A SIMPLIFIED STABILITY STUDY FOR A BIPED WALK WITH UNDER AND OVER ACTUATED PHASES S. MIOSSEC, Y. AOUSTIN Institut de Recherche en Communications et Cybernétique de Nantes, France ABSTRACT This paper is devoted to the stability study of a walking gait for a biped. The walking gait is periodic and it is composed of a single support, a passive impact, and a double support. The reference trajectories are described in function of the shin orientation versus the ground of the stance leg. We use the Poincaré map to study the stability of the walking gait of the biped. With the assumption of no perturbation in the tracking of the joint configurations of the biped, the Poincaré map is of dimension one. With a particular control law in double support it is shown theoretically and in simulation that a perturbation error in velocity of the shin angle can be eliminated in one half step only. Therefore, with this possibility, it is shown that it is possible for the biped to reach a periodic regime from a stopped position in one half step. 1 INTRODUCTION Studies dedicated to bipeds walk can be divided in three categories: static walk, dynamic walk and purely dynamic walk. Static walk consists in walking sufficiently slowly so that dynamics can be neglected. The stability criterion is then a static criterion. Dynamic walk consists in taking partially into account the dynamics of the biped, for example by measuring reaction forces and using the Zero Momentum Point (ZMP) criterion, defined in [1]. For us, this criterion is a necessary but not sufficient criterion for stability of the walk, and is in fact a physical constraint during walk, such as a no take off of the legs constraint. Purely dynamic walk consists in taking into account the dynamics by using a dynamic model of the biped. This approach allows to study theoretically the stability of the walk but is for the moment restricted for simple bipeds, for which the dynamic model is not too complicated. Simple bipeds considered are generally planar bipeds without feet [2-8]. For bipeds without feet the purely dynamic approach is generally necessary since such bipeds are under actuated. For this type of studies, the work can be to generate reference trajectories [5, 6], to study the stability of the walk [2, 3, 4, 7], and to control the biped [2, 8]. Recent theoretical results have been