Tracking and determining orientation of object using coordinate transformation means, system and process

• US 3,983,474 A
• Filed: 02/21/1975
• Issued: 09/28/1976
• Est. Priority Date: 02/21/1975
• Status: Expired due to Term

• Current Assignee: Kaiser Aerospace & Electronics Corporation
• Original Assignee: Polhemus Navigation Sciences Incorporated
• Inventors: Kuipers, Jack
• Primary Examiner(s): Corcoran, Robert J.
• Application Number:
  US05/551,984
• Time in Patent Office: 585 Days
• Field of Search: 324/41, 324/43 R, 324/34 R, 340/258 C, 318/16, 318/447, 318/453, 343/100 CS
• US Class Current: 324/207.18
• CPC Class Codes: G01S 1/42 Conical-scan beacons transmitting signals which indicate at a mobile receiver any displacement of the receiver from the conical-scan axis, e.g. for "beam-riding" missile control
• CPC Class Codes: G01S 13/422 sequential lobing, e.g. conical scan

Abstract

An electromagnetic field which nutates about a pointing vector is used to both track or locate a remote object in addition to determining the relative orientation of the object. Apparatus for generating such a field includes mutually orthogonal dipole radiators, defining a reference coordinate frame, and circuitry for supplying excitations, such that the maximum intensity vector of a vector field produced by these excitations in the radiators nutates about a mean axis or axis of nutation which is called the pointing vector direction of the field. A pointing coordinate frame has the x-axis coincident with the pointing vector and the y-axis in the x-y plane of the reference frame. Mutually orthogonal sensors at the object sense the field and establish a sense coordinate frame, which can be coincident with the coordinate frame of the remote body.

Coordinate transformer means, system and process are used in connection with determining the pointing and angular position of the sense frame with respect to the reference frame. A first error signal relating the sense frame to the pointing frame is transformed into a second error signal relating the sense frame to the reference frame. This second error signal is used to generate the three Euler angles defining the orientation of the sense frame relative to the reference frame and to generate the pointing angles defining the translation of the sense frame from the reference frame.

Means, system and process are described, thus, capable of continuously measuring five independent angles through the use of one field generating means, one field sensing means at the remote object, and signal processing means. Two of the angles specify the direction to, or location of, the remote object and the remaining three angles define the angular orientation of the remote object, the angles defining the sense frame with respect to the fixed reference coordinate frame of the field generating means.

Claims

1. An object locating system in which the object is free to translate and orient in three dimensions and which comprises:

three orthogonal radiators for defining a reference coordinate frame and for radiating a directable nutating field about a pointing vector direction;

a pointing coordinate frame having the x-axis coincident with the pointing vector direction and the y-axis in the x-y plane of the reference frame;

three orthogonal sensors located at the object to be tracked for sensing the nutating field and for defining a sense coordinate frame;

sources of signals to be passed through each of the three radiators;

means for measuring signals induced in the sensors;

means for processing the signals induced in the sensors to determine the translation displacement of the sense frame with respect to the x-axis of the pointing frame and the orientation displacement of the sense frame with respect to the pointing frame; and

means for determining the translation displacement of the sense frame with respect to the pointing vector defined in the reference frame and the orientation displacement of the sense frame with respect to the reference frame.

2. The system as set forth in claim 1 wherein said means for determining the translation and orientation displacements of the sense frame with respect to the reference frame includes:

a decoupling matrix to decouple the signals representing the translation and orientation displacements of the sense frame with respect to the pointing frame so that each signal represents only one translation or orientation displacement with respect to the pointing frame;

a translation coordinate transformer apparatus having as inputs two signals decoupled by said decoupling matrix, representing the translation displacement of the sense frame from the x-axis of the pointing frame and having as outputs two signals representing the translation displacement of the sense frame from the pointing vector defined in the reference frame; and

an orientation coordinate transformer apparatus having as inputs three signals decoupled by said decoupling matrix, representing the orientation displacement of the sense frame from the pointing frame and having as outputs three signals representing the difference between the actual Euler angles which define the sense frame with respect to the reference frame and previously assumed Euler angles defining the sense frame with respect to the reference frame.

