An Open-Source Trajectory Generation Library Useful for Robotics Applications

Requirements

Programming Language

Python

Import Libraries

More information can be found in the individual scripts (.py).

Supported on the following operating systems

Windows, Linux, macOS

Project Description

An 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.

/rparak/Transformation

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.

Multi-Axis Trajectory of a Trapezoidal Profile

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

Multi-Axis Trajectory of a Polynomial Profile

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

Multi-Segment Linear Trajectory with Trapezoidal Blends

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

Multi-Segment Linear Trajectory with Polynomial Blends

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

Contact Info

Roman.Parak@outlook.com

Citation (BibTex)

@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}}
}