Biped Walking with Variable ZMP, Frictional Constraint, and Inverted Pendulum Model

In this paper, characteristics of dynamic biped walking is discussed. With ZMP (zero moment point) concept, frictional constraint, and inverted pendulum model, stable biped walking condition is given out. With this, biped walking is separated into initial acceleration, double support, deceleration, and acceleration phases; consequently, the nature that biped walking is in fact a continuous acceleration and deceleration motion is revealed. The motion characteristics such as walking velocity, walking time and stride, and their constraint conditions are investigated. The approach for adjusting walking velocity by controlling landing point is naturally developed. Two walking patterns of fixed ZMP case and variable ZMP case are discussed in detail and their characteristics are summarized. The motion planning is also presented based on the discussed motion constraints and numerical example is given out. Experiment with fixed ZMP walking pattern is implemented. The analyzing and planning approach used in this paper is expected to extend to analyze the motion of running and jumping robot