dynkin 0.2.1

A toolkit for 3D dynamics and kinematics

pydynkin - A python version of dynkin

A toolkit for 3D dynamics and kinematics of rigid bodies using the YPR euler angle convention.

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Note: dynkin is also available in a C++ version, available here: https://github.com/freol35241/dynkin

General

dynkin is a set of tools for handling the dynamics and kinematics of rigid bodies in 3 dimensions (6DOFs). Some features:

• Homogenous transformation matrices
• Chained reference frames
• Idealized rigid body implementation

The fundamentals of reference frames and the kinematic relations of these are based on Theory of Applied Robotics (Reza N. Jazar) , the idealized rigid body implementation follows the outline suggested in the lectures by Fossen.

Installation

pip install dynkin

Theory intro

Some basic notions:

• A reference Frame is defined in dynkin as an object which positions, vectors, velocities, accelerations etc can be decomposed in. dynkin represents reference Frames by (4x4) homogenous transformation matrices. A Frame is aligned (positioned, rotated) and moves (linear and angular velocity) in relation to another Frame or the inertial frame (represented by None).
• The pose of a Frame is its generalized position and the twist of a Frame is its generalized velocity, both in relation to the inertial frame.
• All rotations in dynkin are internally represented by rotation matrices but the external API, so far, deals only with Euler angles of the YPR (Yaw-Pitch-Roll) convention.
• A kinematic chain is a single-linked list of Frames, where each Frame holds a reference to its closest parent. Any number of Frames may be attached into such a chain and the chain may also have any number of branches, it is however the user´s responsibility to ensure no kinematic loops occur.
• A transform is an object relating two Frames enabling transformation of positions, vectors, velocities etc from one Frame to the other. The Frames do not need to be part of the same kinematic chain.
• A RigidBody is a 3D body with arbitrary extent that may be described by a generalized inertia matrix (6x6). It accelerates when subject to generalized external forces (wrenches) and rotational velocities give rise to inertial forces (coriolis and centripetal contributions).

Examples

Single frame

from dynkin import Frame, transform

frame1 = Frame(position=[1, 2, 3], attitude=[0, 0, 90], degrees=True)

# Find transformation from the inertial frame to frame1
ti1 = transform(None, frame1)

# Transformation of vector
v1_decomposed_in_frame1 = ti1.apply_vector(v1_decomposed_in_inertial_frame)

# Transformation of position
p1_decomposed_in_frame1 = ti1.apply_position(p1_decomposed_in_inertial_frame)

# Transformation of wrench
w1_decomposed_in_frame1 = ti1.apply_wrench(w1_decomposed_in_inertial_frame)

# Find the inverse transformation
t1i = ti1.inv()

# Pose of this frame, decomposed in inertial frame
frame1.get_pose()

# Twist of this frame, decomposed in inertial frame
frame.get_twist()

Two frames

from dynkin import Frame, transform

frame1 = Frame(position=[1, 2, 3], attitude=[0, 0, 90], degrees=True)
frame2 = Frame(position=[3, 2, 1], attitude=[0, 0, -90], degrees=True)

# Find transformation from frame1 to frame2
t12 = transform(frame1, frame2)

# Transformation of vector
v1_decomposed_in_frame2 = t12.apply_vector(v1_decomposed_in_frame1)

# Transformation of position
p1_decomposed_in_frame2 = t12.apply_position(p1_decomposed_in_frame1)

# Transformation of wrench
w1_decomposed_in_frame2 = t12.apply_wrench(w1_decomposed_in_frame1)

# Find the inverse transformation
t21 = t12.inv()

Kinematic chains

from dynkin import Frame, transform

frame1 = Frame(position=[1, 2, 3], attitude=[0, 0, 90], degrees=True)
frame2 = frame1.align_child(position=[3, 2, 1], attitude=[0, 0, -90], degrees=True)
frame3 = frame2.align_child(position=[1, 1, 1], attitude=[0, 0, 0], degrees=True)

# Find transformation from inertial frame to frame3
ti3 = transform(None, frame3)

# Transformation from frame3 and frame1
t31 = transform(frame3, frame1)

...

TODO: RigidBody example

License

Distributed under the terms of the MIT license, dynkin is free and open source software