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Articles 1 - 30 of 30
Full-Text Articles in Engineering
Ultracompact High-Efficiency Polarizing Beam Splitter With A Hybrid Photonic Crystal And Conventional Waveguide Structure, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
Ultracompact High-Efficiency Polarizing Beam Splitter With A Hybrid Photonic Crystal And Conventional Waveguide Structure, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
Faculty Publications
We propose an ultracompact high-efficiency polarizing beam splitter that operates over a wide wavelength range and is based on a hybrid photonic crystal and a conventional waveguide structure. Within a small area (15 mm 3 10 mm), this polarizing beam splitter separates TM- and TE-polarized modes into orthogonal output waveguides. Results of simulations with the two-dimensional finite-difference time-domain method show that 99.3% of TM-polarized light is def lected by the photonic crystal structure (with a 28.0-dB extinction ratio), whereas 99.0% of TE-polarized light propagates through the structure (with a 32.2-dB extinction ratio). Wave vector diagrams are employed to explain the …
Multiple Uav Cooperative Search Under Collision Avoidance And Limited Range Communication Constraints, Randal W. Beard, Timothy W. Mclain
Multiple Uav Cooperative Search Under Collision Avoidance And Limited Range Communication Constraints, Randal W. Beard, Timothy W. Mclain
Faculty Publications
This paper focuses on the problem of cooperatively searching, using a team of unmanned air vehicles (UAVs), an area of interest that contains regions of opportunity and regions of potential hazard. The objective of the UAV team is to visit as many opportunities as possible, while avoiding as many hazards as possible. To enable cooperation, the UAVs are constrained to stay within communication range of one another. Collision avoidance is also required. Algorithms for team-optimal and individually-optimal/team-suboptimal solutions are developed and their computational complexity compared. Simulation results demonstrating the feasibility of the cooperative search algorithms are presented.
Dynamic Modeling Of Compliant Constant-Force Compression Mechanisms, Cameron Boyle, Larry L. Howell, Spencer P. Magleby, Mark S. Evans
Dynamic Modeling Of Compliant Constant-Force Compression Mechanisms, Cameron Boyle, Larry L. Howell, Spencer P. Magleby, Mark S. Evans
Faculty Publications
A mathematical dynamic model is derived for compliant, constant-force compression-mechanisms, based on the pseudo-rigid-body model simplification of the device. The compliant constant-force compression mechanism (CFCM) is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully calibrated with empirical data from five separate mechanisms, comprising two basic configurations of CFCMs. The dynamic equation is derived from a generalized pseudo-rigid-body model. This allows every configuration to be represented by the same model, so a separate treatment is not required for each configuration. An unexpected dynamic trait of the constant-force …
Parallel Microgenetic Algorithm Design For Photonic Crystal And Waveguide Structures, J. Cai, L. Li, Gregory P. Nordin, J. Jiang
Parallel Microgenetic Algorithm Design For Photonic Crystal And Waveguide Structures, J. Cai, L. Li, Gregory P. Nordin, J. Jiang
Faculty Publications
We have developed a powerful parallel genetic algorithm design tool for photonic crystal and waveguide structures. The tool employs a small-population-size genetic algorithm (microgenetic algorithm) for global optimization and a two-dimensional finite-difference time-domain method to rigorously design and optimize the performance of photonic devices. We discuss the implementation and performance of this design tool. We demonstrate its application to two photonic devices, a defect taper coupler to connect conventional waveguides and photonic crystal waveguides, and a sharp 90˚ waveguide bend for low index contrast waveguides.
