Contact constraints, such as those between a foot and the ground or a hand and an object, are inherent in many robotic tasks. These constraints define a manifold of feasible states; while well understood mathematically, they pose numerical challenges to many algorithms for planning and controlling whole-body dynamic motions. In this paper, we present an approach to the synthesis and stabilization of complex trajectories for both fully-actuated and underactuated robots subject to contact constraints. We introduce an extension to the direct collocation trajectory optimization algorithm that naturally incorporates the manifold constraints to produce a nominal trajectory with third-order integration accuracy\97 a critical feature for achieving reliable tracking control. We adapt the classical time-varying linear quadratic regulator to produce a local cost-to-go in the tangent plane of the manifold. Finally, we descend the cost-to-go using a quadratic program that incorporates unilateral friction and torque constraints. This approach is demonstrated on three complex walking and climbing locomotion examples in simulation.
PDF@inproceedings{Posa2016a,
address = {Stockholm, Sweden},
author = {Posa, Michael and Kuindersma, Scott and Tedrake, Russ},
booktitle = {IEEE International Conference on Robotics and Automation (ICRA)},
doi = {10.1109/ICRA.2016.7487270},
isbn = {9781467380263},
issn = {10504729},
month = may,
pages = {1366--1373},
title = {{Optimization and stabilization of trajectories for constrained dynamical systems}},
volume = {2016-June},
year = {2016},
youtube = {iTDtMTJ1Z14},
url = {https://ieeexplore.ieee.org/abstract/document/7487270/}
}