Method and device for determining the relative position, velocity and/or acceleration of a body
AssigneeAlbert-Ludwigs-Universität Freiburg
InventorsChristian Peters, Alexander Buhmann, Yiannos Manoli
Life of this patent
Estimating the term…
Abstract
In a method for determining the relative position, velocity, acceleration, and/or the rotation center of a body displaceable in a three dimensional space, at least twelve linear acceleration sensors are provided and in each case arranged on a position which is stationarily fixed with respect to the body. At least one acceleration measurement signal is captured by the linear acceleration sensors. A position, velocity, acceleration, and/or rotation center signal is generated for the body from the acceleration measurement signal and data describing the position and orientation of the linear acceleration sensors in the body-fixed coordinate system.
Claims15
A method for determining the relative position, velocity, and/or acceleration of a body displaceable in a three dimensional space, wherein a plurality of n linear acceleration sensors, which in each case have a sensitive measurement axis, is provided, wherein said plurality n is at least twelve, wherein the individual linear acceleration sensors are in each case arranged on a position Pi which is stationarily fixed with respect to the body and which can be described by a stationary position vector,
- r
- →
- i
- =
- (
- r
- xi
- r
- yi
- r
- zi
- )
- which indicates the respective position Pi from a body-fixed reference point, wherein the linear acceleration sensors are aligned so that their measurement axes are always oriented toward a direction vector
- Θ
- →
- i
- =
- (
- Θ
- xi
- Θ
- yi
- Θ
- zi
- )
- ,
- wherein the respective linear acceleration sensor and the x, y, z axes of a body-fixed coordinate system passing through the reference point are designated in each case by iε[1, 2, 3, 4, . . . n], wherein the position vectors {right arrow over (r)}i and the direction vectors {right arrow over (Θ)}i are selected so that the rank of a twelve column matrix formed from the column vectors
- s
- →
- 1
- =
- (
- Θ
- x
-
-
- 1
- Θ
- x
-
-
- 2
- Θ
- x
-
-
- 3
- Θ
- x
-
-
- 4
- ⋮
- Θ
- xn
- )
- ,
- s
- →
- 2
- =
- (
- Θ
- y
-
-
- 1
- Θ
- y
-
-
- 2
- Θ
- y
-
-
- 3
- Θ
- y
-
-
- 4
- ⋮
- Θ
- yn
- )
- ,
- s
- →
- 3
- =
- (
- Θ
- z
-
-
- 1
- Θ
- z
-
-
- 2
- Θ
- z
-
-
- 3
- Θ
- z
-
-
- 4
- ⋮
- Θ
- zn
- )
- ,
- s
- →
- 4
- =
- (
- Θ
- z
-
-
- 1
-
- r
- y
-
-
- 1
- -
- Θ
- y
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- z
-
-
- 2
-
- r
- y
-
-
- 2
- -
- Θ
- y
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- z
-
-
- 3
-
- r
- y
-
-
- 3
- -
- Θ
- y
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- z
-
-
- 4
-
- r
- y
-
-
- 4
- -
- Θ
- y
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- zn
-
- r
- yn
- -
- Θ
- yn
-
- r
- zn
- )
- ,
-
- s
- →
- 5
- =
- (
- Θ
- x
-
-
- 1
-
- r
- z
-
-
- 1
- -
- Θ
- z
-
-
- 1
-
- r
- x
-
-
- 1
- Θ
- x
-
-
- 2
-
- r
- z
-
-
- 2
- -
- Θ
- z
-
-
- 2
-
- r
- x
-
-
- 2
- Θ
- x
-
-
- 3
-
- r
- z
-
-
- 3
- -
- Θ
- z
-
-
- 3
-
- r
- x
-
-
- 3
- Θ
- x
-
-
- 4
-
- r
- z
-
-
- 4
- -
- Θ
- z
-
-
- 4
-
- r
- x
-
-
- 4
- ⋮
- Θ
- xn
-
- r
- zn
- -
- Θ
- zn
-
- r
- xn
- )
- ,
- s
- →
- 6
- =
- (
- Θ
- y
-
-
- 1
-
- r
- x
-
-
- 1