The Distribution Of Internal Interfaces In Polycrystals, Brent L. Adams, Bassem S. El-Dasher, Gregory S. Rohrer, Anthony D. Rollett, David M. Saylor, Paul Wynblatt
The Distribution Of Internal Interfaces In Polycrystals, Brent L. Adams, Bassem S. El-Dasher, Gregory S. Rohrer, Anthony D. Rollett, David M. Saylor, Paul Wynblatt
Faculty Publications
This work was supported by the MRSEC program of the National Science Foundation under Award Number DMR-0079996. Recent advances both in experimental instrumentation and computing power have made it possible to interrogate the distribution of internal interfaces in polycrystals and the three dimensional structure of the grain boundary network with an unprecedented level of detail. The purpose of this paper is to review techniques that can be used to study the mesoscopic crystallographic structure of grain boundary networks and to summarize current findings. Recent studies have shown that grain surfaces within dense polycrystals favor the same low energy planes that …
An Improved Simulation Model For Spaceborne Scatterometer Measurements, David G. Long, Peter K. Yoho
An Improved Simulation Model For Spaceborne Scatterometer Measurements, David G. Long, Peter K. Yoho
Faculty Publications
Development of scatterometer designs and applications requires extensive data simulation. The advancing capabilities of instruments motivates our proposal for an improved simulation model for noisy scatterometer measurements. Previous simulation models do not separately account for the two forms of random variation - signal fading and additive noise - which affect scatterometer measurements. The proposed model is able to generate data that are statistically equivalent (in a mean and variance sense) to actual instrument measurements by accounting for both variations, while maintaining ease of implementation. The model is particularly adept at handling design tradeoffs related to signal-to-noise ratios by appropriately separating …
Predictive Joint Motion Limiting In Robotic Applications, Edward Red, Brian Fielding
Predictive Joint Motion Limiting In Robotic Applications, Edward Red, Brian Fielding
Faculty Publications
Three joint space algorithms slow the Cartesian path motion when it appears that joint motion is approaching a joint, speed, or acceleration limit. All three algorithms use quadratic curve fitting to predict where the joint motion is heading, followed by a prediction as to how much time would elapse until a limit is reached.
Seven Principles Of Efficient Human Robot Interaction, Michael A. Goodrich, Dan R. Olsen Jr.
Seven Principles Of Efficient Human Robot Interaction, Michael A. Goodrich, Dan R. Olsen Jr.
Faculty Publications
Advances in robot technology and artificial intelligence have increased the range of robot applications as well as the importance of supporting human interaction with robots and robot teams. Previous work by the authors has highlighted the importance of creating neglect tolerant autonomy and efficient interfaces. In this paper, lessons learned from evaluating neglect tolerance and interface efficiency are compiled into a set of principles for efficient interaction. Emphasis is placed on designing efficient interfaces, but many of the principles require autonomy levels that support the principles. Each principle is illustrated by an example and motivated by citing relevant factors from …
A Texture Evolution Model In Cubic-Orthotropic Polycrystalline System, Brent L. Adams, H. Garmestani, D. S. Li
A Texture Evolution Model In Cubic-Orthotropic Polycrystalline System, Brent L. Adams, H. Garmestani, D. S. Li
Faculty Publications
This work has been funded under the AFOSR Grant # F49620-03-1-0011 and Army Research Lab Contract # DAAD17-02-P-0398 and DAAD 19-01-1-0742. B.L. Adams acknowledges support of Army Research Office, Proposal No. 42566-MS. The authors express their sincere gratitude to Professor Surya Kalidindi, for helpful suggestions and correspondence for the derivation of the processing path functions. A new methodology based on a conservation principle in the orientation space is developed to simulate the texture evolution in a cubic-orthotropic polycrystalline system. A least squares error method was used to improve the accuracy of the simulation results obtained from the texture evolution function. …
Evaluating Tmr Techniques In The Presence Of Single Event Upsets, Paul S. Graham, Nathaniel Rollins, Michael J. Wirthlin, Michael P. Caffrey
Evaluating Tmr Techniques In The Presence Of Single Event Upsets, Paul S. Graham, Nathaniel Rollins, Michael J. Wirthlin, Michael P. Caffrey
Faculty Publications
Sponsorship: Los Alamos National Labs (LA-UR-03-7525). Field programmable gate arrays (FPGAs) are sensitive to radiation-induced single event upsets (SEUs) within the configuration memory. Triple modular redundancy (TMR) is a technique commonly used to mitigate against design failures caused by SEUs. This paper evaluates the effectiveness and cost of TMR on two different counter designs in the presence of SEUs. The evaluation measures the reliability, area cost, and speed of different TMR styles. The tests show that when feedback TMR is used with triplicated clocks, it is possible to have counter design which is insensitive to any single configuration upset.
