Non-concentricity compensation in position and orientation measurement systems

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:

• a source for generating electromagnetic fields, said source having spatially independent components defining a source reference coordinate frame;
• a driver for applying to said source signals which generate a plurality of electromagnetic fields, said electromagnetic fields being distinguishable from one another;
• a remote sensor having a plurality of field-sensing antennas displaced from a sensor common center for sensing said generated electromagnetic fields, said remote sensor being disposed on a remote object and said field-sensing antennas having spatially independent components defining a sensor reference coordinate frame;
• and
• a processor for processing outputs of said field-sensing antenna into remote object position and orientation of said remote sensor relative to said source reference coordinate frame, wherein said processor compensates said position and orientation as a function of non-concentricity of said field-sensing antennas with respect to said sensor common center.

A method of determining the position and orientation of a remote object relative to a reference coordinate frame comprising:

• providing a source including a plurality of field-generating elements for generating electromagnetic fields, said field-generating elements having spatially independent components defining a source reference coordinate frame;
• applying multiplexed electrical signals to said field-generating elements and thus generating a set of distinguishable electromagnetic fields;
• providing a remote sensor including a plurality of field-sensing elements disposed on a remote object and having spatially independent components defining a sensor reference coordinate frame, sensing said electromagnetic fields and generating a set of signals that is representative of the sensed components of said electromagnetic fields;
• and
• processing said set of signals into remote object position and orientation in said reference coordinate frame including compensating for one of (a) displacement of at least one of said components of said field-generating elements from said source reference coordinate frame and (b) displacement of at least one of said field-sensing elements from said sensor reference coordinate frame.

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:

• providing a source including a plurality of field-generating antennas for generating electromagnetic fields, said field-generating antennas having spatially independent components defining a source reference coordinate frame;
• applying multiplexed electrical signals to said field-generating antennas and thus generating a set of distinguishable electromagnetic fields;
• providing a remote sensor including a plurality of field-sensing antennas disposed on a remote object and having spatially independent components for defining a sensor reference coordinate frame, sensing said electromagnetic fields and generating a set of signals that is representative of the sensed components of said electromagnetic fields;
• processing said set of signals into remote object position and orientation in said reference coordinate frame including compensating as a function of non-concentricity of said components of said field-generating antennas with respect to a common center thereof or of non-concentricity of said components of said field-receiving antennas with respect to a common center thereof by:
• establishing a signal matrix S representative of the received components of said electromagnetic fields;
• calculating ##EQU21## where k is a scalar constant;
• a.sub.i is a vector pointing along the sensor's i.sup.th receiving axis;
• ##EQU22## r.sub.ij is a vector representative of the position of the sensor's i.sup.th coil relative to the source's j.sup.th coil;
• r.sub.ij is the magnitude of the vector r.sub.ij ;
• r is a vector representative of the position of the sensor;
• r is the magnitude of the vector r;
• I is the identity matrix;
• m.sub.j is a vector pointing along the source's magnetic moment axis;
• adjusting said signal matrix as a function of

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:

• providing a source including a plurality of field-generating antennas for generating electromagnetic fields, said field-generating antennas having spatially independent components defining a source reference coordinate frame;
• applying multiplexed electrical signals to said field-generating antennas and thus generating a set of distinguishable electromagnetic fields;
• providing a remote sensor including a plurality of field-sensing antennas disposed on a remote object and having spatially independent components for defining a sensor reference coordinate frame, sensing said electromagnetic fields and generating a set of signals that is representative of the sensed components of said electromagnetic fields;
• processing said set of signals into remote object position and orientation in said reference coordinate frame including compensating as a function of non-concentricity of said components of said field-generating antennas with respect to a common magnetic center thereof or of non-concentricity of said components of said field-receiving antennas with respect to a common magnetic center thereof by:
• establishing a signal matrix S representative of the received components of said electromagnetic fields;
• calculating ##EQU23## where k is a scalar constant;
• a.sub.i is a vector pointing along the sensor's i.sup.th receiving axis;
• ##EQU24## r.sub.ij is a vector representative of the position of the sensor's i.sup.th coil relative to the source's j.sup.th coil;
• r.sub.ij is the magnitude of the vector r.sub.ij ;
• r is a vector representative of the position of the sensor;
• r is the magnitude of the vector r;
• I is the identity matrix;
• m.sub.j is a vector pointing along the source's magnetic moment axis;
• adjusting said signal matrix as a function of .DELTA.s.sub.ij.