pycapacity 1.0.2

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:

All you need to do to install it is:

pip install pycapacity

And include it to your python project

import pycapacity

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

• Velocity (manipulability) ellipsoid
• Acceleration (dynamic manipulability) ellipsoid
• Force ellipsoid

And polytopes:

• Velocity polytope
• Acceleration polytope
• Force polytope
• 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)

Module functions

• 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.
• hyper_plane_shift_method: Hyper plane shifting method implementation used to solve problems of a form:
• make_2d: Take a list of 3D(cooplanar) points and make it 2D
• make_unique: Remove repetitions of columns
• order_index: Order clockwise 2D points
• 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


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

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