Autonomous Vehicle Technologies For Small Fixed Wing Uavs, Derek B. Kingston, Randal Beard, Timothy Mclain, Michael Larsen, Wei Ren
Autonomous Vehicle Technologies For Small Fixed Wing Uavs, Derek B. Kingston, Randal Beard, Timothy Mclain, Michael Larsen, Wei Ren
Faculty Publications
Autonomous unmanned air vehicle flight control systems require robust path generation to account for terrain obstructions, weather, and moving threats such as radar, jammers, and unfriendly aircraft. In this paper, we outline a feasible, hierarchal approach for real-time motion planning of small autonomous fixed-wing UAVs. The approach divides the trajectory generation into four tasks: waypoint path planning, dynamic trajectory smoothing, trajectory tracking, and low-level autopilot compensation. The waypoint path planner determines the vehicle's route without regard for the dynamic constraints of the vehicle. This results in a significant reduction in the path search space, enabling the generation of complicated paths …
Learning Real-Time A* Path Planner For Sensing Closely-Spaced Targets From An Aircraft, Jason K. Howlett, Michael A. Goodrich, Timothy W. Mclain
Learning Real-Time A* Path Planner For Sensing Closely-Spaced Targets From An Aircraft, Jason K. Howlett, Michael A. Goodrich, Timothy W. Mclain
Faculty Publications
This work develops an any-time path planner, based on the learning real-time A* (LRTA*) search, for generating flyable paths that allow an aircraft with a specified sensor footprint to sense a group of closely-spaced targets. The LRTA* algorithm searches a tree of flyable paths for the branch that accomplishes the desired objectives in the shortest distance. The tree of paths is created by assembling primitive turn and straight sections of a specified step size. The operating parameters for the LRTA* search directly influence the running time and path-length performance of the search. A modified LRTA* search is presented that terminates …
Large-Scale Inverse Ku-Band Backscatter Modeling Of Sea Ice, David G. Long, Quinn P. Remund
Large-Scale Inverse Ku-Band Backscatter Modeling Of Sea Ice, David G. Long, Quinn P. Remund
Faculty Publications
Polar sea ice characteristics provide important inputs to models of several geophysical processes. Microwave scatterometers are ideal for monitoring these regions due to their sensitivity to ice properties and insensitivity to atmospheric distortions. Many forward electromagnetic scattering models have been proposed to predict the normalized radar cross section (σ˚) from sea ice characteristics. These models are based on very small scale ice features and generally assume that the region of interest is spatially homogeneous. Unfortunately, spaceborne scatterometer footprints are very large (5-50 km) and usually contain very heterogeneous mixtures of sea ice surface parameters. In this paper, we use scatterometer …
Micro-Genetic Algorithm Design Of Hybrid Conventional Waveguide And Photonic Crystal Structures, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
Micro-Genetic Algorithm Design Of Hybrid Conventional Waveguide And Photonic Crystal Structures, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
Faculty Publications
We previously proposed the hybrid integration of photonic crystals (PhCs) and conventional index-guided waveguides (CWGs) as a potentially attractive method of realizing compact waveguide elements for large-scale planar lightwave circuits (PLCs). We now examine 90-deg bends and beamsplitters in PhC/CWG structures in which the waveguide core has a high refractive index (3.25) and yet a low refractive index contrast (1.54%) with the clad material. A PhC structure composed of a triangular or square array of air holes is placed at the intersection of input and output waveguides to obtain high efficiency 90-deg bends. We find that diffraction from the boundary …
A Self-Retracting Fully Compliant Bistable Micromechanism, Nathan D. Masters, Larry L. Howell
A Self-Retracting Fully Compliant Bistable Micromechanism, Nathan D. Masters, Larry L. Howell
Faculty Publications
A new class of fully compliant bistable mechanisms with the added benefit of integrated self-retraction has been developed (hereafter identified as Self-Retracting Fully compliant Bistable Mechanism or SRFBM). A technique using tensural pivots to manage compressive loading in compliant mechanisms is introduced and implemented in the SRFBM. The elimination of traditional kinematic joints and their associated clearance allows a total displacement between stable positions of 8.5 m, and the mechanism size is less than 300 m square when using 2.0 m minimum line widths. Maximum actuation force is approximately 500 N. The SRFBM's small linear displacement and reasonable actuation force …
In Situ Uv-Visible Assessment Of Extent Of Reduction During Oxidation Reactions On Oxide Catalysts, Morris D. Argyle, Kaidong Chen, Carlo Resini, Catherine Krebs, Alexis T. Bell, Enrique Iglesia
In Situ Uv-Visible Assessment Of Extent Of Reduction During Oxidation Reactions On Oxide Catalysts, Morris D. Argyle, Kaidong Chen, Carlo Resini, Catherine Krebs, Alexis T. Bell, Enrique Iglesia
Faculty Publications
The extent of reduction of active centers during oxidative alkane dehydrogenation on VOx/Al2O3 was measured from pre-edge UV-visible spectral features and found to increase with increasing VOx domain size and propane/O2 ratio.
