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More information can be found in the individual scripts (.py).Supported on the following operating systems
Windows, Linux, macOSAn open-source library for generating trajectories using two different methods (trapezoidal, polynomial). The library provides access to various classes for working with multi-axis (Trapezoidal_Profile_Cls, Polynomial_Profile_Cls) trajectories as well as multi-segment (Multi_Segment_Cls) trajectories.
The trajectory profile, which contains position, velocity, and acceleration, is generated from input constraints explained in the individual classes.
The repository also contains a transformation library with the necessary project-related functions. See link below.
The library can be used within the Robot Operating System (ROS), Blender, PyBullet, Nvidia Isaac, or any program that allows Python as a programming language.
A simple program that describes how to work with the library can be found below. The whole program is located in the individual evaluation folder.
# System (Default)
import sys
# Numpy (Array computing) [pip3 install numpy]
import numpy as np
# Custom Lib.:
# ../Trajectory/Utilities
import Trajectory.Utilities
# ../Transformation/Utilities/Mathematics
import Transformation.Utilities.Mathematics as Mathematics
def main():
"""
Description:
A program to generate multi-axis trapezoidal trajectories.
Further information can be found in the programme below.
../Trajectory/Profile.py
"""
# Initialization of multi-axis constraints for trajectory generation.
Ax_Constraints_0 = [np.array([Mathematics.Degree_To_Radian(10.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(-10.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(-45.0), 0.0], dtype=np.float32)]
Ax_Constraints_f = [np.array([Mathematics.Degree_To_Radian(90.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(-90.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(45.0), 0.0], dtype=np.float32)]
# Initialization of the class to generate trajectory.
Trapezoidal_Cls = Trajectory.Utilities.Trapezoidal_Profile_Cls(delta_time=0.01)
# Obtain multi-axis trajectories.
for i, (ax_0_i, ax_f_i) in enumerate(zip(Ax_Constraints_0, Ax_Constraints_f)):
# Generation of trajectories from input parameters.
(s, s_dot, s_ddot) = Trapezoidal_Cls.Generate(ax_0_i[0], ax_f_i[0], ax_0_i[1], ax_f_i[1],
0.0, 1.0)
if __name__ == '__main__':
sys.exit(main())Position
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trapezoidal_Profile
$ ../Evaluation/Trapezoidal_Profile/> python3 test_position.py
Velocity
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trapezoidal_Profile
$ ../Evaluation/Trapezoidal_Profile/> python3 test_velocity.py
Acceleration
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trapezoidal_Profile
$ ../Evaluation/Trapezoidal_Profile/> python3 test_acceleration.py
A simple program that describes how to work with the library can be found below. The whole program is located in the individual evaluation folder.
# System (Default)
import sys
# Numpy (Array computing) [pip3 install numpy]
import numpy as np
# Custom Lib.:
# ../Trajectory/Utilities
import Trajectory.Utilities
# ../Transformation/Utilities/Mathematics
import Transformation.Utilities.Mathematics as Mathematics
def main():
"""
Description:
A program to generate multi-axis polynomial trajectories.
Further information can be found in the programme below.
../Trajectory/Profile.py
"""
# Initialization of multi-axis constraints for trajectory generation.
Ax_Constraints_0 = [np.array([Mathematics.Degree_To_Radian(10.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(-10.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(-45.0), 0.0], dtype=np.float32)]
Ax_Constraints_f = [np.array([Mathematics.Degree_To_Radian(90.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(-90.0), 0.0], dtype=np.float32),
np.array([Mathematics.Degree_To_Radian(45.0), 0.0], dtype=np.float32)]
# Initialization of the class to generate trajectory.
Polynomial_Cls = Trajectory.Utilities.Polynomial_Profile_Cls(delta_time=0.01)
# Obtain multi-axis trajectories.
for i, (ax_0_i, ax_f_i) in enumerate(zip(Ax_Constraints_0, Ax_Constraints_f)):
# Generation trajectories from input parameters.
(s, s_dot, s_ddot) = Polynomial_Cls.Generate(ax_0_i[0], ax_f_i[0], ax_0_i[1], ax_f_i[1],
0.0, 1.0)
if __name__ == '__main__':
sys.exit(main())Position
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Polynomial_Profile
$ ../Evaluation/Polynomial_Profile/> python3 test_position.py
Velocity
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Polynomial_Profile
$ ../Evaluation/Polynomial_Profile/> python3 test_velocity.py
Acceleration
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Polynomial_Profile
$ ../Evaluation/Polynomial_Profile/> python3 test_acceleration.py
A simple program that describes how to work with the library can be found below. The whole program is located in the individual evaluation folder.
