Gyro stabilized inertial reference system with gimbal lock prevention means

A four axis gyro-stabilized inertial reference system comprising:

• A. a platform having an associated cartesian coordinate system with a fixed spatial orientation, said coordinate system including X, Y and Z axes,
• B. an inner gimbal, said inner gimbal being larger than and disposed about said platform and further being rotationally coupled to said platform about a platform axis,
• C. a middle gimbal, said middle gimbal being larger than and disposed about said inner gimbal and further being rotationally coupled to said inner gimbal about an inner gimbal axis, said inner gimbal axis being perpendicular to said platform axis,
• D. an outer gimbal, said outer gimbal being larger than and disposed about said middle gimbal and further being rotationally coupled to said middle gimbal about a middle gimbal axis, said middle gimbal axis being perpendicular to said inner gimbal axis,
• E. an outer casing, said outer casing being larger than and disposed about said outer gimbal and further being rotationally coupled to said outer gimbal about an outer gimbal axis, said outer gimbal axis being perpendicular to said middle gimbal axis,
• F. a platform stabilizing means for maintaining said platform in a fixed spatial orientation, wherein said stabilizing means comprises:
• i. a platform axis control means including:
• a. a Y-gyro having a first detection means for detecting angular displacement of said platform about said Y-axis, and means for generating an associated J error signal proportional thereto,
• b. a platform axis motor and associated control circuit responsive to said J-error signal to displace said platform about said platform axis so as to null said J-error signal,
• ii. an inner axis control means including:
• a. an X-gyro having a second detection means for detecting the angular displacement of said platform about said X-axis, and means for generating an associated X-error signal e.sub.x proportional thereto,
• b. a Z-gyro having a third detection means for detecting the angular displacement of said platform about said Z axis, and means for generating a Z-error signal e.sub.z proportional thereto,
• c. an x-z angular error resolver, said first resolver being responsive to said X and Z-error signals to the angular displacement, E, of said inner gimbal about said platform axis, to generate a V-error signal proportional to:
• e.sub.x sin E + e.sub.z cos E
• d. an inner axis motor and associated control circuit responsive to said V-error signal to displace said inner gimbal about said inner gimbal axis so as to null said V-error signal,
• iii. a middle axis control means including:
• a. said X-gyro and Z-gyro,
• b. said x-z angular error resolver, said resolver being further responsive to said X and Z-error signals and to the angular displacement, E, of said inner gimbal about said platform axis to generate a first control signal proportional to:
• e.sub.x cos E - e.sub.z sin E
• c. means for detecting the angular displacement, M, of said outer gimbal about said middle gimbal axis, and associated first generating means for generating a second control signal proportional to:
• sin M
• d. a middle axis motor and associated control circuit, said middle axis motor and circuit being responsive to said first control signal to:
• i. displace said middle gimbal about said middle gimbal axis in a first direction, so as to null said first control signal when the current values of the I and M are in zones (1), (3), (5) and (6) of twelve predetermined I-M zones,
• ii. displace said middle gimbal about said middle gimbal axis in the other direction so as to null said first control signal when the current values of I and M are in zones (2), (4), (7) and (8) of said predetermined I-M zones,
• said middle axis motor and circuit being responsive to said second control signal to:
• iii. displace said middle gimbal about said middle gimbal axis in a first direction so as to null said second control signal when the current values of I and M are in zones (9) and (10) of said predetermined I-M zones,