Effects Of Solvent Model Flexibility On Aqueous Electrolyte Behavior Between Electrodes, Richard L. Rowley, John N. Harb, Clint G. Guymon, Matthew L. Hunsaker, Douglas Henderson
Effects Of Solvent Model Flexibility On Aqueous Electrolyte Behavior Between Electrodes, Richard L. Rowley, John N. Harb, Clint G. Guymon, Matthew L. Hunsaker, Douglas Henderson
Faculty Publications
Molecular dynamics simulations have been carried out for aqueous electrolyte solutions between model electrode surfaces. The effect of solvent model flexibility on bult and double layer properties was observed for electrode surface charge densities of 0, 0.1 and 0.2 and ion concentrations of 0, 0.5 and 1 M. Two flexible models were used to isolate the effects of flexibility from the effects of a change in the condensed-phase dipole moment. Model flexibility increases the pure water self-diffusion coefficient while a larger liquid diple moment substantially decreases it. There is an increase in ion contact adsorption and counter ion affinity with …
Cooperative Path Planning For Timing Critical Missions, Timothy W. Mclain, Randal W. Beard
Cooperative Path Planning For Timing Critical Missions, Timothy W. Mclain, Randal W. Beard
Faculty Publications
This paper presents a cooperative path planning approach for teams of vehicles operating under timing constraints. A cooperative control approach based on coordination variables and coordination functions is introduced and applied to cooperative timing problems. Three types of timing constraints are considered: simultaneous arrival, tight sequencing, and loose sequencing. Simulation results demonstrating the approach are presented.
Microstructure Sensitive Design Of An Orthotropic Plate Subjected To Tensile Load, Brent L. Adams, Mark Lyons, Joshua R. Houskamp, Surya R. Kalidindi
Microstructure Sensitive Design Of An Orthotropic Plate Subjected To Tensile Load, Brent L. Adams, Mark Lyons, Joshua R. Houskamp, Surya R. Kalidindi
Faculty Publications
Financial support for this work was provided by the Army Research Office, Proposal No. 42566-MS, Dr. David Stepp, Program Director and Army Research Lab, Dr. Scott Schoenfeld, Point of Contact. Microstructure Sensitive Design (MSD) is a newly developed mathematical framework that facilitates rigorous solutions to inverse problems in microstructure design of materials. In this paper, this methodology is applied to an orthotropic thin plate containing a circular hole subjected to an in-plane uniaxial tensile load. The primary design objective is to maximize the load carrying capacity of the plate while avoiding plastic deformation in the plate. Making use of the …
Building Solid Models From Boreholes And User-Defined Cross-Sections, Alan M. Lemon, Norman L. Jones
Building Solid Models From Boreholes And User-Defined Cross-Sections, Alan M. Lemon, Norman L. Jones
Faculty Publications
Solid models of geologic structures are useful tools for geologists and engineers. Solid models completely and unambiguously define the stratigraphy for the site being modeled, including complex boundaries and embedded seams. Past research has focused on the “set operations” approach to create solid models. Whereas the set operations approach is flexible, it requires significant user intervention and is therefore difficult to use. A simple approach for generating solid models from borehole data, called the horizons method, is presented. The horizons method can be used to build solids directly from borehole data with minimal user intervention. The user first assigns horizon …
Interaction Energy Surfaces Of Small Hydrocarbon Molecules, Richard L. Rowley, Jukka-Pekka Jalkanen, Tapani A. Pakkanen, Yan Yang
Interaction Energy Surfaces Of Small Hydrocarbon Molecules, Richard L. Rowley, Jukka-Pekka Jalkanen, Tapani A. Pakkanen, Yan Yang
Faculty Publications
