Ultra-precision position control device and method for determining position and attitude information associated with a 6-degree-of-freedom stage thereof

摘要

A method of determining and controlling position and attitude information associated with a 6-degree-of-freedom stage includes: receiving, from a plurality of sensors associated with the 6-degree-of-freedom stage, displacement information associated with the 6-degree-of-freedom stage. A plurality of equations associated with the plurality of sensors are determined by a control unit based on the displacement information to represent an amount of change in position and attitude associated with each measurement axis of each of the plurality of sensors. The control unit determines position information and attitude information associated with the 6-degree-of-freedom stage using the equations. Movement of the 6-degree-of-freedom stage is caused, at least in part, to be controlled based on the position information, the attitude information, or both the position information and the attitude information. Three coordinate values associated with each valid measurement point of each of the plurality of sensors are associated with at least one degree of freedom.

主权项

1. A method, comprising:
receiving, from at least six sensors associated with a 6-degree-of-freedom stage, displacement information associated with movement of the 6-degree-of-freedom stage; determining, by a control unit and based on the displacement information, a plurality of equations associated with the at least six sensors to represent an amount of change in position and attitude associated with each measurement axis of each of the at least six sensors; determining, by the control unit, position information (X, Y, Z) and attitude information (Tx, Ty, Tz) associated with the 6-degree-of-freedom stage using the equations; and causing, at least in part, the movement of the 6-degree-of-freedom stage to be controlled based on the position information (X, Y, Z), the attitude information (Tx, Ty, Tz), or both the position information (X, Y, Z) and the attitude information (Tx, Ty, Tz), wherein three coordinate values associated with each valid measurement point of each of the at least six sensors are associated with at least one degree of freedom, wherein the plurality of equations respectively corresponding to the at least six sensors are determined using the following six expressions:
Measurement Information of First Sensor=−X1a+t(1,1)/pqrs(1,1)  First ExpressionMeasurement Information of Second Sensor=−X2a+t(2,2)/pqrs(2,1)  Second ExpressionMeasurement Information of Third Sensor=−Yb+t(3,3)/pqrs(3,2)  Third ExpressionMeasurement Information of Fourth Sensor=−Z4c+t(4,4)/pqrs(4,3)  Fourth ExpressionMeasurement Information of Fifth Sensor=−Z5c+t(5,5)/pqrs(5,3)  Fifth ExpressionMeasurement Information of Sixth Sensor=−Z6c+t(6,6)/pqrs(6,3),  Sixth Expression wherein:pqrs=[100-X⁢⁢1⁢a100-X⁢⁢2⁢a010-Yb001-Z⁢⁢4⁢c001-Z⁢⁢5⁢c001-Z⁢⁢6⁢c],⁢SC=[00YaZ⁢⁢4⁢aZ⁢⁢5⁢aZ⁢⁢6⁢aX⁢⁢1⁢bX⁢⁢2⁢b0Z⁢⁢4⁢bZ⁢⁢5⁢bZ⁢⁢6⁢bX⁢⁢1⁢cX⁢⁢2⁢cYc000111111],⁢Rx=[10000cos⁢⁢(Tx)-sin⁡(Tx)00sin⁡(Tx)cos⁢⁢(Tx)00001]Ry=[cos⁡(Ty)0sin⁡(Ty)00100-sin⁡(Ty)0cos⁢⁢(Ty)00001]Rz=[cos⁡(Tz)-sin⁡(Tz)00sin⁡(Tz)cos⁢⁢(Tz)0000100001],⁢t=-1⁢pqrs×Rz-1×Ry-1×Rx-1×SC, and wherein valid measurement points associated with the at least six sensors are P1(X1a, X1 b, X1 c) for a first sensor of the at least six sensors, P2(X2a, X2b, X2c) for a second sensor of the at least six sensors, P3(Ya, Yb, Yc) for a third sensor of the at least six sensors, P4(Z4a, Z4b, Z4c) for a fourth sensor of the at least six sensors, P5(Z5a, Z5b, Z5c) for a fifth sensor of the at least six sensors, and P6(Z6a, Z6b, Z6c) for a sixth sensor of the at least six sensors.