Browsing by Author "Ladd, Andrew M."
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Analysis of probabilistic roadmap methods for motion planning and applications to polygon manipulation(2003) Ladd, Andrew M.; Kavraki, Lydia E.Motion planning deals with the problem of finding trajectory between two configurations in some space under some constraints. The science of motion planning deals with solving this problem efficiently in different spaces and under varying sets of constraints. This thesis provides an extended analysis of the PRM algorithm by using tools from measure theory to obtain greater generality. We then apply the results to planning in finite CW complexes and detail an application to planning with a polygonal robot in a polygonal workspace when contact is allowed. The final part of thesis deals with an application of motion planning to untangling mathematical knots. This problem is particularly interesting as it addresses motion planning with large number of degrees of freedom in a reconfigurable space. Planning applications with flexible robots, reconfigurable robots, molecular biology and other instances that share similar characteristics are some of the most challenging in planning today.Item Motion Planning for Knot Untangling(2004-01-01) Ladd, Andrew M.; Kavraki, Lydia E.When given a very tangled but unknotted circular piece of string it is usually quite easy to move it around and tug on parts of it until it untangles. However, solving this problem by computer, either exactly or heuristically, is challenging. Various approaches have been tried, employing ideas from algebra, geometry, topology and optimization. This paper investigates the application of motion planning techniques to the untangling of mathematical knots. Such an approach brings together robotics and knotting at the intersection of these fields: rational manipulation of a physical model. In the past, simulated annealing and other energy minimization methods have been used to find knot untangling paths for physical models. Using a probabilistic planner, we have untangled some standard benchmarks described by over four hundred variables much more quickly than has been achieved with minimization. We also show how to produce candidates with minimal number of segments for a given knot. We discuss novel motion planning techniques that were used in our algorithm and some possible applications of our untangling planner in computational topology and in the study of DNA rings.Item Motion planning for physical simulation(2007) Ladd, Andrew M.; Kavraki, Lydia E.Motion planning research has been successful in developing planning algorithms which are effective for solving problems with complicated geometric and kinematic constraints. Various applications in robotics and in other fields demand additional physical realism. Some progress has been made for non-holonomic systems. However systems with complex dynamics, significant drift, underactuation and discrete system changes remain challenging for existing planning techniques particularly as the dimensionality of the state space increases. This thesis develops a novel motion planning technique for the solution of problems with these challenging characteristics. The novel approach is called Path Directed Subdivision Tree Exploration algorithm (PDST-EXPLORE) and is based on sampling-based motion planning and subdivision methods. PDST-EXPLORE demonstrates how to link a planner with a physical simulator using the latter as a black box, to generate realistic solution paths for complex systems. The thesis contains experimental results with examples with simplified physics including a second order differential drive robot and a game which exemplifies characteristics of dynamical systems which are difficult for planning. The thesis also contains experimental results for systems with simulated physics, namely a weight lifting robot and a car. Both systems have a degree of physical realism which could not be incorporated into planning before. The new planner is finally shown to be probabilistically complete.Item Robotics-Based Location Sensing based on Wireless Ethernet(2002-04-25) Bekris, Kostas E.; Kavraki, Lydia E.; Ladd, Andrew M.; Marceau, Guillaume; Rudys, Algis; Wallach, Dan S.A key subproblem in the construction of location-aware systems is the determination of the position of a mobile device. This paper describes the design, implementation and analysis of a system for determining position from measured RF signal strengths in the IEEE 802.11b wireless Ethernet network. Previous approaches in the location-aware field with RF signals have been severely hampered by non-linearity, noise and complex correlations due to multi-path effects, interference and absorption. The design of our system begins with the observation that determining position from complex, noisy and non-linear signals is a well-studied problem in the field of robotics. Using only off-the-shelf hardware, we achieve robust position estimation to within a meter in our experimental context and after adequate training of our system. Also, we can coarsely determine our orientation and can track our position as we move. By applying recent advances in probabilistic inference of position and sensor fusion from noisy signals, we show that the RF emissions from base stations as measured by off-the-shelf wireless Ethernet cards are sufficiently rich in information to permit a mobile device to reliable track its location.