attitude angle derivation device according to Configuration 13, wherein 
     the processor derives the first attitude angle ϕ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t as the updated attitude angle, and 
     the first attitude angle ϕ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t satisfy 
       ϕ (t) =ϕ (t-1)   +dϕ   (t)  
 
       θ (t) =θ (t-1)   +dθ   (t)  
 
       ψ (t) =φ (t-1)   +dψ   (t)    (3)
 
     Configuration 15 
     The attitude angle derivation device according to Configuration 10, wherein 
     the attitude angle includes a first quaternion value, a second quaternion value, a third quaternion value, and a fourth quaternion value. 
     Configuration 16 
     The attitude angle derivation device according to Configuration 15, wherein 
     the attitude angle includes the first quaternion value α (t-1)  at the second time (t- 1 ), the second quaternion value β (t-1)  at the second time (t- 1 ), the third quaternion value γ (t-1)  at the second time (t- 1 ), and the fourth quaternion value δ (t-1)  at the second time (t- 1 ), 
     the processor derives a first quaternion value change dam, a second quaternion value change  6 β (t) , a third quaternion value change dγ (t) , and a fourth quaternion value change dδ (t)  as a change of the attitude angle, and 
     the first quaternion value change dα (t) , the second quaternion value change dβ (t) , the third quaternion value change dγ (t) , and the fourth quaternion value change dδ (t)  satisfy 
         dα   (t) =−0.5(β (t-1)   dA   x(t) +γ (t-1)   dA   y(t) +δ (t-1)   dA   z(t) )
 
         dβ   (t) =−0.5(α (t-1)   dA   x(t) −δ (t-1)   dA   y(t) +γ (t-1)   dA   z(t) )
 
         dγ   (t) =−0.5(δ d   (t-1)   dA   x(t) +α (t-1)   dA   y(t) +β (t-1)   dA   z(t) )
 
         dδ   (t) =−0.5(γ (t-1)   dA   x(t) −β (t-1)   dA   y(t) +α (t-1)   dA   z(t) )   (4)
 
     Configuration 17 
     The attitude angle control device according to Configuration 16, wherein 
     the processor derives the first quaternion value α (t)  at the first time t, the second quaternion value β (t)  at the first time t, the third quaternion value γ (t)  at the first time t, and the fourth quaternion value δ (t)  at the first time t as the updated attitude angle, and 
     the first quaternion value α (t)  at the first time t, the second quaternion value β (t)  at the first time t, the third quaternion value γ (t)  at the first time t, and the fourth quaternion value δ (t)  at the first time t satisfy 
     Configuration 18 
     The attitude angle derivation device according to Configuration 17, wherein 
     the processor derives, as the updated attitude angle, the first attitude angle ϕ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t based on the first quaternion value α (t)  at the first time t, the second quaternion value γ (t)  at the first time t, the third quaternion value γ (t)  at the first time t, and the fourth quaternion value δ (t)  at the first time t, and 
     the first attitude angle ϕ (t)  at the first time t, the second attitude angle θ (t)  at the first time t, and the third attitude angle ψ (t)  at the first time t satisfy 
     
       
         
           
             
               
                 
                                    
                   
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                   ( 
                   6 
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               ? 
             
             indicates text missing or illegible when filed 
           
         
       
     
     Configuration 19 
     An attitude angle sensor, comprising: 
     the attitude angle derivation device according to any one of Configurations 1 to 18; and 
     the angle sensor. 
     According to embodiments, an attitude angle derivation device and an attitude angle sensor capable of detecting attitude angles with high accuracy can be provided. 
     In the specification of the application, “perpendicular” and “parallel” refer to not only strictly perpendicular and strictly parallel but also include, for example, the fluctuation due to manufacturing processes, etc. It is sufficient to be substantially perpendicular and substantially parallel. 
     Hereinabove, exemplary embodiments of the invention are described with reference to specific examples. However, the embodiments of the invention are not limited to these specific examples. For example, one skilled in the art may similarly practice the invention by appropriately selecting specific configurations of components included in attitude angle derivation devices and attitude angle sensors from known art. Such practice is included in the scope of the invention to the extent that similar effects thereto are obtained. 
     Further, any two or more components of the specific examples may be combined within the extent of technical feasibility and are included in the scope of the invention to the extent that the purport of the invention is included. 
     Moreover, all attitude angle derivation devices, and attitude angle sensors practicable by an appropriate design modification by one skilled in the art based on the attitude angle derivation devices, and the attitude angle sensors described above as embodiments of the invention also are within the scope of the invention to the extent that the purport of the invention is included. 
     Various other variations and modifications can be conceived by those skilled in the art within the spirit of the invention, and it is understood that such variations and modifications are also encompassed within the scope of the invention. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the invention.