- -
- Θ
- x
-
-
- 1
-
- r
- y
-
-
- 1
- Θ
- y
-
-
- 2
-
- r
- x
-
-
- 2
- -
- Θ
- x
-
-
- 2
-
- r
- y
-
-
- 2
- Θ
- y
-
-
- 3
-
- r
- x
-
-
- 3
- -
- Θ
- x
-
-
- 3
-
- r
- y
-
-
- 3
- Θ
- y
-
-
- 4
-
- r
- x
-
-
- 4
- -
- Θ
- x
-
-
- 4
-
- r
- y
-
-
- 4
- ⋮
- Θ
- yn
-
- r
- xn
- -
- Θ
- xn
-
- r
- yn
- )
- ,
-
- s
- →
- 7
- =
- (
- Θ
- y
-
-
- 1
-
- r
- y
-
-
- 1
- -
- Θ
- z
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- y
-
-
- 2
-
- r
- y
-
-
- 2
- -
- Θ
- z
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- y
-
-
- 3
-
- r
- y
-
-
- 3
- -
- Θ
- z
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- y
-
-
- 4
-
- r
- y
-
-
- 4
- -
- Θ
- z
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- yn
-
- r
- yn
- -
- Θ
- zn
-
- r
- zn
- )
- ,
- s
- →
- 8
- =
- (
- Θ
- x
-
-
- 1
-
- r
- x
-
-
- 1
- -
- Θ
- z
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- x
-
-
- 2
-
- r
- x
-
-
- 2
- -
- Θ
- z
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- x
-
-
- 3
-
- r
- x
-
-
- 3
- -
- Θ
- z
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- x
-
-
- 4
-
- r
- x
-
-
- 4
- -
- Θ
- z
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- xn
-
- r
- xn
- -
- Θ
- zn
-
- r
- zn
- )
- ,
-
- s
- →
- 9
- =
- (
- Θ
- x
-
-
- 1
-
- r
- x
-
-
- 1
- -
- Θ
- y
-
-
- 1
-
- r
- y
-
-
- 1
- Θ
- x
-
-
- 2
-
- r
- x
-
-
- 2
- -
- Θ
- y
-
-
- 2
-
- r
- y
-
-
- 2
- Θ
- x
-
-
- 3
-
- r
- x
-
-
- 3
- -
- Θ
- y
-
-
- 3
-
- r
- y
-
-
- 3
- Θ
- x
-
-
- 4
-
- r
- x
-
-
- 4
- -
- Θ
- y
-
-
- 4
-
- r
- y
-
-
- 4
- ⋮
- Θ
- xn
-
- r
- xn
- -
- Θ
- yn
-
- r
- yn
- )
- ,
- s
- →
- 10
- =
- (
- Θ
- y
-
-
- 1
-
- r
- x
-
-
- 1
- +
- Θ
- x
-
-
- 1
-
- r
- y
-
-
- 1
- Θ
- y
-
-
- 2
-
- r
- x
-
-
- 2
- +
- Θ
- x
-
-
- 2
-
- r
- y
-
-
- 2
- Θ
- y
-
-
- 3
-
- r
- x
-
-
- 3
- +
- Θ
- x
-
-
- 3
-
- r
- y
-
-
- 3
- Θ
- y
-
-
- 4
-
- r
- x
-
-
- 4
- +
- Θ
- x
-
-
- 4
-
- r
- y
-
-
- 4
- ⋮
- Θ
- yn
-
- r
- xn
- +
- Θ
- xn
-
- r
- yn
- )
- ,
-
- s
- →
- 11
- =
- (
- Θ
- z
-
-
- 1
-
- r
- x
-
-
- 1
- +
- Θ
- x
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- z
-
-
- 2
-
- r
- x
-
-
- 2
- +
- Θ
- x
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- z
-
-
- 3
-
- r
- x
-
-
- 3
- +
- Θ
- x
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- z
-
-
- 4
-
- r
- x
-
-
- 4
- +
- Θ
- x
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- zn
-
- r
- xn
- +
- Θ
- xn
-
- r
- zn
- )
-
-
- and
-
-
- s
- →
- 12
- =
- (
- Θ
- z
-
-
- 1
-
- r
- y
-
-
- 1
- +
- Θ
- y
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- z
-
-
- 2
-
- r
- y
-
-
- 2
- +
- Θ
- y
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- z
-
-
- 3
-
- r
- y
-
-
- 3
- +
- Θ
- y
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- z
-
-
- 4
-
- r
- y
-
-
- 4
- +
- Θ
- y
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- zn
-
- r
- yn
- +
- Θ
- yn
-
- r
- zn
- )
- equals twelve, wherein at least one acceleration measurement signal
- a
- →
- =
- (
- a
- 1
- a
- 2
- a
- 3
- a
- 4
- ⋮
- a
- n
- )
- is captured with the linear acceleration sensors, and wherein a position, velocity, and/or acceleration signal is generated for the body from the acceleration measurement signal and data that describe the relative position and orientation of the linear acceleration sensors in the body-fixed coordinate system.
