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We present a method that combines offline trajectory optimization and online Model Predictive Control (MPC), generating robust controllers for complex periodic behavior in domains with unilateral constraints (e.g., contact with the environment). MPC offers robust and adaptive control even in high-dimensional domains; however, the online optimization gets stuck in local minima when the domains has discontinuous dynamics. Some methods of trajectory optimization that are immune to such problems, but these are often too slow to be applied online.
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Erez et al. (2011) studied this question.