Nonsmooth optimal value and policy functions for mechanical systems subject to unilateral constraints
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State-of-the-art approaches to optimal control of contact-rich robot dynamics use smooth approximations of value and policy functions and gradient-based algorithms for improving approximator parameters. Unfortunately, the dynamics of mechanical systems subject to unilateral constraints--i.e. robot locomotion and manipulation--are generally nonsmooth. We show that value and policy functions generally inherit regularity properties like (non)smoothness from the underlying system's dynamics, and demonstrate this effect in a simple mechanical system. We conclude with a discussion of implications for the use of gradient-based algorithms for optimal control of contact-rich robot dynamics.
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