Improved Feasible Region

This python library contains the code used for the computation of the feasibilty criteria in TRO paper. In here you can also find the code used to generate the figures and plots of the manuscript.

What you can do with Jet-leg:

• compute the Support region of legged robots as in Bretl. et al. 2008;
• compute the Feasible region of legged robots as in Orsolino. et al. 2019 with the incorportation of the robot inertial effects as in Abdalla. et al. 2023;
• compute the Reachable region as in Abdalla. et al. 2023;
• compute force polytopes of legged robots given their URDF;
• compare different leg designs and understand their consequences on the robot's balancing capabilities;
• test various formulations of linear, convex or nonlinear trajectory optimization problems;

Setup

This guide assumes that $PROJECT_ROOT refers to the absolute path to this repository.

Installing and Setting Up Virtual Environment

For a quick install, you can set up a virtual environment inside the project directory:

sudo apt install -y python-venv
python -m venv $PROJECT_ROOT/venv
source $PROJECT_ROOT/venv/bin/activate

Now, you are ready to use the virtual environment. To install the dependencies related to this project, make sure you activate the environment and then run:

cd $PROJECT_ROOT/jet_leg_common
pip install -e .

And then

cd $PROJECT_ROOT
pip install -e .

Dependencies

• Numpy
• PyYAML
• Shapely
• Pycddlib
• Scipy
• CVXOPT
• Matplotlib
• Pathos (multiprocessing)

Other dependencies:

• Pinocchio
• Pypoman for the manipulation of polyhedrical object

after cloning remember to do in the jetleg folder:

git submodules update --init --recursive

Optional dependencies:

• [rospkg]

pip install rospkg

• Ipopt and its Python interface Pypi for the solution of large-scale nonlinear optimization problems
• ffmpeg for the generation of Matplotlib animations

sudo apt-get install ffmpeg

• unittest for testing of dependencies installation and for development

Testing the library

After completing the installation navigate to the examples folder:

• single_iterative_projection_example.py can be used to see how to set up an iterative projection problem in order to compute the friction/actuation/feasible region;
• check_stability_lp_example.py can be used to quickly check whether the given robot configuration is statically stable or not (without explicitly computing the feasible region);
• plotIPstatistics.py can be used to generate some statistics about the computation time of the IP algorithm for random feet positions (see Fig. 6 of the preprint);
• plotInstantaneousActuationRegionVariableMass.py can be used to generate a plot that shows how the feasible regions can changes depending on the gravitational force acting on the robot's center of mass (see Fig. 8 of the preprint)

Troubleshooting

• if CVXOPT is not found even after trying the pip-installation, we then suggest to try install the version 1.1.4 of CVXOPT using Synaptic or to clone and install it manually after building.
• IMPORTANTE NOTE: delete every previous installation of cvxopt that is in the system using locate cvxopt (after sudo updatedb)

See also

• The pypoman and pymanoid libraries developed by Stéphane Caron
• Komei Fukuda's Frequently Asked Questions in Polyhedral Computation
• The Polyhedron class in Sage
• The StabiliPy package provides a more general recursive projection method