The first part of this thesis contains our theoretical and technical work. The general problem is formulated in Chapter 1. We extend the formulation of the motion planning problem to the case of closed-chain mechanisms. Chapter 1 also explains some important notions used in the rest of the document. Then, Chapter 2 provides an overview of related works. We present a scope of techniques for solving motion planning problems and loop closure equations. Our approach is detailed in Chapter 3. We introduce samplingbased algorithms into our formulation of the motion planning problem in presence of kinematic closure constraints. The most important technical contribution in this thesis is also described in this chapter. We have developed a general and simple geometric algorithm called Random Loop Generator (RLG) for sampling random congurations satisfying loop
closure constraints. RLG overcomes the most challenging aspect for extending samplingbased motion planning algorithms to closed chains. Some results shown in this chapter demonstrate the qualities of the approach.
The second part of this thesis deals with the dierent elds of application that we have investigated. In Chapter 4, we discuss the application of motion planning algorithms to parallel mechanisms. These mechanisms can be real structures, such as Gough-Stewart-like platforms, or virtual kinematic loops formed by several manipulators grasping the same object. Applied to parallel robots, our algorithms can help designers of these mechanisms,
or can provide useful data for real-time trajectory planning. The same algorithms can also be used as components of manipulation planning techniques involving several coordinated robots. Chapter 5 regards manipulation planning for a robot and a movable object. An algorithm for planning the motions of a single-loop closed kinematic chain is used as a key component of a manipulation planning approach able to treat continuous sets in the definition of the manipulation task. This planner admits continuous sets for modeling both the possible grasps and the stable placements of the movable object, rather than discrete sets generally assumed by the existing planners. Then, intermediate grasp/ungrasp operations required to solve the problem are automatically identied. Finally, in Chapter 6, an interesting application is addressed out of the eld of Robotics. We propose to use motion planing algorithms as effcient filters for the conformational exploration of protein loops. The structural analysis of protein loops is a very active area of research in Computational Biology. Our geometric algorithms can relieve conformational exploration approaches of a part of the heavy energetic treatment, and thus, improve their performance.