Transform Trajectory
Generate trajectory between two homogeneous transforms
- Library:
Robotics System Toolbox / Utilities
Description
The Transform Trajectory block generates an interpolated trajectory between two homogenous transformation matrices. The block outputs the transform at the times given by the Time input, which can be a scalar or vector.
The trajectory is computed using quaternion spherical linear interpolation (SLERP) for the rotation and linear interpolation for the translation. This method finds the shortest path between positions and rotations of the transformation. Select the Use custom time scaling check box to compute the trajectory using a custom time scaling. The block uses linear time scaling by default.
The initial and final values are held constant outside the time period defined in Time interval.
Ports
Input
Time — Time point along trajectory
scalar | vector
Time point along trajectory, specified as a scalar or vector. In general, when specified as a scalar, this value is synced with simulation time and is used to specify the time point for sampling the trajectory. The block outputs a vector of the trajectory variables at that instant in time. If the time is specified as a vector, the block outputs a matrix with each column corresponding to each element of the vector.
Data Types: single | double
T0 — Initial transformation matrix
4-by-4 homogeneous transformation
Initial transformation matrix, specified as a 4-by-4 homogeneous transformation. The function generates a trajectory that starts at the initial orientation, T0, and goes to the final orientation, TF.
Example: trvec2tform([1 10 -1])
Dependencies
To enable this parameter, set the Waypoint source to
External.
Data Types: single | double
TF — Final transformation matrix
4-by-4 homogeneous transformation
Final transformation matrix, specified as a 4-by-4 homogeneous transformation. The function generates a trajectory that starts at the initial orientation, T0, and goes to the final orientation, TF.
Example: trvec2tform([1 10 -1])
Dependencies
To enable this parameter, set the Waypoint source to
External.
Data Types: single | double
TimeInterval — Start and end times for trajectory
two-element vector
Start and end times for the trajectory, specified as a two-element vector.
Example: [0 10]
Dependencies
To enable this parameter, set the Waypoint source to
External.
Data Types: single | double
TSTime — Time scaling time points
scalar | p-element vector
Time scaling time points, specified as a scalar or n p-element vector, where p is the number of points for time scaling. By default, the time scaling is a linear time scaling spanning the TimeInterval. Specify the actual time scaling values in TimeScaling.
If the Time input is specified at a time not specified by these points, interpolation is used to find the right scaling time.
Dependencies
To enable this parameter, select the Use custom time
scaling check box and set Parameter source to
External.
To specify a scalar, the Time input must be a scalar.
Data Types: single | double
TimeScaling — Time scaling vector and first two derivatives
three-element vector | 3-by-p matrix
Time scaling vector and its first two derivatives, specified as a three element vector or a 3-by-p matrix, where m is the length of TSTime. By default, the time scaling is a linear time scaling spanning the TimeInterval.
For a nonlinear time scaling, specify the values of the time points in the first row. The second and third rows are the velocity and acceleration of the time points, respectively. For example, to follow the path with a linear velocity to the halfway point, and then jump to the end, the time-scaling would be:
s(1,:) = [0 0.25 0.5 1 1 1] % Position s(2,:) = [1 1 1 0 0 0] % Velocity s(3,:) = [0 0 0 0 0 0] % Acceleration
Dependencies
To enable this parameter, select the Use custom time
scaling check box and set Parameter source to
External.
To specify a three-element vector, the Time and TSTime inputs must be a scalar.
Data Types: single | double
Output
tform — Homogeneous transformation matrices
4-by-4-by-m homogenous matrix array
Homogeneous transformation matrices, returned as a 4-by-4-by-m homogenous matrix array, where m is the number of points input to Time.
vel — Transform velocities
6-by-m matrix
Transform velocities, returned as a 6-by-m matrix, where
m is the number of points input to Time.
Each row of the vector is the angular and linear velocity of the transform as
[wx wy wz vx vy vz]. w represents an angular
velocity and v represents a linear velocity.
alpha — Transform accelerations
6-by-m matrix
Transform velocities, returned as a 6-by-m matrix, where
m is the number of points input to Time.
Each row of the vector is the angular and linear acceleration of the transform as
[alphax alphay alphaz ax ay az]. alpha
represents an angular acceleration and a represents a linear
acceleration.
Parameters
Waypoint source — Source for waypoints
Internal (default) | External
Specify External to specify the Waypoints
and Time points parameters as block inputs instead of block
parameters.
Initial transform — Initial transformation matrix
trvec2tform([1 10 -1]) (default) | 4-by-4 homogeneous transformation
Initial transformation matrix, specified as a 4-by-4 homogeneous transformation. The function generates a trajectory that starts at the Initial transform and goes to the Final transform.
Data Types: single | double
Final transform — Final transformation matrix
eul2tform([0 pi pi/2]) (default) | 4-by-4 homogeneous transformation
Final transformation matrix, specified as a 4-by-4 homogeneous transformation. The function generates a trajectory that starts at the Initial transform and goes to the Final transform.
Data Types: single | double
Time interval — Start and end times for trajectory
[2 3] | two-element vector
Start and end times for the trajectory, specified as a two-element vector in seconds.
Data Types: single | double
Use custom time scaling — Enable custom time scaling
off (default) | on
Enable to specify custom time scaling for the trajectory using the Parameter Source, Time scaling time, and Time scaling values parameters.
Parameter source — Source for waypoints
Internal (default) | External
Specify External to specify the Time scaling
time and Time scaling values parameters as block
inputs instead of block parameters.
Dependencies
To enable this parameter, select the Use custom time scaling check box.
Time scaling time — Time scaling time points
2:0.1:3 (default) | scalar | p-element vector
Time scaling time points, specified as a scalar or p-element vector, where p is the number of points for time scaling. By default, the time scaling is a linear time scaling spanning the Time interval. Specify the actual time scaling values in Time scaling values.
If the Time input is specified at a time not specified by these points, interpolation is used to find the right scaling time.
Dependencies
To enable this parameter, select the Use custom time scaling check box.
To specify a scalar, the Time input must be a scalar.
Data Types: single | double
Time scaling values — Time scaling vector and first two derivatives
[0:0.1:1; ones(1,11); zeros(1,11)] (default) | three-element vector | 3-by-m matrix
Time scaling vector and its first two derivatives, specified as a three-element vector or 3-by-p matrix, where p is the length of Time scaling time. By default, the time scaling is a linear time scaling spanning the Time interval.
For a nonlinear time scaling, specify the values of the time points in the first row. The second and third rows are the velocity and acceleration of the time points, respectively. For example, to follow the path with a linear velocity to the halfway point, and then jump to the end, the time-scaling would be:
s(1,:) = [0 0.25 0.5 1 1 1] % Position s(2,:) = [1 1 1 0 0 0] % Velocity s(3,:) = [0 0 0 0 0 0] % Acceleration
Dependencies
To enable this parameter, select the Use custom time scaling checkbox.
To specify a three-element vector, the Time and TSTime inputs must be a scalar.
Data Types: single | double
Simulate using — Type of simulation to run
Interpreted execution (default) | Code generation
Interpreted execution— Simulate model using the MATLAB® interpreter. This option shortens startup time but has a slower simulation speed thanCode generation. In this mode, you can debug the source code of the block.Code generation— Simulate model using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is comparable toInterpreted execution.
Tunable: No