A device for determining the relative position, velocity, and/or acceleration of a body displaceable in a three dimensional space, wherein the device for the capture of at least one acceleration measurement signal
- a
- →
- =
- (
- a
- 1
- a
- 2
- a
- 3
- a
- 4
- ⋮
- a
- n
- )
- has a plurality of n linear acceleration sensors in a body-fixed arrangement with respect to the body, wherein the plurality n is at least twelve, wherein the positions Pi on which the linear acceleration sensors are arranged can be described in each case by a stationary position vector
- r
- →
- i
- =
- (
- r
- xi
- r
- yi
- r
- zi
- )
- ,
- which indicates the respective position Pi from a body-fixed reference point, wherein the linear acceleration sensors in each case have a sensitive measurement axis, which is oriented towards a direction vector
- Θ
- →
- i
- =
- (
- Θ
- xi
- Θ
- yi
- Θ
- zi
- )
- ,
- wherein the respective linear acceleration sensor and the x, y, z axes of a body-fixed coordinate system passing through the reference point are designated in each case by iε[1, 2, 3, 4, . . . n], wherein the position vectors {right arrow over (r)}i and the direction vectors {right arrow over (Θ)}i are selected so that the rank of a twelve column matrix formed from the column vectors
- s
- →
- 1
- =
- (
- Θ
- x
-
-
- 1
- Θ
- x
-
-
- 2
- Θ
- x
-
-
- 3
- Θ
- x
-
-
- 4
- ⋮
- Θ
- xn
- )
- ,
- s
- →
- 2
- =
- (
- Θ
- y
-
-
- 1
- Θ
- y
-
-
- 2
- Θ
- y
-
-
- 3
- Θ
- y
-
-
- 4
- ⋮
- Θ
- yn
- )
- ,
- s
- →
- 3
- =
- (
- Θ
- z
-
-
- 1
- Θ
- z
-
-
- 2
- Θ
- z
-
-
- 3
- Θ
- z
-
-
- 4
- ⋮
- Θ
- zn
- )
- ,
- s
- →
- 4
- =
- (
- Θ
- z
-
-
- 1
-
- r
- y
-
-
- 1
- -
- Θ
- y
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- z
-
-
- 2
-
- r
- y
-
-
- 2
- -
- Θ
- y
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- z
-
-
- 3
-
- r
- y
-
-
- 3
- -
- Θ
- y
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- z
-
-
- 4
-
- r
- y
-
-
- 4
- -
- Θ
- y
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- zn
-
- r
- yn
- -
- Θ
- yn
-
- r
- zn
- )
- ,
-
- s
- →
- 5
- =
- (
- Θ
- x
-
-
- 1
-
- r
- z
-
-
- 1
- -
- Θ
- z
-
-
- 1
-
- r
- x
-
-
- 1
- Θ
- x
-
-
- 2
-
- r
- z
-
-
- 2
- -
- Θ
- z
-
-
- 2
-
- r
- x
-
-
- 2
- Θ
- x
-
-
- 3
-
- r
- z
-
-
- 3
- -
- Θ
- z
-
-
- 3
-
- r
- x
-
-
- 3
- Θ
- x
-
-
- 4
-
- r
- z
-
-
- 4
- -
- Θ
- z
-
-
- 4
-
- r
- x
-
-
- 4
- ⋮
- Θ
- xn
-
- r
- zn
- -
- Θ
- zn
-
- r
- xn
- )
- ,
- s
- →
- 6
- =
- (
- Θ
- y
-
-
- 1
-
- r
- x
-
-
- 1
- -
- Θ
- x
-
-
- 1
-
- r
- y
-
-
- 1
- Θ
- y
-
-
- 2
-
- r
- x
-
-
- 2
- -
- Θ
- x
-
-
- 2
-
- r
- y
-
-
- 2
- Θ
- y
-
-
- 3
-
- r
- x
-
-
- 3
- -
- Θ
- x
-
-
- 3
-
- r
- y
-
-
- 3
- Θ
- y
-
-
- 4
-
- r
- x
-
-
- 4
- -
- Θ
- x
-
-
- 4
-
- r
- y
-
-
- 4
- ⋮
- Θ
- yn
-
- r
- xn
- -
- Θ
- xn
-
- r
- yn
- )
- ,
-
- s
- →
- 7
- =
- (
- Θ
- y
-
-
- 1
-
- r
- y
-
-
- 1
