Probabilistic roadmap planners have been used with success to plan paths for flexible objects such as metallic plates or plastic flexible pipes. This paper improves the performance of these planners by using the medial axis of the workspace to guide the random sampling. At a preprocessing stage, the medial axis of the workspace is computed using a recent efficient algorithm. Then the flexible object is fitted at random points along the medial axis. The energy of all generated configurations is minimized and the planner proceeds to connect them with low-energy quasi-static paths in a roadmap that captures the connectivity of the free space. Given an initial and a final configuration, the planner connects these to the roadmap and searches the roadmap for a path. Our experimental results show that the new sampling scheme is successful in identifying critical deformations of the object along solution paths which results in a significant reduction of the computation time. Our work on planning for flexible objects has applications in industrial settings, virtual reality environments, and medicine.

This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to deform in order to achieve a collision-free path from the initial to the final configuration. Any required deformations are automatically computed by our planner according to the principles of elasticity theory from mechanics. The problem considered in this paper differs significantly from that of planning for a rigid or an articulated object. In the first part of the paper we point out these differences and highlight the reasons that make planning for elastic objects an extremely difficult task. We then present a randomized algorithm for computing collision-free paths for elastic objects under the above-mentioned restrictions of manipulation.

This paper addresses the problem of path planning for a class of deformable volumes under fairly general manipulation constraints. The underlying geometric model for the volume is provided by a mass-spring representation. It is augmented by a realistic mechanical model. The latter permits the computation of the shape of the considered object with respect to the grasping constraints by minimizing the energy function of the deformation of the object. Previous research in planning for deformable objects considered the case of elastic plates and proposed a randomized framework for planning paths for plates under manipulation constraints. The present paper modifies and extends the previously proposed framework to handle simple volumes. Our planner builds a roadmap in the configuration space. The nodes of the roadmap are equilibrium configurations of the considered volume under the manipulation constraints, while its edges correspond to quasi-static equilibrium paths. Paths are found by searching the roadmap. We present experimental results that illustrate our approach. Our work finds important applications in industrial settings, in graphics animation, in virtual prototyping, and in medical applications.