Minimum Jerk Polynomial Trajectory
Generate minimum jerk polynomial trajectories through multiple waypoints
Since R2022a
![](minimum_jerk_polynomial_trajectory_block.png)
Libraries:
UAV Toolbox /
Algorithms
Robotics System Toolbox /
Utilities
Description
The Minimum Jerk Polynomial Trajectory block generates minimum jerk
polynomial trajectories that pass through the waypoints at the times specified in time points.
The block outputs positions, velocities, accelerations, jerks, and time of arrival for
achieving this trajectory based on the Time
input.
The block also accepts boundary conditions for waypoints. The block also outputs the coefficients for the polynomials and status of the trajectory generation.
The initial and final values of positions, velocities, accelerations, and jerks of the
trajectory are held constant outside the time period defined in TimePoints
input.
Examples
Ports
Input
Time — Time point along trajectory
scalar | vector
Time point along the trajectory, specified as a scalar or vector.
When the time is 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 instance 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
Waypoints — Waypoints positions along trajectory
n-by-p matrix
Positions of waypoints of the trajectory at given time points, specified as an n-by-p matrix. n is the dimension of the trajectory and p is the number of waypoints.
Data Types: single
| double
TimePoints — Time points for waypoints of trajectory
p-element row vector
Time points for the waypoints of the trajectory, specified as a p-element row vector. p is the number of waypoints.
Data Types: single
| double
VelBC — Velocity boundary conditions for waypoints
n-by-p matrix
Velocity boundary conditions for waypoints, specified as an n-by-p matrix. Each row sets the velocity boundary for the corresponding dimension of the trajectory n at each of p waypoints.
By default, the block uses a value of 0
at the boundary
waypoints and NaN
at the intermediate waypoints.
Dependencies
To enable this input port, select Show boundary conditions input ports
.
Data Types: single
| double
AccelBC — Acceleration boundary conditions for waypoints
n-by-p matrix
Acceleration boundary conditions for waypoints, specified as an n-by-p matrix. Each row sets the acceleration boundary for the corresponding dimension of the trajectory n at each of p waypoints.
By default, the block uses a value of 0
at the boundary
waypoints and NaN
at the intermediate waypoints.
Dependencies
To enable this input port, select Show boundary conditions input ports
.
Data Types: single
| double
JerkBC — Jerk boundary conditions for waypoints
n-by-p matrix
Jerk boundary conditions for waypoints, specified as an n-by-p matrix. Each row sets the jerk boundary for the corresponding dimension of the trajectory n at each of p waypoints.
By default, the block uses a value of 0
at the boundary
waypoints and NaN
at the intermediate waypoints.
Dependencies
To enable this input port, select Show boundary conditions input ports
.
Data Types: single
| double
Output
q — Positions of trajectory
n-element vector | n-by-m matrix
Positions of the trajectory, returned as an n-element vector or n-by-m matrix.
Data Types: single
| double
qd — Velocities of trajectory
n-element vector | n-by-m matrix
Velocities of the trajectory, returned as an n-element vector or n-by-m matrix.
Data Types: single
| double
qdd — Accelerations of trajectory
n-element vector | n-by-m matrix
Accelerations of the trajectory, returned as an n-element vector or n-by-m matrix.
Data Types: single
| double
qddd — Jerks of trajectory
n-element vector | n-by-m matrix
Jerks of the trajectory, returned as an n-element vector or n-by-m matrix.
Data Types: single
| double
TimeOfArrival — Time of arrival at each waypoint
p-element vector
Time of arrival at each waypoint, returned as a p-element vector. p is the number of waypoints.
Data Types: single
| double
PolynomialCoefs — Polynomial coefficients
n(p–
1
)-by-8
matrix
Polynomial coefficients, returned as an
n(p–
1
)-by-8
matrix. n is the dimension of the trajectory and
p is the number of waypoints. Each set of n
rows defines the coefficients for the polynomial that described each variable
trajectory.
Dependencies
To enable this output port, select Show polynomial coefficients output port
.
Data Types: single
| double
Status — Status of trajectory generation
three-element vector of the form [SingularityStatus
MaxIterStatus
MaxTimeStatus]
Status of trajectory generation, returned as a three-element vector of the form
[SingularityStatus
MaxIterStatus
MaxTimeStatus]
.
SingularityStatus returned as 0
or
1
indicates the occurrence of singularity. If singularity occurs
reduce the Maximum segment time
to Minimum segment time
ratio.
MaxIterStatus returned as 0
or
1
indicates if the number of iterations for the solver has
exceeded Maximum iterations
.
MaxTimeStatus returned as 0
or
1
indicates if the time for the solver has exceeded Maximum time
.
Dependencies
To enable this output port, select Show status output port
.
Data Types: uint8
Parameters
Show polynomial coefficients output port — Output polynomial coefficients
off
(default) | on
Select this parameter to output polynomial coefficients at the PolynomialCoefs
port.
Tunable: No
Show status output port — Output status
off
(default) | on
Select this parameter to output status at the Status
port.
Tunable: No
Time allocation — Enable time allocation
off
(default) | on
Enable to specify time allocation for the trajectory using the Time
weight
, Minimum segment time
, Maximum segment time
, Maximum iterations
, and Maximum time
parameters.
Tunable: No
Time weight — Weight for time allocation
100
(default) | positive scalar
Weight for time allocation, specified as a positive scalar.
Tunable: No
Dependencies
To enable this parameter, select Time
allocation
.
Minimum segment time — Minimum time segment length
0.1
(default) | positive scalar | (p–
1
)-element positive row
vector
Minimum time segment length, specified as a positive scalar or
(p–
1
)-element positive row
vector. p is the number of waypoints.
Tunable: No
Dependencies
To enable this parameter, select Time
allocation
.
Maximum segment time — Maximum time segment length
1
(default) | positive scalar | (p–
1
)-element positive row
vector
Maximum time segment length, specified as a positive scalar or
(p–
1
)-element positive row
vector. p is the number of waypoints.
Tunable: No
Dependencies
To enable this parameter, select Time
allocation
.
Maximum iterations — Maximum iterations for solver
1500
(default) | positive integer scalar
Maximum iterations for solver, specified as a positive integer scalar.
Tunable: No
Dependencies
To enable this parameter, select Time
allocation
.
Maximum time — Maximum time for solver
10
(default) | positive scalar
Maximum time for solver, specified as a positive scalar.
Tunable: No
Dependencies
To enable this parameter, select Time
allocation
.
Simulate using — Type of simulation to run
Interpreted execution
(default) | Code generation
Select the type of simulation to run from these options:
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
Tips
For better performance, consider these options:
Minimize the number of waypoint or parameter changes.
Set the
Simulate using
parameter toCode generation
. For more information, see Simulation Modes (Simulink).
References
[1] Bry, Adam, Charles Richter, Abraham Bachrach, and Nicholas Roy. “Aggressive Flight of Fixed-Wing and Quadrotor Aircraft in Dense Indoor Environments.” The International Journal of Robotics Research, 34, no. 7 (June 2015): 969–1002.
[2] Richter, Charles, Adam Bry, and Nicholas Roy. “Polynomial Trajectory Planning for Aggressive Quadrotor Flight in Dense Indoor Environments." Paper presented at the International Symposium of Robotics Research (ISRR 2013), 2013.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2022a
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