Direct determination of rigid body motion using data collected from independent accelerometers

• US 7,657,394 B1
• Filed: 03/12/2007
• Issued: 02/02/2010
• Est. Priority Date: 03/12/2007
• Status: Active Grant

• Current Assignee: Ansys Incorporated
• Original Assignee: Livermore Software Technology Corporation
• Inventors: Slavik, Todd Patrick
• Primary Examiner(s): Feliciano; Eliseo Ramos
• Assistant Examiner(s): O MALLEY, MARY CATHERINE
• Application Number:
  US11/685,010
• Time in Patent Office: 1,058 Days
• Field of Search: 702141-142, 702/149, 702189-190, 702/198, 734/93, 7350401-50403, 7351401-51402, 701/207
• US Class Current: 702/141
• CPC Class Codes: G01C 21/166 Mechanical, construction or arrangement details of inertial navigation systems
• CPC Class Codes: G01P 15/0888 for indicating angular acceleration
• CPC Class Codes: G01P 3/22 transferred to the indicator by electric or magnetic means
• CPC Class Codes: G01P 3/44 for measuring angular speed G01P3/56 takes precedence
• CPC Class Codes: G01P 7/00 Measuring speed by integrating acceleration measuring travelled distance by double integration of acceleration G01C21/16

Abstract

System and method for enabling direct determination of rigid body motion using data collected from a plurality of independent accelerometers are disclosed. A mechanical object that can be theoretically emulated as a rigid body is instrumented with a plurality of accelerometers at different locations. Direct determination of rigid body motion at a location of interest includes following operations at each solution time step: transform local acceleration to global, integrate accelerations to obtain velocities, calculate direction cosine matrix using the angular velocity matrix, form a first set of redundant equations, obtain the angular velocity by solving the first set of equations using either least squares fitting or a selective Gaussian elimination scheme, form a second set of redundant equations and obtain the translational velocity by solving the second set of equations using either the averaged value or a pre-defined rule such as minimizing the contribution from the rotational term.

Claims

1. A method of direct determination of angular and translational velocity at a particular location on a rigid body in a global reference frame based on measured accelerations collected from a plurality of independent accelerometers instrumented on the rigid body, the method comprising:

(a) receiving, in a computer system having an application module for direct determination of angular and translation velocity at a particular location on a rigid body installed thereon, the measured accelerations, orientation of each of the accelerometers and orientation of the rigid body;

(b) forming initial direction cosine matrices for said each of the accelerometers and for the rigid body using the respective orientations in the computer system;

(c) initializing current solution time in the computer system;

(d) transforming measured accelerations to the global reference frame in the computer system;

(e) calculating global velocity by integrating the transformed global accelerations in the computer system;

(f) calculating current direction cosine matrices based on previous direction cosine matrices and the angular velocity matrix in the computer system;

(g) creating a first set of redundant vector equations for the angular velocity in the computer system;

(h) obtaining the angular velocity by solving the first set of redundant equations using a first solution technique in the computer system;

(i) creating a second set of redundant vector equations for the translational velocity in the computer system;

(j) obtaining the translational velocity by solving the second set of redundant equations using a second technique in the computer system;

(k) updating the current solution time in the computer system; and

repeating (d) to (k) until the current time is greater than pre-defined total solution time, wherein both the angular velocity and the translational velocity are displayed to a monitor coupled to the computer system.

2. The method of claim 1, further comprising optionally filtering out high frequency noises of the measured accelerations.

3. The method of claim 1, the orientation of each of the independent accelerometers is represented by an accelerometer reference frame and the orientation of the rigid body is represented by a local reference frame.

4. The method of claim 1, wherein number of the accelerometers is N, wherein N is a positive integer greater or equal to 2.

5. The method of claim 4, wherein number of the first set of redundant vector equations is (N×

(N−

1)/2).

6. The method of claim 4, wherein number of the second set of redundant vector equations is N.

7. The method of claim 1, wherein each of the first set of redundant vector equations is formed for any unique pair of the accelerometers.

8. The method of claim 1, wherein each of the second set of redundant vector equations is formed between the particular location and one of the accelerometers.

9. The method of claim 1, wherein the particular location is the center of mass of the rigid body.

10. The method of claim 1, wherein the first technique includes, but is not limited to, least squares fitting and selective Gaussian elimination.

11. The method of claim 1, wherein the second technique includes, but is not limited to, average value and minimization of the rotational term.

12. The method of claim 1, wherein the first and the second techniques are predefined and used consistently throughout the entire direct determination.

13. The method of claim 1, wherein the first and the second techniques are dynamically decided at each solution cycle.

14. A computer program product including a computer usable medium having computer readable code embodied in the medium for causing an application module to execute on a computer for direct determination of angular and translational velocity at a particular location on a rigid body in a global reference frame based on measured accelerations collected from a plurality of independent accelerometers instrumented on the rigid body, the computer program product comprising:

computer readable code for receiving the measured accelerations, orientation of each of the accelerometers and orientation of the rigid body;

computer readable code for forming initial direction cosine matrices in the global reference frame for said each of the accelerometers and for the rigid body using the respective orientations;

computer readable code for initializing current solution time;

computer readable code for transforming measured accelerations to the global reference frame;

computer readable code for calculating global velocity by integrating the transformed global accelerations;

computer readable code for calculating current direction cosine matrices based on previous direction cosine matrices and the angular velocity matrix;

computer readable code for creating a first set of redundant vector equations for the angular velocity;

computer readable code for obtaining the angular velocity by solving the first set of redundant equations using a first solution technique;

computer readable code for creating a second set of redundant vector equations for the translational velocity; and

computer readable code for obtaining the translational velocity by solving the second set of redundant equations using a second technique.

15. The computer program product of claim 14, wherein each of the first set of redundant vector equations is formed for any unique pair of the accelerometers.

16. The computer program product of claim 14, wherein each of the second set of redundant vector equations is formed between the particular location and one of the accelerometers.

17. A apparatus for direct determination of angular and translational velocity at a particular location on a rigid body in a global reference frame based on measured accelerations collected from a plurality of independent accelerometers instrumented on the rigid body, said apparatus comprising:

a physical computing system comprising an I/O interface, a communication interface, a main memory, a secondary memory and at least one processor coupled to the main memory, the secondary memory, the I/O interface, and the communication interface, wherein said main memory contains executable instructions which when executed by the at least one processor cause the processor to;

(a) receive the measured accelerations, orientation of each of the accelerometers and orientation of the rigid body;

(b) form initial direction cosine matrices in the global reference frame for said each of the accelerometers and for the rigid body using the respective orientations;

(c) initialize current solution time;

(d) transform measured accelerations to the global reference frame;

(e) calculate global velocity by integrating the transformed global accelerations;

calculate current direction cosine matrices based on previous direction cosine matrices and the angular velocity matrix;

(g) create a first set of redundant vector equations for the angular velocity;

(h) obtain the angular velocity by solving the first set of redundant equations using a first solution technique;

(i) create a second set of redundant vector equations for the translational velocity;

(j) obtain the translational velocity by solving the second set of redundant equations using a second technique;

(k) update the current solution time; and

repeating (d) to (k) until the current time is greater than pre-defined total solution time.

18. The apparatus of claim 17, wherein each of the first set of redundant vector equations is formed for any unique pair of the accelerometers.

19. The apparatus of claim 17, wherein each of the second set of redundant vector equations is formed between the particular location and one of the accelerometers.