  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 for robot motion and propose a formal
definition of risk in terms of a sequence of motion, namely path. Mathematical
approaches to represent motion risk are also presented, which is in accordance
with our risk definition and properties. The definition and representation of
risk provide a meaningful way to evaluate or construct robot motion or path
plans. The understanding of risk is even of greater interest for the search and
rescue community: the deconstructed environments cast extra risk onto the
robot, since they are working under extreme conditions. A proper risk
representation has the potential to reduce robot failure in the field.
