@conference {1162566,
	title = {Variational Contact-Implicit Trajectory Optimization},
	booktitle = {International Symposium on Robotics Research (ISRR)},
	year = {2017},
	address = {Puerto Varas, Chile},
	abstract = {Contact constraints arise naturally in many robot planning problems. In recent years, a variety of contact-implicit trajectory optimization algorithms have been developed that avoid the pitfalls of mode pre-specification by simultaneously optimizing state, input, and contact force trajectories. However, their reliance on first-order integrators leads to a linear tradeoff between optimization problem size and plan accuracy. To address this limitation, we propose a new family of trajectory optimization algorithms that leverage ideas from discrete variational mechanics to derive higher-order generalizations of the classic time-stepping method of Stewart and Trinkle. By using these dynamics formulations as constraints in direct trajectory optimization algorithms, it is possible to perform contact-implicit trajectory optimization with significantly higher accuracy. For concreteness, we derive a second-order method and evaluate it using several simulated rigid body systems including an underactuated biped and a quadruped.},
	author = {Zachary Manchester and Scott Kuindersma}
}
