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Python utilites for movements in 3d space

Project description

![Title](docs/Images/skinematics.png) — scikit-kinematics —

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: 04-10-2019 Ver: 0.8.4 Licence: BSD 2-Clause License (<>) Copyright (c) 2020, 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

&gt;&gt;&gt; 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.

## Errata The file [Errata.pdf](Errata.pdf) contains the a list of mistakes in the manuscript, and the corresponding corrections.

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