This work is dedicated to the study of the walk of a biped without actuation of the ankle. The robot motion is restricted to the sagittal plan. A particularity of this study is the consideration of a double support, over-actuated phase, in addition to the single support, under-actuated phase. This work deals with three distinct points. Firstly, it deals with the study of the collision of the free leg with the ground, when considering feet or not. We have found that with the impact model used, the only way to obtain the double support phase is to avoid the impact. Furthermore this study has brought us to call into question the usual hypothesis that leads to the collision model we used, when a contact already exists at the moment of collision. Secondly, this work deals with the walking motion generation, that we pose rigorously under the form of an optimisation problem with a hierarchy of constraints. This hierarchy of constraints consist in a sequence of constraints where a constraint needs to be satisfied so that subsequent constraints are defined. An adaptation of optimisation programs has been developed in order to deal with such problems. Furthermore, the analytic gradient has been determined in order to improve the optimisation process. Thirdly, this work deals with the stability study of the dynamics of the under-actuated single support phase that are not controlled, considering the over-actuated double support phase. Stability conditions are given as the the convergence domain of these dynamics not controlled during the single support phase. It is also proven all the interest of this over-actuated phase to improve the stability of the walk.