• iv. displace said middle gimbal about said middle gimbal axis in the other direction so as to null said second control signal when the current values of I and M are in zones (11) and (12) of said predetermined I-M zones,
• iv. an outer axis control means including:
• a. said X-gyro, said Z-gyro, and said resolver,
• b. means for generating a selected angle signal, E.sub.c,
• c. second generating means responsive to said selected angle signal and to the angular displacement, E, of said inner gimbal about said platform axis, for generating a third control signal proportional to:
• sin (E - E.sub.c)
• d. means for detecting the angular displacement, I, of said middle gimbal about said inner gimbal axis, and associated generating means for generating a fourth control signal proportional to:
• sin I
• e. an outer axis motor means and associated control circuit, said outer axis motor means and circuit being responsive to said first control signal to:
• i. displace said outer gimbal about said outer gimbal axis in a first direction so as to null said first control signal when the current values of I and M are in zones (9) and (12) of said predetermined I-M zones,
• ii. displace said outer gimbal about said outer gimbal axis in the other direction so as to null said first signal when the current values of I and M are in zones (10) and (11) of said predetermined I-M zones,
• said outer axis motor and circuit being responsive to said third control signal to:
• i. displace said outer gimbal about said outer gimbal axis in a first direction so as to null said third control signal when the current values of I and M are in zones (1) and (4) of said predetermined I-M zones,
• ii. displace said outer gimbal about said outer gimbal axis in the other direction when the current values of I and M are in zones (2) and (3) of said predetermined I-M zones,
• said outer axis motor and circuit being responsive to said fourth control signal to:
• i. displace said outer gimbal about said outer gimbal axis in a first direction so as to null said fourth control signal when the current values of I and M are in zones (5) and (7) of said predetermined I-M zones, and
• ii. displace said outer gimbal about said outer gimbal axis in the other direction so as to null said fourth control signal when the current values of I and M are in zones (6) and (8) of said predetermined I-M zones,
• where said twelve predetermined I-M zones are defined to be:
• ______________________________________ Zone (1):
• [-a + 2.pi.m] <
• I <
• [+b + 2.pi.m] radians [-q + 2.pi.n] <
• M <
• [+r + 2.pi.n] radians Zone (2):
• [d + 2.pi.m] <
• I <
• [-c + 2.pi.(m + 1)] radians [-q + 2.pi.n] <
• M <
• [+r + 2.pi.n] radians Zone (3):
• [-a + 2.pi.m] <
• I <
• [+b + 2.pi.m] radians [+t + 2.pi.n] <
• M <
• [-s + 2.pi.(n + 1)] radians Zone (4):
• [+d + 2.pi.m] <
• I <
• [-c + 2.pi.(m + 1)] radians [+t + 2.pi.n] <
• M <
• [-s + 2.pi.(n + 1)] radians Zone (5):
• [-a + 2.pi.m] <
• I <
• [+b + 2.pi.m] radians [+r + 2.pi.n] <
• M <
• [+t + 2.pi.n] radians Zone (6):
• [-a + 2.pi.m] <
• I <
• [+b + 2.pi.m] radians [-s + 2.pi.n] <
• M <
• [-q + 2.pi.n] radians Zone (7):
• [+d + 2.pi.m] <
• I <
• [-c + 2.pi.(m + 1)] radians [+r + 2.pi.n] <
• M <
• [+t + 2.pi.n] radians Zone (8):
• [+d + 2.pi.m] <
• I <
• [-c + 2.pi.(m + 1)] radians [-s + 2.pi.n] <
• M <
• [-q + 2.pi.n] radians Zone (9):
• [-c + 2.pi.m] <
• I <
• [-a + 2.pi.m] radians [-q + 2.pi.n] <
• M <
• [+r + 2.pi.n] radians Zone (10):
• [+b + 2.pi.m] <
• I <
• [+d + 2.pi.m] radians [-q + 2.pi.n] <
• M <
• [+r + 2.pi.n] radians Zone (11):
• [-c + 2.pi.m] <
• I <
• [-a + 2.pi.m] radians [+t + 2.pi.n] <
• M <
• [-s + 2.pi.(n + 1)] radians Zone (12):
• [+b + 2.pi.m] <
• I <
• [+d + 2.pi.m] radians [+t + 2.pi.n] <
• M <
• [-s + 2.pi.(n + 1)] radians ______________________________________
• and m and n are integers, where a, b, q, and r are greater than or equal to zero and less than .pi./2 radians, and, c, d, s, and t are greater than .pi./2 radians and less than or equal to .pi. radians.