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This paper presents a formal definition and explicit representation of robot motion risk. Currently, robot motion risk has not been formally defined, but has already been used in motion and path planning. Risk is either implicitly represented as model uncertainty using probabilistic approaches, where the definition of risk is somewhat avoided, or explicitly modeled as a simple function of states, without a formal definition. In this work, we provide formal reasoning behind what risk is forarXiv:1904.08003v1 fatcat:kcn7ooii5ncpjiktsaeexoglm4