Method for measuring 6 degrees of freedom motion and device therefor

• US 6,128,955 A
• Filed: 07/09/1999
• Issued: 10/10/2000
• Est. Priority Date: 07/09/1999
• Status: Expired due to Fees

• Current Assignee: Nobuharu Mimura
• Original Assignee: Nobuharu Mimura
• Inventors: Mimura, Nobuharu
• Primary Examiner(s): MOLLER, RICHARD ALAN
• Application Number:
  US09/349,598
• Time in Patent Office: 459 Days
• Field of Search: 73/510, 73/511, 73/512
• US Class Current: 73/510
• CPC Class Codes: G01C 21/166 Mechanical, construction or arrangement details of inertial navigation systems
• CPC Class Codes: G01C 21/188 for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems
• CPC Class Codes: G01P 15/18 in two or more dimensions

Abstract

A method and device for measuring a motion of a rigid body, using the least possible accelerometers that are simply arranged. One-axis uni-directional accelerometers 1 through 6 are each fixed to the rigid body through a base 12. Thus, no Coriolis force is developed even though an external force is applied thereto. The six one-axis uni-directional accelerometers 1 through 6 are mounted to three or more different positions relative to the rigid body. Consequently, a processing unit 21 can perform processing so that centrifugal and angular effects included in each one-axis uni-directional accelerometer may be separated. As the one-axis uni-directional accelerometers 1 through 6 are arranged on the same plane, you have only to consider two-dimensional positional relationship among the accelerometers for the accuracy of the arrangement thereof.

Claims

1. A method for measuring a 6 DOF motion of a rigid body, which comprises the steps of:

fixing at least six one-axis uni-directional accelerometers to three or more different positions on the same plane as that of a rigid body; and

carrying out processing, using acceleration signals output from each of the one-axis uni-directional accelerometers so that the effects of centrifugal acceleration and rotational angular acceleration included in each one-axis uni-directional accelerometer may be separated therefrom.

2. A method for measuring a 6 DOF motion of a rigid body according to claim 1,

wherein the one-axis uni-directional accelerometers are mounted to arbitrary positions denoted by position vector °

r_i on the rigid body so that vectors in the sensing directions may become °

u_i (i=1,2, . . . n, its left affix indicating a coordinate system to which the vector belongs), whereby a 6 degrees of freedom acceleration of the rigid body in a static coordinate standard system Σ

o shown by the following equation;

space="preserve" listing-type="equation">[°

pb.sup.T °

ω

b.sup.T ].sup.T

is calculated, based on the following equation;

##EQU14## where the °

p_b indicates the position of the origin of a coordinate system Σ

b fixed to the rigid body as viewed from the static coordinate standard system Σ

o, and the °

ω

_b indicates an angular velocity of the rigid body rotating around the origin of the coordinate system Σ

b, while the one-axis acceleration "a" and the matrix °

R are expressed by the following equations, respectively;

##EQU15##

3. A method for measuring a 6 DOF motion of a rigid body according to claim 2, wherein the number (n) of said one-axis uni-directional accelerometers is six, while the said one-axis uni-directional accelerometers are arranged so that the matrix °

R may become regular, whereby a 6 degrees of freedom acceleration of the rigid body in the static coordinate standard system Σ

o shown by the following equation;

space="preserve" listing-type="equation">[°

pb.sup.T °

ω

b.sup.T ].sup.T

is calculated, based on the following equation;

##EQU16##

4. A method for measuring a 6 DOF motion according to claim 3, wherein a 6 degrees of freedom acceleration of the rigid body in the coordinate system Σ

b fixed to the rigid body is calculated based on the following equation;

5. A method for measuring a 6 DOF motion according to claim 3, wherein data from each one-axis uni-directional accelerometer are obtained at sampling intervals of Δ

t (second), whereby a 6 degrees of freedom acceleration of the rigid body in the static coordinate standard system To shown by the following equation;

space="preserve" listing-type="equation">[°

pb.sup.T °

ω

b.sup.T ].sup.T

is calculated based on the following equations;

##EQU17## where a(n) indicates the nth sampling value of measured value vector, and ##EQU18## where

space="preserve" listing-type="equation">When t=0, °

pb(1)=°

ω

b(1)=0 ##EQU19##

6. A method for measuring a 6 DOF motion according to claim 1, wherein the frequency response characteristic and phase characteristic of each one-axis uni-directional accelerometer is uniform.