3. The system as set forth in claim 2 wherein said translation coordinate transformer apparatus includes:

a resolver means receiving a first and second input signal, the first input signal representing a vector component which in turn represents the translation displacement of the sense frame from the x-axis of the pointing frame, the resolver means being continuously set to resolve the input signals into a first intermediate signal and a first output signal component which is oriented with respect to the reference frame;

feedback means connected to the resolver means so as to receive the first intermediate signal as an input, the feedback means being operable to provide the second input signal to the resolver which after resolution in said resolver means will result in the first intermediate signal being zero or essentially zero; and

a connecting means coupled to the resolver means for receiving a third input signal representing a vector component which in turn represents the translation displacement of the sense frame about one of said pointing frame axes and for providing a second output signal component from the resolver means which is oriented with respect to the reference frame.

4. The system as set forth in claim 2 wherein said orientation coordinate transformer apparatus includes:

a first resolver means receiving a first and second input signal representing vector components which in turn represent the orientation displacement of the sense frame about two of the pointing frame axes, the first resolver means being continuously set to resolve the first and second input signals into a first and a second intermediate output component;

a first summer means summing a third input signal representing a vector component which in turn represents the orientation displacement of the sense frame about one of the pointing frame axes and a translation displacement signal with respect to one of the axes of the reference frame and providing a third intermediate output signal;

a second resolver means receiving the first and third intermediate output signals and being continuously set to resolve the first and third intermediate output signals into a fourth intermediate signal and a first output signal component oriented with respect to the reference frame;

a second summer means summing the second intermediate output signal, a translation displacement signal with respect to one of the axes of the reference frame and a fifth intermediate output signal providing a sixth intermediate output signal;

a third resolver means receiving the fourth and sixth intermediate output signals and being continuously set to resolve the fourth and sixth intermediate output signals into a seventh intermediate output signal and a second output signal component oriented with respect to the reference frame; and

feedback means connected to the third resolver means so as to receive the seventh intermediate output signal as an input, the feedback means being operable to provide a third output signal component and said fifth intermediate output signal oriented with respect to the reference frame.

5. An object tracking system for tracking the position and angular orientation of an object free to translate and orient in three dimensions, said system comprising:

means for generatng a series of three primary reference signals, said primary reference signals being a DC signal, a first AC signal and a second AC signal in phase quadrature with said first AC signal and said primary reference signals being aligned along the axes of a pointing coordinate frame, the DC signal being aligned with the x-axis, the first AC signal being aligned with the y-axis and the second AC signal being aligned with the z-axis;

first means for transforming said primary reference signals in accordance with a first transformation representing a presumed pointing angle so the signals defined in the pointing frame are now defined in an orthogonal reference coordinate frame;

means including three orthogonal radiators coincident with the axes of the reference frame for radiating said transformed primary reference signals;

means including three orthogonal sensors defining a sense coordinate frame for sensing the transformed primary reference signals to produce sense signals, said sensing means being rigidly affixed to the object;

second means for transforming said sense signals in accordance with a second transformation which is the inverse of a presumed set of orientation angles of the sense frame with respect to the reference frame;

third means for transforming said sense signals in accordance with a third transformation which is the inverse of said first transformation, said third means receiving as inputs the outputs from the second means;

means for deriving from the sense signals so transformed by the second and third means the deviation of the position and orientation of the sense frame from the presumed pointing and orientation angles as expressed with respect to the pointing coordinate frame;

a decoupling matrix to receive and decouple the signals representing the translation and orientation displacements of the sense frame with respect to the pointing frame so that each signal represents only one translation or orientation displacement with respect to the pointing frame;

a translation coordinate transformer apparatus having as inputs two signals representing the translation displacement of the sense frame from the x-axis of the pointing frame and having as outputs two signals representing the translation displacement of the sense frame from the pointing vector defined in the reference frame;

an orientation coordinate transformer apparatus having as inputs three signals representing the orientation displacement of the sense frame from the pointing frame and having as outputs three signals representing the difference between the actual Euler angles which define the sense frame with respect to the reference frame and presumed Euler angles defining the sense frame with respect to the reference frame; and

means for altering the presumed pointing and orientation angles as defined in the reference frame in accordance with errors in the presumed pointing and orientation angles as defined in the reference frame.

