Parametric formulation is a systematic method that ties the constraint functions to the resulting joint profiles for bipedal robots. Acceptable joint profiles for continuous and steady walking must satisfy the additional condition of being repeatable. This extra condition imposes restrictions on the selection of constraint functions, gait parameters and the initial posture of each step, and can make the synthesis of joint profiles extremely challenging. This paper presents a correlation between the gait parameters used in a class of specific constraint functions and the initial posture that will create repeatable gait. Furthermore, a general necessary and sufficient condition for repeatable gait is proposed. This condition provides a guideline for selecting constraint functions and their associated gait parameters in the context of producing repeatable gait. This research can not only provide valuable insights into bipedal walking, but also serve as a stepping stone for employing parametric formulation with various constraint functions.
