Transform Sensor

Sensor that measures the relative spatial relationship between two frames

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Libraries:
Simscape / Multibody / Frames and Transforms

Description

The Transform Sensor block measures the relative spatial relationship between frames connected to ports F and B of the block. The measured quantities include the relative pose, velocity, and acceleration, which are time-varying physical signals.

You can measure the absolute translational or rotational quantities of a frame by connecting the frame ports F and B of the block to this frame and the world frame of the model, respectively.

The default block units are meter-kilogram-second or MKS (SI). You can use the Simulink-PS Converter or PS-Simulink Converter block to specify the units of an input or output signal, respectively.

Measurement Frame

The measurement frame is:

• The frame to use to express the measured quantities.

• The location where the observer observes how the measured quantities change over time.

The selection of the measurement frame does not affect the rotational quantities. To see whether a particular quantity is affected, see the Output section.

The Transform Sensor block has five different options for the Measurement Frame parameter. For more information about these options, see the Measurement Frame parameter in the Parameters section.

Rotational and Translational Measurements

The block has four parameterizations to express the measured rotations: angle-axis, quaternion, rotation matrix, and rotation sequence. To enable these parameterizations, in the block dialog box, under Rotation, select corresponding parameters. For example, select the Angle and Axis parameters to use the angle-axis parameterization or select the Quaternion, Transform, or Rotation Sequence parameter to use the quaternion, rotation matrix, or rotation sequence parameterization.

Also, the block has various parameterizations to express rotational velocities and accelerations: x-, y-, and z- coordinates; the time derivatives of a quaternion or rotation sequence; or matrix. To enable these parameterizations, you can select the corresponding parameters under Angular Velocity or Angular Acceleration. For more information, see Rotational Measurements.

The block has three coordinate systems to express the translational measurements: Cartesian, cylindrical, and spherical. You can select one or more of them at the same time. For more information, see Translational Measurements.

The tables summarize the coordinates of the three systems, and the images show the diagrams of these coordinate systems. For simplicity purpose, in the images, specify the Measurement Frame parameter as Base.

Cartesian Coordinates

Coordinate	Description
X	The projection of the vector BF on the x-axis of the measurement frame.
Y	The projection of the vector BF on the y-axis of the measurement frame.
Z	The projection of the vector BF on the z-axis of the measurement frame.

Cylindrical Coordinates

Coordinate	Description
Radius	The length of the projection of the vector BF, in the x-y plane of the measurement frame.
Azimuth	The angle of the Radius with respect to the positive x-axis of the measurement frame. The angle falls in the range of [-π, π).
Z	The projection of the vector BF on the z-axis of the measurement frame.

Spherical Coordinates

Coordinate	Description
Distance	The distance between origins of the base and follower frames.
Azimuth	The angle of the projection of the vector BF in the x-y plane with respect to the positive x-axis. The angle is resolved in the measurement frame and falls in the range of [-π, π).
Inclination	The angle of the vector BF with respect to the x-y plane of the measurement frame. The angle falls in the range of [-π/2, π/2].

To use a specific coordinate system, select the corresponding parameters. For example, if you want to use the Cartesian system to express the measured relative linear velocity of the follower frame, under Velocity, select the X, Y, and Z parameters.

Examples

Fairground Carousel Ride

A fairground carousel ride. A torque applied to the wheel causes the carousel to rotate and a hydraulic actuator provides the force to lift the arm. The cabs are free to rotate about an axis approximately tangential to the wheel radius. When the wheel is near vertical, the centrifugal acceleration acting on the cabs (caused by the rotation of the wheel) ensures that the cabs are close to a near vertical position. Consequently, the riders are close to 'up-side-down' at the top of the rotation.

• Open Model

Ports

Frame

B — Base frame

frame

Frame port associated with the base frame.

F — Follower frame

frame

Frame port associated with the follower frame.

Output

q — Angle of rotation, rad

physical signal

Angle of rotation, returned as a scalar. The angle indicates the rotation of the follower frame with respect to the base frame about the axis specified by the vector output by port axs. The angle falls in the range [0, π].

Use ports q and axs to output the rotation signals using the axis-angle parameterization. For more information, see Rotational Measurements. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Rotation, select Angle.

axs — Axis of rotation, unitless

physical signal

Axis of rotation, returned as a 3-by-1 unit vector. Use ports q and axs to output the rotation signals using the axis-angle parameterization.

The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Rotation, select Axis.

Q — Quaternion, unitless

physical signal

Relative rotation, returned as a quaternion. For more information about the quaternions, see Rotational Measurements.

The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Rotation, select Quaternion.