6. The system as set forth in claim 5 wherein said translation coordinate transformer apparatus includes:

a resolver means receiving a first and second input signal, the first input signal representing a vector component which in turn represents the translation displacement of the sense frame from the x-axis of the pointing frame, the resolver means being continuously set to resolve the input signals into a first intermediate signal and a first output signal component which is oriented with respect to the reference frame;

feedback means connected to the resolver means so as to receive the first intermediate signal as an input, the feedback means being operable to provide the second input signal to the resolver which after resolution in said resolver means will result in the first intermediate signal being zero or essentially zero; and

a connecting means coupled to the resolver means for receiving a third input signal representing a vector component which in turn represents the translation displacement of the sense frame about one of said pointing frame axes and for providing a second output signal component from the resolver means which is oriented with respect to the reference frame.

7. The system as set forth in claim 5 wherein said orientation coordinate transformer apparatus includes:

a first resolver means receiving a first and second input signal representing vector components which in turn represent the orientation displacement of the sense frame about two of the pointing frame axes, the first resolver means being continuously set to resolve the first and second input signals into a first and a second intermediate output component;

a first summer means summing a third input signal representing a vector component which in turn represents the orientation displacement of the sense frame about one of the pointing frame axes and a translation displacement signal with respect to one of the axes of the reference frame and providing a third intermediate output signal;

a second resolver means receiving the first and third intermediate output signals and being continuously set to resolve the first and third intermediate output signals into a fourth intermediate signal and a first output signal component oriented with respect to the reference frame;

a second summer means summing the second intermediate output signal, a translation displacement signal with respect to one of the axes of the reference frame and a fifth intermediate output signal providing a sixth intermediate output signal;

a third resolver means receiving the fourth and sixth intermediate output signals and being continuously set to resolve the fourth and sixth intermediate output signals into a seventh intermediate output signal and a second output signal component oriented with respect to the reference frame; and

feedback means connected to the third resolver means so as to receive the seventh intermediate output signal as an input, the feedback means being operable to provide a third output signal component and said fifth intermediate output signal oriented with respect to the reference frame.

8. A process for tracking an object free to translate and to orient in three dimensions relative to a reference frame defined by a radiator grouping the process comprising:

radiating a nutating field describing a conical motion about a pointing vector which defines the x-axis of a pointing coordinate frame, the y-axis of the pointing frame being in the x-y plane of the reference frame;

sensing the radiated field in three orthogonal axes of a sense coordinate frame attached to the object, to produce an output signal for each axis;

determining the position and orientation error as defined in the pointing frame with respect to a presumed angular position of the object and a presumed angular orientation of the object by comparing said sensed output signals in each of said three orthogonal axes due to said sensed radiation field with presumed output signals that would be sensed in said three orthogonal axes in said presumed angular position and orientation, and determining the difference between said sensed output signals and said presumed output signals;

transforming the errors of the angular position and angular orientation of the object from the pointing frame to the reference frame; and

altering, if said difference between said sensed output signals and said presumed output signals is not zero, the presumed angular position and orientation as defined in the reference frame in accordance with the generated errors of the presumed angular position and orientation as defined in the reference frame.

9. The process as set forth in claim 8 wherein determining the position and orientation error as defined in the pointing frame and transforming the errors of the angular position and angular orientation of the object from the pointing frame to the reference frame includes:

decoupling the signals representing the translation and orientation displacements of the sense frame with respect to the pointing frame so that each signal represents only one translation or orientation displacement with respect to the pointing frame;

transforming coordinates of two signals representing the translation displacement of the sense frame from the x-axis of the pointing frame to produce as outputs two signals representing the translation displacement of the sense frame from the pointing vector defined in the reference frame; and

transforming coordinates of three signals representing the orientation displacement of the sense frame from the pointing frame to produce as outputs three signals representing the difference between the actual Euler angles which define the sense frame with respect to the reference frame and the presumed Euler angles which presumably define the sense frame with respect to the reference frame.

10. The process as set forth in claim 9 wherein the radiator grouping includes electrically conducting coils and the field includes electromagnetic radiation.