Nonbonding interactions of small alkane molecules were studied with ab initio methods. Previously reported energy data for ethane and propane dimers were supplemented with 1747 new configurations of dimers involving slightly larger hydrocarbons. The completed work provides interaction energy surfaces for all combinations of dimer pairs involving ethane, propane, isobutane, and neopentane and thus contains information of all chemical groups found in acyclic alkanes. The strongest attraction of the studied molecule pairs was encountered in isobutane C2h dimer, where an energy minimum of -1.784 kcal mol^-1 at 4.28 Angstroms separation of centermost carbon atoms was observed. The composite data set …
Advances In Experimental Method And Analysis For Estimation Of Geometrically-Necessary Dislocations, Brent L. Adams, Bassem S. El-Dasher, Anthony D. Rollett
Advances In Experimental Method And Analysis For Estimation Of Geometrically-Necessary Dislocations, Brent L. Adams, Bassem S. El-Dasher, Anthony D. Rollett
Faculty Publications
The authors wish to thank The Alcoa Technical Research Center for supplying the specimens and performing the compression tests. This work was supported by the MRSEC program of the National Science Foundation under DMR-0079996 as well as Lawrence Livermore Laboratory DOE/DoD Joint Program. An behavior of grain boundaries of the polycrystalline materials over a wide range of length scales during plastic deformation is considered. Electron backscattering diffraction and orientation imaging microscopy provide automated scanning measurements of the lattice orientation near grain boundaries. These methods are useful to set the necessary length scales. The data are presented for directionally-solidified pure Al …
An Advanced Ambiguity Selection Algorithm For Seawinds, David G. Long, David W. Draper
An Advanced Ambiguity Selection Algorithm For Seawinds, David G. Long, David W. Draper
Faculty Publications
SeaWinds on QuikSCAT, a spaceborne Ku-band scatterometer, estimates ocean winds via the relationship between the normalized radar backscatter and the vector wind. Scatterometer wind retrieval generates several possible wind vector solutions or ambiguities at each resolution cell, requiring a separate ambiguity selection step to give a unique solution. In processing SeaWinds on QuikSCAT data, the ambiguity selection is "nudged" or initialized using numerical weather prediction winds. We describe a sophisticated new ambiguity selection approach developed at Brigham Young University (BYU) that does not require nudging. The BYU method utilizes a low-order data-driven Karhunen-Loeve wind field model to promote self-consistency. Ambiguity …
High-Resolution Measurements With A Spaceborne Pencil-Beam Scatterometer Using Combined Range/Doppler Discrimination Techniques, David G. Long, Michael W. Spencer, Wu-Yang Tsai
High-Resolution Measurements With A Spaceborne Pencil-Beam Scatterometer Using Combined Range/Doppler Discrimination Techniques, David G. Long, Michael W. Spencer, Wu-Yang Tsai
Faculty Publications
Conically scanning pencil-beam scatterometer systems, such as the SeaWinds radar, constitute an important class of instruments for spaceborne climate observation. In addition to ocean winds, scatterometer data are being applied to a wide range of land and cryospheric applications. A key issue for future scatterometer missions is improved spatial resolution. Pencil-beam scatterometers to date have been real-aperture systems where only range discrimination is used, resulting in a relatively coarse resolution of approximately 25 km. In this paper, the addition of Doppler discrimination techniques is proposed to meet the need for higher resolution. The unique issues associated with the simultaneous application …
A Joint Trajectory Generator For Motion Recovery, Edward Red, Wei Li
A Joint Trajectory Generator For Motion Recovery, Edward Red, Wei Li
Faculty Publications
This paper describes an adaptive S-curve used to recover a tool path upon a system crash in the Windows operating system (OS). For a mechanism such as a robot or machine tool, the joint values, being delivered as setpoints to the servo-controller, are dynamically recorded by the real-time operating system also residing on the computer. The real-time OS can control the abort and record pertinent motion data after Windows OS crash.
