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Algebraic connectivity and graph robustness

Feddema, John T.

Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

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Advanced robot locomotion

Byrne, Raymond H.; Neely, Jason C.; Buerger, Stephen B.; Feddema, John T.; Novick, David K.; Rose, Scott E.; Spletzer, Barry L.; Sturgis, Beverly R.

This report contains the results of a research effort on advanced robot locomotion. The majority of this work focuses on walking robots. Walking robot applications include delivery of special payloads to unique locations that require human locomotion to exo-skeleton human assistance applications. A walking robot could step over obstacles and move through narrow openings that a wheeled or tracked vehicle could not overcome. It could pick up and manipulate objects in ways that a standard robot gripper could not. Most importantly, a walking robot would be able to rapidly perform these tasks through an intuitive user interface that mimics natural human motion. The largest obstacle arises in emulating stability and balance control naturally present in humans but needed for bipedal locomotion in a robot. A tracked robot is bulky and limited, but a wide wheel base assures passive stability. Human bipedal motion is so common that it is taken for granted, but bipedal motion requires active balance and stability control for which the analysis is non-trivial. This report contains an extensive literature study on the state-of-the-art of legged robotics, and it additionally provides the analysis, simulation, and hardware verification of two variants of a proto-type leg design.

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Advanced mobile networking, sensing, and controls

Feddema, John T.; Byrne, Raymond H.; Lewis, Christopher L.; Harrington, John J.; Kilman, Dominique K.; Van Leeuwen, Brian P.; Robinett, R.D.

This report describes an integrated approach for designing communication, sensing, and control systems for mobile distributed systems. Graph theoretic methods are used to analyze the input/output reachability and structural controllability and observability of a decentralized system. Embedded in each network node, this analysis will automatically reconfigure an ad hoc communication network for the sensing and control task at hand. The graph analysis can also be used to create the optimal communication flow control based upon the spatial distribution of the network nodes. Edge coloring algorithms tell us that the minimum number of time slots in a planar network is equal to either the maximum number of adjacent nodes (or degree) of the undirected graph plus some small number. Therefore, the more spread out that the nodes are, the fewer number of time slots are needed for communication, and the smaller the latency between nodes. In a coupled system, this results in a more responsive sensor network and control system. Network protocols are developed to propagate this information, and distributed algorithms are developed to automatically adjust the number of time slots available for communication. These protocols and algorithms must be extremely efficient and only updated as network nodes move. In addition, queuing theory is used to analyze the delay characteristics of Carrier Sense Multiple Access (CSMA) networks. This report documents the analysis, simulation, and implementation of these algorithms performed under this Laboratory Directed Research and Development (LDRD) effort.

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Glider communications and controls for the sea sentry mission

Feddema, John T.; Dohner, Jeffrey L.

This report describes a system level study on the use of a swarm of sea gliders to detect, confirm and kill littoral submarine threats. The report begins with a description of the problem and derives the probability of detecting a constant speed threat without networking. It was concluded that glider motion does little to improve this probability unless the speed of a glider is greater than the speed of the threat. Therefore, before detection, the optimal character for a swarm of gliders is simply to lie in wait for the detection of a threat. The report proceeds by describing the effect of noise on the localization of a threat once initial detection is achieved. This noise is estimated as a function of threat location relative to the glider and is temporally reduced through the use of an information or Kalman filtering. In the next section, the swarm probability of confirming and killing a threat is formulated. Results are compared to a collection of stationary sensors. These results show that once a glider has the ability to move faster than the threat, the performance of the swarm is equal to the performance of a stationary swarm of gliders with confirmation and kill ranges equal to detection range. Moreover, at glider speeds greater than the speed of the threat, swarm performance becomes a weak function of speed. At these speeds swarm performance is dominated by detection range. Therefore, to future enhance swarm performance or to reduce the number of gliders required for a given performance, detection range must be increased. Communications latency is also examined. It was found that relatively large communication delays did little to change swarm performance. Thus gliders may come to the surface and use SATCOMS to effectively communicate in this application.

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Analysis and control of distributed cooperative systems

Feddema, John T.; Schoenwald, David A.; Parker, Eric P.; Wagner, John S.

