Abstract : This thesis deals with the development and analysis of motion planning algorithms for high dimensional systems : humanoid robots and digital actors. Several adaptations of generic randomized motion planning methods are proposed and discussed. A first contribution concerns the use of linear dimensionality reduction techniques to speed up sampling algorithms. This method identifies on line when a planning process goes through a narrow passage of some configuration space, and adapts the exploration accordingly. This algorithm is particularly suited to difficult problems of motion planning for computer animation. The second contribution is the development of randomized algorithms for motion planning under constraints. It consists in the integration of prioritized inverse kinematics tools within randomized motion planning. We demonstrate the use of this method on different manipulation planning problems for humanoid robots. This contribution is generalized to whole-body motion planning with locomotion. The last contribution of this thesis is the use of previous methods to solve complex manipulation tasks by humanoid robots. More specifically, we present a formalism that represents information specific to a manipulated object usable by a motion planner. This formalism is presented under the name of "documented object".