7. A method for measuring a 6 DOF motion according to claim 1, wherein the one-axis uni-directional accelerometers are paired respectively, disposed close to one another nearly on the same position, in which a first one of each pair of one-axis uni-directional accelerometers has a sensing direction directed to the Z-axis, while the second one of each pair of uni-directional accelerometers has a sensing direction parallel to the X-Y plane, with the height of the first one of each pair of one-axis uni-directional accelerometers aligned to the center of the second one of each pair of one-axis uni-directional accelerometers.

8. A device for measuring a 6 DOF motion of a rigid body, which comprises:

at least six one-axis uni-directional accelerometers fixed to three or more different positions on the same plane as that of a rigid body; and

a processing unit for calculating the 6 DOF motion of the rigid body, said processing unit carrying out processing, using acceleration signals output from each of the one-axis uni-directional accelerometers so that the effects of centrifugal acceleration and rotational angular acceleration included in each one-axis uni-directional accelerometer may be separated therefrom.

9. A device for measuring a 6 DOF motion of a rigid body according to claim 8,

wherein the one-axis uni-directional accelerometers are mounted to arbitrary positions denoted by position vector °

r_i on the rigid body so that vectors in the sensing directions may become °

u_i (i=1,2, . . . n, its left affix indicating a coordinate system to which the vector belongs), whereby a 6 degrees of freedom acceleration of the rigid body in a static coordinate standard system Σ

o shown by the following equation;

space="preserve" listing-type="equation">[°

pb.sup.T °

ω

b.sup.T ].sup.T

is calculated by said processing unit, based on the following equation;

##EQU20## where the °

pb indicates the position of the origin of a coordinate system Σ

b fixed to the rigid body as viewed from the static coordinate standard system Σ

o, and the °

ω

b indicates an angular velocity of the rigid body rotating around the origin of the coordinate system Σ

b, while the one-axis acceleration "a" and the matrix °

R are expressed by the following equations, respectively;

##EQU21##10.

10. A device for measuring a 6 DOF motion of a rigid body according to claim 9, wherein the number (n) of said one-axis uni-directional accelerometers is six, while the said one-axis uni-directional accelerometers are arranged so that the matrix °

R may become regular, whereby a 6 degrees of freedom acceleration of the rigid body in the static coordinate standard system Σ

o shown by the following equation;

space="preserve" listing-type="equation">[°

pb.sup.T °

ω

b.sup.T ].sup.T

is calculated by said processing unit, based on the following equation;

##EQU22##

11. A device for measuring a 6 DOF motion according to claim 10, wherein a 6 degrees of freedom acceleration of the rigid body in the coordinate system Σ

b fixed to the rigid body is calculated by said processing unit based on the following equation;

12. A device for measuring a 6 DOF motion according to claim 10, wherein said processing unit obtains data from each one-axis uni-directional accelerometer at sampling intervals of Δ

t (second), whereby a 6 degrees of freedom acceleration of the rigid body in the static coordinate standard system Σ

o shown by the following equation;

space="preserve" listing-type="equation">[°

pb.sup.T °

ω

b.sup.T ].sup.T

is calculated by said processing unit, based on the following equations;

##EQU23## where a(n) indicates the nth sampling value of measured value vector ##EQU24## where

space="preserve" listing-type="equation">When t=0, °

pb(1)=°

ω

b(1)=0 ##EQU25##

13. A device for measuring a 6 DOF motion according to claim 8, wherein the frequency response characteristic and phase characteristic of each one-axis uni-directional accelerometer is uniform.

14. A device for measuring a 6 DOF motion according to claim 8, wherein the one-axis uni-directional accelerometers are paired respectively, disposed close to one another nearly on the same position, in which a first one of each pair of one-axis uni-directional accelerometers has a sensing direction directed to the Z-axis, while the second one of each pair of uni-directional accelerometers has a sensing direction parallel to the X-Y plane, and wherein said device further comprises a level regulator for allowing the height of the first one of each pair of one-axis uni-directional accelerometers to be aligned to the center of the second one of each pair of one-axis uni-directional accelerometers.