pycapacity 1.0.4

A Real-time capable robot capacity calculation module

Python real-time capable robot task-space capacity calculation module

This module provides a framework for the generic robot capacity calculation called in a form of a python module pycapacity.

This module integrates several velocity, force and acceleration capacity calculation functions based on ellipsoids:

• Velocity (manipulability) ellipsoid
  E_vel = {dx | dx = J.dq, ||dq||<1 }
• Acceleration (dynamic manipulability) ellipsoid
  E_acc = {ddx | ddx = J.M^(-1).t, ||t||<1 }
• Force ellipsoid
  E_for = {f | J^T.f = t, ||t||<1 }

And polytopes:

• Velocity polytope
  P_vel = {dx | dx = J.dq, dq_min < dq < dq_max}
• Acceleration polytope
  P_acc = {ddx | ddx = J.M^(-1).t, t_min < t < t_max}
• Force polytope
  P_for = {f | J^T.f = t, t_min < t < t_max}
• Force polytopes Minkowski sum and intersection

The force polytope functions have been implemented according to the paper:
On-line force capability evaluation based on efficient polytope vertex search
by Antun Skuric, Vincent Padois and David Daney
Published on ICRA2021

And the velocity and acceleration polytopes are resolved using the Hyper-plane shifting method:
Characterization of Parallel Manipulator Available Wrench Set Facets
by Gouttefarde M., Krut S.
In: Lenarcic J., Stanisic M. (eds) Advances in Robot Kinematics: Motion in Man and Machine. Springer, Dordrecht (2010)

Installation

All you need to do to install it is:

pip install pycapacity

And include it to your python project

import pycapacity

Other way to install the code is by installing it directly from the git repo:

pip install git+https://gitlab.inria.fr/askuric/pycapacity

Installation to enable modifying the source

Clone or download the repository to your pc:

cd your/project/path
git clone https://gitlab.inria.fr/askuric/pycapacity.git

Put the folder in your project directory:

my_project:
|
├── your
├── project 
├── files
|
└── pycapacity

And then import it in your python code for example:

import pycapacity.pycapacity as capacity

Note: if you do not install the module using pip you will need to import it using double name pycapacity.pycapacity.

All the smarts is placed in the pycapacity.py file so that is where you will find all the implementations and where to go to modify the code.

Module functions docs

See full docs at the link

• acceleration_ellipsoid: acceleration ellipsoid calculation (dynamic manipulability ellipsoid)
• acceleration_polytope: Acceleration polytope calculating function
• acceleration_polytope_withfaces: Acceleration polytope calculating function
• force_ellipsoid: force manipulability ellipsoid calculation
• force_polytope: Force polytope representing the capacities of the two robots in a certain configuration
• force_polytope_intersection: Force polytope representing the intersection of the capacities of the two robots in certain configurations.
• force_polytope_intersection_withfaces: Force polytope representing the intersection of the capacities of the two robots in certain configurations.
• force_polytope_sum_withfaces: Force polytope representing the minkowski sum of the capacities of the two robots in certain configurations.
• force_polytope_withfaces: Force polytope representing the capacities of the two robots in a certain configuration.
• velocity_ellipsoid: velocity manipulability ellipsoid calculation
• velocity_polytope: Velocity polytope calculating function
• velocity_polytope_withfaces: Velocity polytope calculating function, with faces

Algorithms:

• hyper_plane_shift_method: Hyper plane shifting method implementation used to solve problems of a form:

---

Code examples

"""
A simple example program 3d force polytope 
evaluation of a randomised 6dof robot 
"""
from pycapacity import force_polytope_withfaces as polytope
import numpy as np

m = 3 # 3d forces
n = 6 # robot dof

J = np.array(np.random.rand(m,n)) # random jacobian matrix

t_min = np.ones((n,1))  # joint torque limits max and min
t_max = -np.ones((n,1))

vertices, faces = polytope(J,t_min, t_max) # calculate the polytope vertices and faces

print(vertices) # display the vertices

See demo_notebook.ipynb for one example use case of the module.