R — Rotation matrix, unitless

physical signal

Relative rotation, returned as a 3-by-3 matrix. For more information about the rotation matrix, see Rotational Measurements. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Rotation, select Transform.

seq — Angles of three successive rotations, rad

physical signal

Relative rotation, returned as a 3-by-1 vector. The vector contains the angles for the three successive elementary rotations that represent the rotation of the follower frame with respect to the base frame.

The three rotations are about an intermediate frame and can be one of 12 different rotation sequences. For more information about the rotation sequence measurements, see Rotational Measurements. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Rotation, select Rotation Sequence.

wx — X-component of relative angular velocity, rad/s

physical signal

X-component of the relative angular velocity between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Omega X.

wy — Y-component of relative angular velocity, rad/s

physical signal

Y-component of the relative angular velocity between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Omega Y.

wz — Z-component of relative angular velocity, rad/s

physical signal

Z-component of the relative angular velocity between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Omega Z.

w — Relative angular velocity, rad/s

physical signal

Angular velocity of the follower frame with respect to the base frame, returned as a 3-by-1 vector. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Omega XYZ.

Qd — Relative angular velocity expressed as time derivative of quaternion, unitless

physical signal

Relative angular velocity, returned as a 4-by-1 vector that equals the time derivative of the signal from port Q. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Quaternion.

Rd — Relative angular velocity expressed as time derivative of rotation matrix, unitless

physical signal

Relative angular velocity, returned as a 3-by-3 matrix. The matrix equals the time derivative of the signal from port R. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Transform.

seqd — Relative angular velocity expressed as time derivative of rotation sequence angles, rad/s

physical signal

Relative angular velocity, returned as a 3-by-1 vector. The vector equals the time derivative of the output from the port seq. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Angular Velocity, select Rotation Sequence.

bx — X-component of relative angular acceleration, rad/s^2

physical signal

X-component of the relative angular acceleration between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Acceleration, select Alpha X.

by — Y-component of relative angular acceleration, rad/s^2

physical signal

Y-component of the relative angular acceleration between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Acceleration, select Alpha Y.

bz — Z-component of relative angular acceleration, rad/s^2

physical signal

Z-component of the relative angular acceleration between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Acceleration, select Alpha Z.

b — Relative angular acceleration, rad/s^2

physical signal

Angular acceleration of the follower frame with respect to the base frame, returned as a 3-by-1 vector. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Angular Acceleration, select Alpha XYZ.

Qdd — Relative angular acceleration expressed as second time derivative of quaternion, unitless

physical signal

Relative angular acceleration, returned as a 4-by-1 vector. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Angular Acceleration, select Quaternion.

Rdd — Relative angular acceleration expressed as second time derivative of rotation matrix, unitless

physical signal

Relative angular acceleration, returned as a 3-by-3 matrix. The setting of the Measurement Frame parameter does not affect the expression of this signal.

Dependencies

To enable this port, under Angular Acceleration, select Transform.

x — X-component of relative translation, m

physical signal

X-component of the relative translation between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Translation, select X.

y — Y-component of relative translation, m

physical signal

Y-component of the relative translation between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Translation, select Y.

z — Z-component of relative translation, m

physical signal

Z-component of the relative translation between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Because both the Cartesian and cylindrical coordinate systems have the z-axis, the Transform Sensor block has only one output port for both coordinate systems.

Dependencies

To enable this port, under Translation, select Z.

p — Relative translation, m

physical signal

Translation of the follower frame with respect to the base frame, returned as a 3-by-1 vector expressed in the Cartesian coordinate system. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Translation, select XYZ.

rad — Cylindrical radius coordinate of relative translation, m

physical signal

Cylindrical radius coordinate of the relative translation vector, returned as a nonegative scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Translation, select Radius.

azm — Azimuth of relative translation, rad

physical signal

Azimuth of the relative translation vector, returned as scalar. The angle falls in the range of [-π, π). The azimuth is undefined if the origins of the base and follower frames coincide with each other. The setting of the Measurement Frame parameter affects the expression of this signal.

Because the azimuth exists in both the cylindrical and spherical coordinate systems, the Transform Sensor block has only one output port for both coordinate systems.

Dependencies

To enable this port, under Translation, select Azimuth.

dst — Spherical radius coordinate of relative translation, m

physical signal

Spherical radius coordinate of the relative translation vector, returned as a scalar. The value equals the distance between the origins of the base and follower frames. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Translation, select Distance.

inc — Inclination of relative translation, rad

physical signal

Inclination of the relative translation vector, expressed in the spherical coordinate system, returned as a scalar. The angle falls in the range of [-π/2, π/2]. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Translation, select Inclination.

vx — X-coordinate of relative linear velocity, m/s

physical signal

X-component of the relative linear velocity between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Velocity, select X.

vy — Y-coordinate of relative linear velocity, m/s

physical signal

Y-component of the relative linear velocity between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Velocity, select Y.

vz — Z-coordinate of relative linear velocity, m/s

physical signal

Z-component of the relative linear velocity between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Because both the Cartesian and cylindrical coordinate systems have the z-axis, the Transform Sensor block has only one output port for both coordinate systems.