Experimental Characterization Of The Mimo Wireless Channel: Data Acquisition, Analysis, And Modeling, Michael A. Jensen, Jon W. Wallace, A. Lee Swindlehurst, Brian D. Jeffs
Experimental Characterization Of The Mimo Wireless Channel: Data Acquisition, Analysis, And Modeling, Michael A. Jensen, Jon W. Wallace, A. Lee Swindlehurst, Brian D. Jeffs
Faculty Publications
Detailed performance assessment of space-time coding algorithms in realistic channels is critically dependent upon accurate knowledge of the wireless channel spatial characteristics. This paper presents an experimental measurement platform capable of providing the narrowband channel transfer matrix for wireless communications scenarios. The system is used to directly measure key multiple-input-multiple-output parameters in an indoor environment at 2.45 GHz. Linear antenna arrays of different sizes and construction with up to ten elements at transmit and receive are utilized in the measurement campaign. This data is analyzed to reveal channel properties such as transfer matrix element statistical distributions and temporal and spatial …
Real Time Dynamic Trajectory Smoothing For Uninhabited Aerial Vehicles, Erik Anderson, Randal Beard, Timothy W. Mclain
Real Time Dynamic Trajectory Smoothing For Uninhabited Aerial Vehicles, Erik Anderson, Randal Beard, Timothy W. Mclain
Faculty Publications
Sponsorship: AFOSR, DARPA. This paper presents a real-time, feasible trajectory generation algorithm for unmanned air vehicles (UAVs) flying through a sequence of waypoints. The algorithm produces extremal trajectories that transition between straight-line path segments in a time-optimal fashion. In addition, the algorithm can be configured so that the dynamically feasible trajectory has the same path length as the straight-line waypoint path. Implementation issues associated with the algorithm are described in detail. Simulation studies show the effectiveness of the proposed method.
High-Pressure Coal Pyrolysis In A Drop Tube Furnace, Koichi Matsuoka, Zhi-Xin Ma, Hiroyuki Akiho, Zhan-Guo Zhang, Akira Tomita, Thomas H. Fletcher, Marek A. Wojtowicz, Stephen Niksa
High-Pressure Coal Pyrolysis In A Drop Tube Furnace, Koichi Matsuoka, Zhi-Xin Ma, Hiroyuki Akiho, Zhan-Guo Zhang, Akira Tomita, Thomas H. Fletcher, Marek A. Wojtowicz, Stephen Niksa
Faculty Publications
To obtain useful and reliable pyrolysis data under high pressures, continuous pyrolysis experiments were carried out using a drop tube furnace. To ascertain the reliability of data, a mass balance during pyrolysis was carefully checked. The pyrolysis data obtained in this equipment was compared with previous results, and it was found that the weight loss observed in the drop tube furnace was somewhat larger than those obtained with other apparatuses. The experimental results were compared with those predicted by three pyrolysis models. Although discrepancies between predictions and experimental results were observed under a certain condition, the agreement between the experimental …
High-Pressure Intrinsic Oxidation Kinetics Of Two Coal Chars, William C. Hecker, Peter M. Madsen, Michael R. Sherman, Jared W. Allen, Rebecca J. Sawaya, Thomas H. Fletcher
High-Pressure Intrinsic Oxidation Kinetics Of Two Coal Chars, William C. Hecker, Peter M. Madsen, Michael R. Sherman, Jared W. Allen, Rebecca J. Sawaya, Thomas H. Fletcher
Faculty Publications
Chars were produced from two coals (North Dakota lignite and Pittsburgh No. 8 hva bituminous coal) in a flat flame burner at atmospheric pressure. Intrinsic char reactivities to oxygen were then measured in a high-pressure thermogravimetric analyzer as a function of temperature, total pressure, and partial pressure of oxygen. Care was taken to avoid mass transfer effects. Reactivities were normalized by the available mass of char at any given time (g/(gavailâs)). Reactivity data were obtained over a wide range of char burnout and were found to be independent of burnout level between char burnouts of 20 and 60%. Data were …
Motion Planning Using Potential Fields, Randal W. Beard, Timothy W. Mclain
Motion Planning Using Potential Fields, Randal W. Beard, Timothy W. Mclain
Faculty Publications
The objective of these notes is to describe a reactive approach to motion planning for mobile robots. In a reactive approach, trajectories are not planned explicitly. Rather, robot interactions are defined explicitly and the robot motion is said to "emerge." The drawback of reactive methods is that it is sometimes difficult to get the robot to do exactly what you want. The reactive approach that will be described in these notes is called the "virtual fields" method and is commonly used in robotics.