Method for the control of positioning systems

Claim 1

A method for controlling a positioning system by means of a control system comprising the steps of: a) positioning a body (W), which is desired to be positioned, in relation to any desired reference coordinate system by the control system, wherein said positioning is performed on a basis of a plurality of specifiable motion sets, and wherein a spatial position of the body (W) is given by a location (P) and an orientation (R) of the body; b) coupling an imaginary axis (X W ) with said body (W), wherein said imaginary axis (X W ) passes through the location (P) and can be selected at will; c) tracing a first space curve (k1) and a second space curve (k2) by the body orientation (R) when the body (W) moves, whereby a tip of a polar vector (X W ) sweeps along said first and second space curves (k1, k2); d) specifying a first concatenation orientation (UP1) on the first space curve (k1) of a first motion set; e) specifying a second concatenation orientation (UP2) on the second space curve (k2) of a second motion set, wherein said second motion set follows said first motion set; f) forming a X H -Y H principal plane of an auxiliary Cartesian coordinate system (X H , Y H , Z H ) by a plane which passes through an X W1 axis of the body orientation (R(UP1)) in the first concatenation orientation (UP1) and passes through an X W2 axis of the body orientation (R(UP2)) in the second concatenation orientation (UP2), wherein an origin of said auxiliary Cartesian coordinate system is the location (P) of the body, wherein the X W1 axis is coincident with the X H axis of the auxiliary Cartesian coordinate system; g) determining a first and a second roll angle (A1, A2), a first and a second pitch angle (B1, B2), and a first and second yaw angle (C1, C2) for the first and second concatenation orientations (UP1, UP2) relative to the auxiliary Cartesian coordinate system; h) interpolating an orientation relative to the auxiliary Cartesian coordinate system between the first and second concatenation orientation (UP1, UP2), whereby said interpolating is performed using said first and second roll angles (A1, A2), said first and second pitch angles (B1, B2) and said first and second yaw angles (C1, C2); i) determining a first and second vectorial orientation velocities on the concatenation orientations (UP1, UP2); j) transforming the first and second vectorial orientation velocities to the auxiliary Cartesian coordinate system resulting in a first and second prime vectorial orientation velocities; k) transforming the first and second prime vectorial orientation velocities into a first and a second roll angular velocity (A1', A2'), a first and a second pitch angular velocity (B1', B2'), and a first and a second yaw angular velocity (C1', C2'); and l) specifying a first, second and third scalar path-time function from said first and second roll, pitch and yaw angles (A1, B1, C1, A2, B2, C2) and said first and second roll, pitch and yaw angular velocities (A1', B1', C1', A2', B2', C2'); m) moving said body according to the first, second and third scalar path-time functions, whereby a continuous velocity is assured for a transition from the first motion set to the second motion set.

Claim 2

A method for controlling a positioning system by means of a control system comprising the steps of: a) positioning a body (W), which is desired to be positioned, in relation to any desired reference coordinate system by the control system, wherein said positioning is performed on a basis of a plurality of specifiable motion sets, and wherein a spatial position of the body (W) is given by a location (P) and an orientation (R) of the body; b) coupling an imaginary axis (X W ) with said body (W), wherein said imaginary axis (X W ) passes through the location (P) and can be selected at will; c) tracing a first space curve (k1) and a second space curve (k2) by the body orientation (R) when the body (W) moves, whereby a tip of a polar vector (X W ) sweeps along said first and second space curves (k1, k2); d) specifying a first concatenation orientation (UP1) on the first space curve (k1) of a first motion set; e) specifying a second concatenation orientation (UP2) on the second space curve (k2) of a second motion set, wherein said second motion set follows said first motion set; f) forming a X H -Y H principal plane of an auxiliary Cartesian coordinate system (X H , Y H , Z H ) by a plane which passes through an X W1 axis of the body orientation (R(UP1)) in the first concatenation orientation (UP1) and passes through an X W2 axis of the body orientation (R(UP2)) in the second concatenation orientation (UP2), wherein an origin of said auxiliary Cartesian coordinate system is the location (P) of the body, wherein the X W1 axis is coincident with the X H axis of the auxiliary Cartesian coordinate system; g) determining a first and a second roll angle (A1, A2), a first and a second pitch angle (B1, B2), and a first and second yaw angle (C1, C2) for the first and second concatenation orientations (UP1, UP2) relative to the auxiliary Cartesian coordinate system; h) interpolating an orientation relative to the auxiliary Cartesian coordinate system between the first and second concatenation orientation (UP1, UP2), whereby said interpolating is performed using said first and second roll angles (A1, A2), said first and second pitch angles (B1, B2) and said first and second yaw angles (C1, C2); i) determining a first and second vectorial orientation velocities on the concatenation orientations (UP1, UP2); j) transforming the first and second vectorial orientation velocities to the auxiliary Cartesian coordinate system resulting in a first and second prime vectorial orientation velocities; k) transforming the first and second prime vectorial orientation velocities into a first and a second roll angular velocity (A1', A2'), a first and a second pitch angular velocity (B1', B2'), and a first and a second yaw angular velocity (C1', C2'); and l) specifying a first, second and third scalar path-time function from said first and second roll, pitch and yaw angles (A1, B1, C1, A2, B2, C2) and said first and second roll, pitch and yaw angular velocities (A1', B1', C1', A2', B2', C2'); m) moving said body according to the first, second and third scalar path-time functions, whereby a continuous velocity is assured for a transition from the first motion set to the second motion set.