AbsoluteSensor

Description

Absolute kinematic quantities of frame_a aredetermined and provided at the conditional output signal connectors.For example, if parameter "get_r = true", the connector"r" is enabled and contains the absolute vector from the world frameto the origin of frame_a. The following quantities can be providedas output signals:

1. Absolute position vector (= r)
2. Absolute velocity vector (= v)
3. Absolute acceleration vector (= a)
4. Three angles to rotate world frame into frame_a (= angles)
5. Absolute angular velocity vector (= w)
6. Absolute angular acceleration vector (= z)

Via parameter resolveInFrame it is defined, in which framea vector is resolved:

If resolveInFrame = Types.ResolveInFrameA.frame_resolve, the conditional connector"frame_resolve" is enabled and the vectors are resolved in the frame, towhich frame_resolve is connected. Note, if this connector is enabled, it mustbe connected.

In the following figure the animation of an AbsoluteSensorcomponent is shown. The light blue coordinate system isframe_a and the yellow arrow is the animated sensor.

Velocity, acceleration, angular velocity and angular acceleration aredetermined by differentiating them in the world frame and then transformingthem in to the frame defined by resolveInFrame.

For example, if resolveInFrame = Types.ResolveInFrameA.frame_a, then

   v0 = der(frame_a.r0);   v  = resolve2(frame_a.R, v0);

is returned, i.e., the derivative of the absolute distance from theworld frame to the origin of frame_a, resolved in frame_a.

The cut-force and the cut-torque in frame_resolve arealways zero, whether frame_resolve is connected or not.

If get_angles = true, the 3 angles to rotate the worldframe into frame_a along the axes defined by parameter sequenceare returned. For example, if sequence = {3,1,2} then the world frame isrotated around angles[1] along the z-axis, afterwards it is rotatedaround angles[2] along the x-axis, and finally it is rotated aroundangles[3] along the y-axis and is then identical to frame_a.The 3 angles are returned in the range

    -p <= angles[i] <= p

There are two solutions for "angles[1]" in this range.Via parameter guessAngle1 (default = 0) thereturned solution is selected such that |angles[1] - guessAngle1| isminimal. The absolute transformation matrix of frame_amay be in a singular configuration with respect to "sequence", i.e.,there is an infinite number of angle values leading to the same absolutetransformation matrix. In this case, the returned solution isselected by setting angles[1] = guessAngle1. Then angles[2]and angles[3] can be uniquely determined in the above range.

The parameter sequence has the restriction thatonly values 1,2,3 can be used and that sequence[1] ≠ sequence[2]and sequence[2] ≠ sequence[3]. Often used values are:

  sequence = {1,2,3}  // Cardan or Tait-Bryan angle sequence           = {3,1,3}  // Euler angle sequence           = {3,2,1}