Dependencies

To enable this port, under Velocity, select Z.

v — Relative linear velocity, m/s

physical signal

Linear velocity of the follower frame with respect to the base frame, returned as a 3-by-1 vector expressed in Cartesian coordinate system. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Velocity, select XYZ.

vrad — Cylindrical radius coordinate of relative linear velocity, m/s

physical signal

Cylindrical radius coordinate of the relative linear velocity, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Velocity, select Radius.

vazm — Azimuth coordinate of relative linear velocity, rad/s

physical signal

Azimuth coordinate of the relative linear velocity, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Because the azimuth coordinate exists in both the cylindrical and spherical coordinate systems, the Transform Sensor block has only one output port for both coordinate systems.

Dependencies

To enable this port, under Velocity, select Azimuth.

vdst — Spherical radius coordinate of relative linear velocity, m/s

physical signal

Spherical radius coordinate of the relative linear velocity, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Velocity, select Distance.

vinc — Inclination coordinate of relative linear velocity, rad/s

physical signal

Inclination coordinate of the relative linear velocity, expressed in the spherical coordinate system, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Velocity, select Inclination.

ax — X-component of relative linear acceleration, m/s^2

physical signal

X-component of the relative linear acceleration between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Acceleration, select X.

ay — Y-component of relative linear acceleration, m/s^2

physical signal

Y-component of the relative linear acceleration between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Acceleration, select Y.

az — Z-component of relative linear acceleration, m/s^2

physical signal

Z-component of the relative linear acceleration between the two frames, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Because both the Cartesian and cylindrical coordinate systems have the z-axis, the Transform Sensor block has only one output port for both coordinate systems.

Dependencies

To enable this port, under Acceleration, select Z.

a — Relative linear acceleration, m/s^2

physical signal

Linear acceleration of the follower frame with respect to the base frame, returned as a 3-by-1 vector expressed in Cartesian coordinate system. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Acceleration, select XYZ.

arad — Cylindrical radius coordinate of relative linear acceleration, m/s^2

physical signal

Cylindrical radius coordinate of the relative linear acceleration, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Acceleration, select Radius.

aazm — Azimuth coordinate of relative linear acceleration, rad/s^2

physical signal

Azimuth coordinate of the relative linear acceleration, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Because the azimuth coordinate exists in both cylindrical and spherical coordinate systems, the Transform Sensor block has only one output port for both coordinate systems.

Dependencies

To enable this port, under Acceleration, select Azimuth.

adst — Spherical radius coordinate of relative linear acceleration, m/s^2

physical signal

Spherical radius coordinate of the relative linear acceleration, returned as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port under Acceleration, select Distance.

ainc — Inclination coordinate of relative linear acceleration, rad/s^2

physical signal

Inclination coordinate of the relative linear acceleration, expressed in the spherical coordinate system, specified as a scalar. The setting of the Measurement Frame parameter affects the expression of this signal.

Dependencies

To enable this port, under Acceleration, select Inclination.

Parameters

Measurement Frame — Frame to use to express measurements

World (default) | Base | Follower | Non-Rotating Base | Non-Rotating Follower

Frame to use to specify how to express and where to observe the measured quantiles. The specification of this parameter does not affect the rotational quantities.

Measurement Frame Types

Measurement Frame	Description
World	The world frame is an inertial frame.
Base	The base frame of the Transform Sensor block. It is a non-inertial frame.
Follower	The follower frame of the Transform Sensor block. It is a non-inertial frame.
Non-Rotating Base	The non-rotating base frame is an inertial frame that is always instantaneously coincident with the base frame of the Transform Sensor block.
Non-Rotating Follower	The non-rotating follower frame is an inertial frame that is always instantaneously coincident with the follower frame of the Transform Sensor block.

The non-rotating base and non-rotating follower frames are not actual frames that move through space and exist over time. Therefore, the measurements expressed in the non-rotating frames do not support standard derivative relationships. If the block uses a non-rotating frame as the measurement frame, the expressed acceleration measurements often do not involve centripetal and Coriolis terms.

Sequence — Sequence of rotation axis

X-Y-X (default) | X-Y-Z | X-Z-X | X-Z-Y | Y-X-Y | Y-X-Z | Y-Z-X | Y-Z-Y | Z-X-Y | Z-X-Z | Z-Y-X | Z-Y-Z

Sequence of the rotation axis for three successive elementary rotations. See Rotation Sequence Measurements for more information.

Dependencies

To enable this parameter, under Rotation, select Rotation Sequence.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2012a