Trajectory optimization algorithms comprise a powerful collection of methods for planning motions of nonlinear dynamical systems. Generally speaking, these algorithms aim to find an input trajectory that minimizes a cost function subject to a set of constraints on the system's states and inputs. Trajectory optimization has a long history of successful application to systems with smooth dynamics. However, many robotic systems experience discontinuous frictional contact with the environment as an essential part of their routine operation. The non-smooth dynamics encountered in these situations pose significant challenges.
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