Robust real-time walking pattern generation with dynamical consistency: An analytical method combined with optimal solution

This paper proposes a novel method toward real-time walking pattern generation with guaranteeing the dynamical consistency during the whole cycle. Extending the conventional Linear Inverted Pendulum Model (LIPM), this paper takes the dynamics of the Double Support Phase (DSP) into consideration. Considering the Zero-Moment-Point (ZMP) movement during the DSP, the reference ZMP trajectory is first planned. Then the Center of Mass (CoM) trajectory is obtained by analytically solving the differential equation derived from LIPM. To determine the boundary conditions, an offline numerical optimization algorithm is utilized. Furthermore, in order to enhance the robustness, the sudden change of step location and timing should be considered. With guaranteeing the dynamical continuity, a Quadratic Programming (QP) problem with equality constraints is proposed and solved to obtain the CoM trajectory during the current Single Support Phase (SSP). For bipedal walking with or without the sudden adjustment of step location and timing, the simulation and hardware experiments have been done to demonstrate the effectiveness.