1. A desired ZMP trajectory generating device for a mobile robot which generates a desired ZMP trajectory as a trajectory of a desired position of a zero moment point (ZMP) of the mobile robot, the device comprising: a polynomial function coefficient group determining section which determines, by regarding the desired ZMP trajectory as a trajectory expressed by a polynomial function of degree 2 or higher with time as a variable, a desired coefficient group comprising desired values of coefficients in respective terms of the polynomial function, wherein the polynomial function coefficient group determining section is configured to use a quadratic evaluation function configured to include square values of the coefficients included in the desired coefficient group as variables and a plurality of constraint conditions each configured by a linear equality or linear inequality about the coefficients, to determine the desired coefficient group, so as to minimize a value of the evaluation function while fulfilling the constraint conditions by a solution method for a quadratic programming problem, and the constraint conditions are configured to include a linear inequality which expresses a first constraint condition that a desired position of the ZMP at one or more sampling time in the desired ZMP trajectory exists within a predetermined polygonal region set in accordance with a desired position and desired posture of a floor-contacting site of the mobile robot at the sampling time.