@conference {Posa16,
	title = {Optimization and stabilization of trajectories for constrained dynamical systems},
	booktitle = {Proceedings of the International Conference on Robotics and Automation (ICRA)},
	year = {2016},
	note = {[[{"fid":"3193341","view_mode":"default","type":"media","attributes":{"height":"360","width":"480","alt":"ICRA 2016 video on YouTube","title":"ICRA 2016 video","class":"media-element file-default"}}]]},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Stockholm, Sweden},
	abstract = {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 a trajectory optimization algorithm (DIRCON) that extends the direct collocation method, naturally incorporating manifold constraints to produce a nominal trajectory with third-order integration accuracy{\textendash}-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 manifold tangent plane. 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.},
	author = {Posa, Michael and Scott Kuindersma and Russ Tedrake}
}
