Flexible Linear Inverted Pendulum Model for cost-effective biped robots

In the area of biped walking control, the Linear Inverted Pendulum Model (LIPM) achieved a great impact, as it is easily applicable due to its simplicity and linearity. Nevertheless, it is capable to generate stable walking motions on a variety of platforms. However, cost-effective robots tend to have flexibility in joints and links due to the lightweight form-factor and PD controlled joint servos. LIPM is not able to reflect this issue and is therefore not applicable in this case. This paper proposes a new model called Flexible Linear Inverted Pendulum Model (FLIPM) that is derived from LIPM and adds a damped spring and a second center of mass. Additionally, a state-space representation is given and a preview controller presented that utilizes the new model. The evaluation proves the advantage by comparing a walk with LIPM and FLIPM on a physical robot where only FLIPM leads to a stable motion.