I present a calculus variations problem for an optimal zero-moment point (ZMP) pattern, and derive a closed-form solution satisfying two-boundary conditions of ZMP and an additional constraint, which is a difference between a current capture point and another. In addition, I present a closed-form solution for the equation of motion of the linear inverted pendulum model, or a cart-table model using the optimal ZMP pattern. Through the closed-form solutions, a current walking pattern
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.