transformMotion

Compute motion quantities between two relatively fixed frames

Since R2020a

Syntax

[posS,orientS,velS,accS,angvelS] = transformMotion(posSFromP,orientSFromP,posP)

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP)

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP,velP)

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP,velP,accP)

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP,velP,accP,angvelP)

Description

[posS,orientS,velS,accS,angvelS] = transformMotion(posSFromP,orientSFromP,posP) computes motion quantities of the sensor frame relative to the navigation frame (posS, orientS, velS, accS, and angvelS) using the position of sensor frame relative to the platform frame, posSFromP, the orientation of the sensor frame relative to the platform frame, orientSFromP, and the position of the platform frame relative to the navigation frame, posP. Note that the position and orientation between the sensor frame and the platform frame are assumed to be fixed. Also, the unspecified quantities between the navigation frame and the platform frame (such as orientation, velocity, and acceleration) are assumed to be zero.

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP) additionally specifies the orientation of the platform frame relative to the navigation frame, orientP. The output arguments are the same as those of the previous syntax.

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP,velP) additionally specifies the velocity of the platform frame relative to the navigation frame, velP. The output arguments are the same as those of the previous syntax.

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP,velP,accP) additionally specifies the acceleration of the platform frame relative to the navigation frame, accP. The output arguments are the same as those of the previous syntax.

[___] = transformMotion(posSFromP,orientSFromP,posP,orientP,velP,accP,angvelP) additionally specifies the angular velocity of the platform frame relative to the navigation frame, angvelP. The output arguments are the same as those of the previous syntax.

Examples

Transform State to Sensor Frame

Define the pose, velocity, and acceleration of the platform frame relative to the navigation frame.

posPlat = [20 -1 0];
orientPlat = quaternion(1, 0, 0, 0);
velPlat = [0 0 0];
accPlat = [0 0 0];
angvelPlat = [0 0 1];

Define the position and orientation offset of IMU sensor frame relative to the platform frame.

posPlat2IMU = [1 2 3];
orientPlat2IMU = quaternion([45 0 0], 'eulerd', 'ZYX', 'frame');

Calculate the motion quantities of the sensor frame relative to the navigation frame and print the results.

[posIMU, orientIMU, velIMU, accIMU, angvelIMU] ...
    = transformMotion(posPlat2IMU, orientPlat2IMU, ...
    posPlat, orientPlat, velPlat, accPlat, angvelPlat);

fprintf('IMU position is:\n');

IMU position is:

fprintf('%.2f %.2f %.2f\n', posIMU);

21.00 1.00 3.00

orientIMU

orientIMU = quaternion
     0.92388 +       0i +       0j + 0.38268k

velIMU

velIMU = 1×3

    -2     1     0

accPlat

accPlat = 1×3

     0     0     0

Input Arguments

posSFromP — Position of sensor frame relative to platform frame

1-by-3 vector of real scalars

Position of the sensor frame relative to the platform frame, specified as a 1-by-3 vector of real scalars.

Example: [1 2 3]

orientSFromP — Orientation of sensor frame relative to platform frame

quaternion | 3-by-3 rotation matrix

Orientation of the sensor frame relative to the platform frame, specified as a quaternion or a 3-by-3 rotation matrix.

Example: quaternion(1,0,0,0)

posP — Position of platform frame relative to navigation frame

N-by-3 matrix of real scalars

Position of platform frame relative to navigation frame, specified as an N-by-3 matrix of real scalars. N is the number of position quantities.

Example: [1 2 3]

orientP — Orientation of platform frame relative to navigation frame

N-by-1 array of quaternion | 3-by-3-by-N array of scalars

Orientation of platform frame relative to navigation frame, specified as an N-by-1 array of quaternions, or a 3-by-3-by-N array of scalars. Each 3-by-3 matrix must be a rotation matrix. N is the number of orientation quantities.

Example: quaternion(1,0,0,0)

velP — Velocity of platform frame relative to navigation frame

N-by-3 matrix of real scalars

Velocity of platform frame relative to navigation frame, specified as an N-by-3 matrix of real scalars. N is the number of velocity quantities.

Example: [ 4 8 6]

accP — Acceleration of platform frame relative to navigation frame

N-by-3 matrix of real scalars

Acceleration of platform frame relative to navigation frame, specified as an N-by-3 matrix of real scalars. N is the number of acceleration quantities.

Example: [4 8 6]

angvelP — Angular velocity of platform frame relative to navigation frame

N-by-3 matrix of real scalars

Angular velocity of platform frame relative to navigation frame, specified as an N-by-3 matrix of real scalars. N is the number of angular velocity quantities.

Example: [4 2 3]

Output Arguments

posS — Position of sensor frame relative to navigation frame

N-by-3 matrix of real scalars

Position of sensor frame relative to navigation frame, returned as an N-by-3 matrix of real scalars. N is the number of position quantities specified by the posP input.

orientS — Orientation of sensor frame relative to navigation frame

N-by-1 array of quaternion | 3-by-3-by-N array of scalars

Orientation of sensor frame relative to navigation frame, returned as an N-by-1 array of quaternions, or a 3-by-3-by-N array of scalars. N is the number of orientation quantities specified by the orientP input. The returned orientation quantity type is same with the orientP input.

velS — Velocity of sensor frame relative to navigation frame

N-by-3 matrix of real scalars

Velocity of sensor frame relative to navigation frame, returned as an N-by-3 matrix of real scalars. N is the number of position quantities specified by the velP input.

accS — Acceleration of sensor frame relative to navigation frame

N-by-3 matrix of real scalars

Acceleration of sensor frame relative to navigation frame, returned as an N-by-3 matrix of real scalars. N is the number of position quantities specified by the accP input.

angvelS — Angular velocity of sensor frame relative to navigation frame

N-by-3 matrix of real scalars

Angular velocity of sensor frame relative to navigation frame, returned as an N-by-3 matrix of real scalars. N is the number of position quantities specified by the angvelP input.

More About

Motion Quantities Used in transformMotion

The transformMotion function calculates the motion quantities of the sensor frame (S), which is fixed on a rigid platform, relative to the navigation frame (N) using the mounting information of the sensor on the platform and the motion information of the platform frame (P).

As shown in the figure, the position and orientation of the platform frame and the sensor frame are fixed on the platform. The position of the sensor frame relative to the platform frame is p_SP, and the orientation of the sensor frame relative to the platform frame is r_SP. Since the two frames are both fixed, p_SP and r_SP are constant.

To compute the motion quantities of the sensor frame relative to the navigation frame, the quantities describing the motion of the platform frame relative to the navigation frame are required. These quantities include: the platform position (p_PN), orientation (r_PN), velocity, acceleration, angular velocity, and angular acceleration relative to the navigation frame. You can specify these quantities through the function input arguments except the angular acceleration, which is always assumed to be zero in the function. The unspecified quantities are also assumed to be zero.

Version History

Introduced in R2020a