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Arguments based on elastic stability and flexure, as opposed to the more conventional ones based on yield strength, require that living organisms adopt forms whereby lengths increase as the (2/3) power of diameter. The somatic dimensions of several species of animals and of a wide variety of trees fit this rule well. It is a simple matter to show that(More)
Reachable volumes are a new technique that allows one to efficiently restrict sampling to feasible/reachable regions of the planning space even for high degree of freedom and highly constrained problems. However, they have so far only been applied to graph-based sampling-based planners. In this paper we develop the methodology to apply reachable volumes to(More)
Designs are described for flexible hollow waveguides with low ir loss over distances on the order of 1 m. Transmission losses at 10.6 microm are calculated, and the effect of bends and twists is discussed. A hollow combination metal-dielectric-walled rectangular waveguide is proposed that can have transmission as high as 95% for a 1-m length, while bent(More)
We introduce a new concept, reachable volumes, that denotes the set of points that the end effector of a chain or linkage can reach. We show that the reachable volume of a chain is equivalent to the Minkowski sum of the reachable volumes of its links, and give an efficient method for computing reachable volumes. We present a method for generating(More)
Reachable volumes are a geometric representation of the regions the joints of a robot can reach. They can be used to generate constraint satisfying samples for problems including complicated linkage robots (e.g. closed chains and graspers). They can also be used to assist robot operators and to help in robot design.We show that reachable volumes have an(More)
Probabilistic Roadmap Methods (PRMs) are one of the most used classes of motion planning methods. These sampling-based methods generate robot configurations (nodes) and then connect them to form a graph (roadmap) containing representative feasible pathways. A key step in PRM roadmap construction involves identifying a set of candidate neighbors for each(More)
— Sampling-Based Motion Planning (SBMP) has been successful in planning the motion for a wide variety of robot types. An important primitive of these methods is selecting candidate neighbors and validating/invalidating the pathways between nodes of the map. These neighbors are commonly selected based on some distance metric (DM). An ideal distance metric(More)