- -
- Θ
- z
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- y
-
-
- 2
-
- r
- y
-
-
- 2
- -
- Θ
- z
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- y
-
-
- 3
-
- r
- y
-
-
- 3
- -
- Θ
- z
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- y
-
-
- 4
-
- r
- y
-
-
- 4
- -
- Θ
- z
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- yn
-
- r
- yn
- -
- Θ
- zn
-
- r
- zn
- )
- ,
- s
- →
- 8
- =
- (
- Θ
- x
-
-
- 1
-
- r
- x
-
-
- 1
- -
- Θ
- z
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- x
-
-
- 2
-
- r
- x
-
-
- 2
- -
- Θ
- z
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- x
-
-
- 3
-
- r
- x
-
-
- 3
- -
- Θ
- z
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- x
-
-
- 4
-
- r
- x
-
-
- 4
- -
- Θ
- z
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- xn
-
- r
- xn
- -
- Θ
- zn
-
- r
- zn
- )
- ,
-
- s
- →
- 9
- =
- (
- Θ
- x
-
-
- 1
-
- r
- x
-
-
- 1
- -
- Θ
- y
-
-
- 1
-
- r
- y
-
-
- 1
- Θ
- x
-
-
- 2
-
- r
- x
-
-
- 2
- -
- Θ
- y
-
-
- 2
-
- r
- y
-
-
- 2
- Θ
- x
-
-
- 3
-
- r
- x
-
-
- 3
- -
- Θ
- y
-
-
- 3
-
- r
- y
-
-
- 3
- Θ
- x
-
-
- 4
-
- r
- x
-
-
- 4
- -
- Θ
- y
-
-
- 4
-
- r
- y
-
-
- 4
- ⋮
- Θ
- xn
-
- r
- xn
- -
- Θ
- yn
-
- r
- yn
- )
- ,
- s
- →
- 10
- =
- (
- Θ
- y
-
-
- 1
-
- r
- x
-
-
- 1
- +
- Θ
- x
-
-
- 1
-
- r
- y
-
-
- 1
- Θ
- y
-
-
- 2
-
- r
- x
-
-
- 2
- +
- Θ
- x
-
-
- 2
-
- r
- y
-
-
- 2
- Θ
- y
-
-
- 3
-
- r
- x
-
-
- 3
- +
- Θ
- x
-
-
- 3
-
- r
- y
-
-
- 3
- Θ
- y
-
-
- 4
-
- r
- x
-
-
- 4
- +
- Θ
- x
-
-
- 4
-
- r
- y
-
-
- 4
- ⋮
- Θ
- yn
-
- r
- xn
- +
- Θ
- xn
-
- r
- yn
- )
- ,
-
- s
- →
- 11
- =
- (
- Θ
- z
-
-
- 1
-
- r
- x
-
-
- 1
- +
- Θ
- x
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- z
-
-
- 2
-
- r
- x
-
-
- 2
- +
- Θ
- x
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- z
-
-
- 3
-
- r
- x
-
-
- 3
- +
- Θ
- x
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- z
-
-
- 4
-
- r
- x
-
-
- 4
- +
- Θ
- x
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- zn
-
- r
- xn
- +
- Θ
- xn
-
- r
- zn
- )
-
-
- and
-
-
- s
- →
- 12
- =
- (
- Θ
- z
-
-
- 1
-
- r
- y
-
-
- 1
- +
- Θ
- y
-
-
- 1
-
- r
- z
-
-
- 1
- Θ
- z
-
-
- 2
-
- r
- y
-
-
- 2
- +
- Θ
- y
-
-
- 2
-
- r
- z
-
-
- 2
- Θ
- z
-
-
- 3
-
- r
- y
-
-
- 3
- +
- Θ
- y
-
-
- 3
-
- r
- z
-
-
- 3
- Θ
- z
-
-
- 4
-
- r
- y
-
-
- 4
- +
- Θ
- y
-
-
- 4
-
- r
- z
-
-
- 4
- ⋮
- Θ
- zn
-
- r
- yn
- +
- Θ
- yn
-
- r
- zn
- )
- equals twelve, and wherein the linear acceleration sensors are connected to an evaluator, which is configured to generate a position, velocity, and/or acceleration signal for the body from the acceleration measurement signal {right arrow over (a)} and data that describe the relative position and orientation of the linear acceleration sensors in the body-fixed coordinate system.
Dependencies are inferred from the claim text.