As part of DARPA Information Processing Technology Office (IPTO) Software for Distributed Robotics (SDR) Program, Sandia National Laboratories has developed analysis and control software for coordinating tens to thousands of autonomous cooperative robotic agents (primarily unmanned ground vehicles) performing military operations such as reconnaissance, surveillance and target acquisition; countermine and explosive ordnance disposal; force protection and physical security; and logistics support. Due to the nature of these applications, the control techniques must be distributed, and they must not rely on high bandwidth communication between agents. At the same time, a single soldier must easily direct these large-scale systems. Finally, the control techniques must be provably convergent so as not to cause undo harm to civilians. In this project, provably convergent, moderate communication bandwidth, distributed control algorithms have been developed that can be regulated by a single soldier. We have simulated in great detail the control of low numbers of vehicles (up to 20) navigating throughout a building, and we have simulated in lesser detail the control of larger numbers of vehicles (up to 1000) trying to locate several targets in a large outdoor facility. Finally, we have experimentally validated the resulting control algorithms on smaller numbers of autonomous vehicles.

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Self-Reconfigurable Robots

Hensinger, David M.; Johnston, Gabriel J.; Hinman-Sweeney, Elaine H.; Feddema, John T.; Eskridge, Steven E.; Hinman-Sweeney, Elaine H.

A distributed reconfigurable micro-robotic system is a collection of unlimited numbers of distributed small, homogeneous robots designed to autonomously organize and reorganize in order to achieve mission-specified geometric shapes and functions. This project investigated the design, control, and planning issues for self-configuring and self-organizing robots. In the 2D space a system consisting of two robots was prototyped and successfully displayed automatic docking/undocking to operate dependently or independently. Additional modules were constructed to display the usefulness of a self-configuring system in various situations. In 3D a self-reconfiguring robot system of 4 identical modules was built. Each module connects to its neighbors using rotating actuators. An individual component can move in three dimensions on its neighbors. We have also built a self-reconfiguring robot system consisting of 9-module Crystalline Robot. Each module in this robot is actuated by expansion/contraction. The system is fully distributed, has local communication (to neighbors) capabilities and it has global sensing capabilities.

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Assembly of LIGA using Electric Fields

Feddema, John T.; Warne, Larry K.; Johnson, William Arthur.; Routson, Allison J.; Armour, David L.

The goal of this project was to develop a device that uses electric fields to grasp and possibly levitate LIGA parts. This non-contact form of grasping would solve many of the problems associated with grasping parts that are only a few microns in dimensions. Scaling laws show that for parts this size, electrostatic and electromagnetic forces are dominant over gravitational forces. This is why micro-parts often stick to mechanical tweezers. If these forces can be controlled under feedback control, the parts could be levitated, possibly even rotated in air. In this project, we designed, fabricated, and tested several grippers that use electrostatic and electromagnetic fields to grasp and release metal LIGA parts. The eventual use of this tool will be to assemble metal and non-metal LIGA parts into small electromechanical systems.

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Cooperative sentry vehicles and differential GPS leapfrog

Feddema, John T.; Lewis, Christopher L.; Lafarge, Robert A.

As part of a project for the Defense Advanced Research Projects Agency, Sandia National Laboratories Intelligent Systems and Robotics Center is developing and testing the feasibility of using a cooperative team of robotic sentry vehicles to guard a perimeter, perform a surround task, and travel extended distances. This paper describes the authors most recent activities. In particular, this paper highlights the development of a Differential Global Positioning System (DGPS) leapfrog capability that allows two or more vehicles to alternate sending DGPS corrections. Using this leapfrog technique, this paper shows that a group of autonomous vehicles can travel 22.68 kilometers with a root mean square positioning error of only 5 meters.

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Prospecting for lunar ice using a multi-rover cooperative team

Klarer, Paul R.; Feddema, John T.; Lewis, Christopher L.

A multi-rover cooperative team or swarm developed by Sandia National Laboratories is described, including various control methodologies that have been implemented to date. How the swarm's capabilities could be applied to a lunar ice prospecting mission is briefly explored. Some of the specific major engineering issues that must be addressed to successfully implement the swarm approach to a lunar surface mission are outlined, and potential solutions are proposed.

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18 Results
18 Results