Source code for https://hal.archives-ouvertes.fr/hal-01349880
We present a multi-contact walking pattern generator based on preview-control of the 3D acceleration of the center of mass (COM). A key point in the design of our algorithm is the calculation of contact-stability constraints. Thanks to a mathematical observation on the algebraic nature of the frictional wrench cone, we show that the 3D volume of feasible COM accelerations is a always a downward-pointing cone. We reduce its computation to a convex hull of (dual) 2D points, for which optimal O(n log n) algorithms are readily available. This reformulation brings a significant speedup compared to previous methods, which allows us to compute time-varying contact-stability criteria fast enough for the control loop. Next, we propose a conservative trajectory-wide contact-stability criterion, which can be derived from COM-acceleration volumes at marginal cost and directly applied in a model-predictive controller. We finally implement this pipeline and exemplify it with the HRP-4 humanoid model in multi-contact dynamically walking scenarios.
Authors: Stéphane Caron and Abderrahmane Kheddar
On Ubuntu 14.04, once you have installed OpenRAVE, do:
sudo apt-get install cython python python-dev python-pip python-scipy python-shapely
sudo pip install pycddlib quadprog pyclipperThen, clone the repository and its submodule via:
git clone --recursive https://github.com/stephane-caron/3d-com-mpc.gitIf you already have pymanoid installed on your system, be sure that its version matches that of the submodule.
There are three subfolders in this repository, corresponding to different Sections of the paper:
- Section IV: cones/ contains scripts to display and play with the COM acceleration cones
- Section VI: staircase/ walks the humanoid model around a circular staircase with tilted stepping stones
- Appendix: sep/ compares four algorithms calculating the static-equilibrium polygon
Due to the copyright problem, we cannot release the COLLADA model HRP4R.dae
used to produce the accompanying video and paper illustrations. We have replaced
it with JVRC-1,
which has the same kinematic chain.
Feel free to post your questions or comments in the issue tracker.