# System (Default)
import sys
# Numpy (Array computing) [pip3 install numpy]
import numpy as np
# Custom Lib.:
# ../Trajectory/Core
import Trajectory.Core
# ../Transformation/Utilities/Mathematics
import Transformation.Utilities.Mathematics as Mathematics
def main():
"""
Description:
A program to generate a multi-segment trajectory using the selected method.
Possible methods of generating a multi-segment trajectory are as follows:
1\ Trapezoidal (parabolic)
2\ Polynomial (quintic)
Further information can be found in the programme below.
../Trajectory/Core.py
"""
# Initialization of multi-segment constraints for trajectory generation.
# 1\ Input control points (waypoints) to be used for trajectory generation.
P = np.array([Mathematics.Degree_To_Radian(0.0), Mathematics.Degree_To_Radian(90.0),
Mathematics.Degree_To_Radian(55.0), Mathematics.Degree_To_Radian(-15.0)], dtype=np.float32)
# 2\ Trajectory duration between control points.
delta_T = np.array([5.0, 5.0, 5.0], dtype=np.float32)
# 3\ Duration of the blend phase.
t_blend = np.array([1.0, 1.0, 1.0, 1.0], dtype=np.float32)
# Initialization of the class to generate multi-segment trajectory.
MST_Cls = Trajectory.Core.Multi_Segment_Cls('Trapezoidal', delta_time=0.1)
# Generation multi-segment trajectories from input parameters.
(s, s_dot, s_ddot, T, L) = MST_Cls.Generate(P, delta_T, t_blend)
if __name__ == '__main__':
sys.exit(main())Position
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trajectory
$ ../Evaluation/Trajectory/> python3 test_position.py
Velocity
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trajectory
$ ../Evaluation/Trajectory/> python3 test_velocity.py
Acceleration
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trajectory
$ ../Evaluation/Trajectory/> python3 test_acceleration.py
A simple program that describes how to work with the library can be found below. The whole program is located in the individual evaluation folder.
# System (Default)
import sys
# Numpy (Array computing) [pip3 install numpy]
import numpy as np
# Custom Lib.:
# ../Trajectory/Core
import Trajectory.Core
# ../Transformation/Utilities/Mathematics
import Transformation.Utilities.Mathematics as Mathematics
def main():
"""
Description:
A program to generate a multi-segment trajectory using the selected method.
Possible methods of generating a multi-segment trajectory are as follows:
1\ Trapezoidal (parabolic)
2\ Polynomial (quintic)
Further information can be found in the programme below.
../Trajectory/Core.py
"""
# Initialization of multi-segment constraints for trajectory generation.
# 1\ Input control points (waypoints) to be used for trajectory generation.
P = np.array([Mathematics.Degree_To_Radian(0.0), Mathematics.Degree_To_Radian(90.0),
Mathematics.Degree_To_Radian(55.0), Mathematics.Degree_To_Radian(-15.0)], dtype=np.float32)
# 2\ Trajectory duration between control points.
delta_T = np.array([5.0, 5.0, 5.0], dtype=np.float32)
# 3\ Duration of the blend phase.
t_blend = np.array([1.0, 1.0, 1.0, 1.0], dtype=np.float32)
# Initialization of the class to generate multi-segment trajectory.
MST_Cls = Trajectory.Core.Multi_Segment_Cls('Polynomial', delta_time=0.1)
# Generation multi-segment trajectories from input parameters.
(s, s_dot, s_ddot, T, L) = MST_Cls.Generate(P, delta_T, t_blend)
if __name__ == '__main__':
sys.exit(main())Position
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trajectory
$ ../Evaluation/Trajectory/> python3 test_position.py
Velocity
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trajectory
$ ../Evaluation/Trajectory/> python3 test_velocity.py
Acceleration
$ /> cd Documents/GitHub/Trajectory_Generation/Evaluation/Trajectory
$ ../Evaluation/Trajectory/> python3 test_acceleration.py
@misc{RomanParak_TrajectoryGeneration,
author = {Roman Parak},
title = {An open-source trajectory generation library useful for robotics applications},
year = {2023},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/rparak/Trajectory_Generation}}
}
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