RelativeSensor

Description

Relative kinematic quantities between frame_a and frame_b aredetermined and provided at the conditional output signal connectors.For example, if parameter "get_r_rel = true", the connector"r_rel" is enabled and contains the relative vector fromframe_a to frame_b. The following quantities can be providedas output signals:

1. Relative position vector (= r_rel)
2. Relative velocity vector (= v_rel)
3. Relative acceleration vector (= a_rel)
4. Three angles to rotate frame_a into frame_b (= angles)
5. Relative angular velocity vector (= w_rel)
6. Relative angular acceleration vector (= z_rel)

Via parameter resolveInFrame it is defined, in which framea vector is resolved (before differentiation):

If resolveInFrame = Types.ResolveInFrameAB.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 a RelativeSensorcomponent is shown. The light blue coordinate system isframe_a, the dark blue coordinate system is frame_b, andthe yellow arrow is the animated sensor.

Note, derivativesof relative kinematic quantities are always performed withrespect to the frame, in which the vector to be differentiatedis resolved. After differentiation, it is possible via parameterresolveInFrameAfterDifferentiation (in the "Advanced" menu)to resolve the differentiatedvector in another frame.

For example, if resolveInFrame = Types.ResolveInFrameAB.frame_b, then

r_rel = resolve2(frame_b.R, frame_b.r_0 - frame_a.r0);v_rel = der(r_rel);

is returned (r_rel = resolve2(frame_b.R, frame_b.r_0 - frame_a.r0)), i.e.,the derivative of the relative distance from frame_a to frame_b,resolved in frame_b. IfresolveInFrameAfterDifferentiation = Types.ResolveInFrameAB.world, thenv_rel is additionally transformed to:

v_rel = resolve1(frame_b.R, der(r_rel))

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 frame_ainto frame_b along the axes defined by parameter sequenceare returned. For example, if sequence = {3,1,2} then frame_a 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_b.The 3 angles are returned in the range

-π <= angles[i] <= π

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 relative transformation matrix between frame_a andframe_b may be in a singular configuration with respect to "sequence", i.e.,there is an infinite number of angle values leading to the same relativetransformation 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}