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Python utilites for movements in 3d space

Project description



scikit-kinematics primarily contains functions for working with 3D kinematics, e.g quaternions and rotation matrices. This includes utilities to read in data from the following IMU-sensors: - polulu - XSens - xio - xio-NGIMU - YEI

Compatible with Python >= 3.5


numpy, scipy, matplotlib, pandas, sympy, easygui


Author: Thomas Haslwanter Date: 12-05-2023 Ver: 0.9.0 Licence: BSD 2-Clause License ( Copyright (c) 2023, Thomas Haslwanter All rights reserved.


You can install scikit-kinematics with

pip install scikit-kinematics

and upgrade to a new version with

pip install --upgrade --no-deps scikit-kinematics


Analysis of signals from IMUs (intertial-measurement-units). Read in data, calculate orientation (with one of the algorithms below)

  • get_data ... This method must be taken from one of the existing sensors, or from your own sensor. Currenlty the following sensors types are available:

    • XSens
    • xio (original, and NGIMU)
    • yei

    * polulu

  • calc_position

MARG Systems

  • imus.analytical ... Calculate orientation and position, from angular velocity and linear acceleration
  • imus.kalman ... Calculate orientation from IMU-data using an Extended Kalman Filter.
imus.IMU ... Class for working with data from IMUs

:   -   imus.IMU.calc\_position ... calculate position
    -   imus.IMU.setData ... set the properties of an IMU-object
    -   imus.IMU.set\_qtype ... sets q\_type, and automatically
        performs the relevant calculations.
  • imus.Madgwick ... Class for calculating the 3D orientation with the Madgwick-algorithm
  • imus.Mahony ... Class for calculating the 3D orientation with the Mahony-algorithm


Analysis of signals from video-based marker-recordings of 3D movements

  • markers.analyze_3Dmarkers ... Kinematic analysis of video-basedrecordings of 3D markers
  • markers.find_trajectory ... Calculation of joint-movements from 3D marker positions


Note that all these functions work with single quaternions and quaternion vectors, as well as with arrays containing these.

Quaternion class

quat.Quaternion ... class, including overloading for multiplication and

:   division (e.g. "quatCombined = quat1 \* quat2"), import and

Functions for working with quaternions

  • quat.q_conj ... Conjugate quaternion
  • quat.q_inv ... Quaternion inversion
  • quat.q_mult ... Quaternion multiplication
  • quat.q_scalar ... Extract the scalar part from a quaternion
  • quat.q_vector ... Extract the vector part from a quaternion
  • quat.unit_q ... Extend a quaternion vector to a unit quaternion.

Conversion routines - quaternions --------------------------------=

  • quat.calc_angvel ... Calculates the velocity in space from quaternions
  • quat.calc_quat ... Calculate orientation from a starting orientation and angular velocity.
  • quat.convert ... Convert quaternion to corresponding rotation matrix or Gibbs vector
  • quat.deg2quat ... Convert number or axis angles to quaternion vectors
  • quat.quat2seq ... Convert quaternions to sequention rotations ("nautical" angles, etc)
  • quat.scale2deg ... Convert quaternion to corresponding axis angle

Rotation Matrices

Definition of rotation matrices ------------------------------=

  • rotmat.R ... 3D rotation matrix for rotation about a coordinate axis

Conversion Routines - rotation matrices --------------------------------------=

  • rotmat.convert ... Convert a rotation matrix to the corresponding quaternion
  • rotmat.seq2quat ... Convert nautical angles etc. to quaternions
  • rotmat.sequence ... Calculation of Euler, Fick, Helmholtz, ... angles

Symbolic matrices

  • rotmat.R_s() ... symbolix matrix for rotation about a coordinate axis

For example, you can e.g. generate a Fick-matrix, with

>>> R_Fick = R_s(2, 'theta') * R_s(1, 'phi') * R_s(0, 'psi')

Spatial Transformation Matrices

  • rotmat.stm ... spatial transformation matrix, for combined rotations/translations
  • rotmat.stm_s() ... symbolix spatial transformation matrix

Denavit-Hartenberg Transformations

  • rotmat.dh ... Denavit-Hartenberg transformation matrix
  • rotmat.dh_s ... symbolic Denavit-Hartenberg transformation matrix


Routines for working with vectors These routines can be used with vectors, as well as with matrices containing a vector in each row.

  • vector.normalize ... Vector normalization
  • vector.project ... Projection of one vector onto another one
  • vector.GramSchmidt ... Gram-Schmidt orthogonalization of three points
  • vector.q_shortest_rotation ... Quaternion indicating the shortest rotation from one vector into another.
  • vector.rotate_vector ... Rotation of a vector
  • vector.target2orient ... Convert target location into orientation angles

Interactive Data Analysis ========================-

  • viewer.ts ... interactive viewer for time series data
  • view.orientation ... visualize and animate orientations, expressed as quaternions.


  • simulate_movements ... calculated ideal IMU-signals for combined rotations/translations


The file Errata.pdf contains the a list of mistakes in the manuscript, and the corresponding corrections.

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