Tanygin S.,Analytical Graphics Inc.
Journal of Guidance, Control, and Dynamics | Year: 2017
A new algorithm suitable for fast onboard implementation is presented for designing attitude maneuver paths that achieve desired boresight alignment in the presence of multiple three-axis attitude constraints. It is based on a recently proposed algorithm in which possible attitudes are discretized in a three-dimensional distortion-minimizing projected space. In that space, grid points are enumerated and graph search pathfinding algorithms are employed to find the shortest constrained path between selected initial and target grid points. The new algorithm extends this approach from a single target point to a continuum of target points, representing all possible attitudes that maintain the desired boresight alignment. It augments the original algorithm with the transformation that makes it possible to assign a single value to estimated distances for the whole continuum of target points. This, in turn, allows the pathfinding algorithms to efficiently determine the shortest overall path to the whole continuum, which corresponds to the shortest attitude maneuver path that achieves the desired boresight alignment.
News Article | November 14, 2016
Editors Note: There are two photos associated with this press release. Thoth Technology Inc. in partnership with Analytical Graphics Inc.'s Commercial Space Operations Center (ComSpOC) has developed a deep space radar system for the detection of objects orbiting over North America. Designed to detect and protect key space assets in geostationary orbit, the system also has the capability to locate other space objects including the moon. The team refurbished Canada's largest antenna, a fully steerable 46m dish in Algonquin Park, equipping it with a modern space situational awareness (SSA) system capable of locating targets to within 25 meters. "Space is our business," said Caroline Roberts, CEO of Thoth. "Our new SSA system can provide real time warning of incoming space objects and also detect faults in geostationary spacecraft," she said. As part of Thoth's calibration activity, the SSA system tracked the moon for approximately two hours during its close approach to Earth. "Although it's closer than it's been since 1948, it's still more than 350,000 kilometers from Algonquin Park, and to me that's not that close. It takes the radio waves more than 2.3 seconds to travel to the moon and back to the observatory," said Brendan Quine, Thoth's CTO and the system's designer. "The moon is a great calibration target for us, and it's so beautiful when it is this bright. We should be able to learn a lot about the moon from the data," he said. Thoth plans further enhancements of its SSA capability to include imaging of space objects shortly. To view the photos associated with this press release, please visit the following links:
Tanygin S.,Analytical Graphics Inc.
Journal of Guidance, Control, and Dynamics | Year: 2013
This paper examines the projective geometry of three-parameter attitude representations that are constructed by projecting a four-parameter unit quaternion representation from its unit hypersphere onto a three-dimensional hyperplane. Using this geometrical perspective, the paper demonstrates how kinematics of relative attitude motion characteristic of attitude tracking problems follow naturally from comparing projections from two different reference directions. The paper also demonstrates that among a continuum of possible projection pole placements there exist optimal distances for which resulting projected parameterizations yield magnitudes that accurately approximate all practical rotation angles. These parameterizations referred to in this paper as proxy-rotation vectors can be custom tuned for any expected range of rotation angles. They and their kinematics are free from trigonometric functions and do not require special handling if the rotation angle approaches zero. It is shown that this computational simplicity of the proxy-rotation vectors can be advantageous for linear feedback attitude controls and for certain classes of time-efficient attitude steering laws, where they can replace the more computationally cumbersome true rotation vector. The paper studies how kinematic singularities affect closed-loop stability and demonstrates that redesigning control laws to ensure closed-loop convergence toward the nearest equilibrium is equivalent to augmenting attitude parameterizations with their shadow counterparts. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Tanygin S.,Analytical Graphics Inc.
Journal of Guidance, Control, and Dynamics | Year: 2012
A class of vectorial attitude parameterizations that are formulated as a product of the unit rotation vector and various functions of the rotation angle is examined. When related to a four-dimensional unit quaternion, these vectorial parameterizations are shown to be analogous to higher-dimensional azimuthal projections from a threedimensional unit hypersphere. Several types of these projections are examined. Singularities are identified and numerical accuracy is evaluated based on the singular value decomposition of the attitude kinematics. It is shown how shadow parameterizations can be constructed in order to alleviate the kinematical singularities. It is also shown that the kinematical passivity and optimality of the Rodrigues and modified Rodrigues parameters are special cases of the more general result that holds for a wider range of vectorial parameterizations. This result is used to formulate and compare passivity-based control laws using various parameterizations. Copyright © 2011 by Sergei Tanygin. Published by the American Institute of Aeronautics and Astronautics, Inc.
Analytical Graphics Inc. | Date: 2012-01-11
Determining a launch window from anywhere within a specified area to avoid or minimize close approaches between a launch vehicle and orbiting space objects. A method and apparatus is disclosed for minimizing close approaches, or conjunctions between spacecraft being launched from anywhere within a specified area and other objects in space during the launch and early deployment phase of their lifetime, by defining a launch window, utilizing and identifying launch window blackout times to avoid close approaches of launch trajectories from anywhere within an area with remaining objects in space as noted in a space object catalog.
Analytical Graphics Inc. | Date: 2014-09-03
Methods, systems, and devices for the visualization of the region of a 3-dimensional space obstructed from a viewing location by an ellipsoid are disclosed. In an embodiment, the obstructed region may be defined from primitive elements which are combined using Boolean operations. The primitive elements chosen may be represented using both implicit functions and/or parametric surfaces. In an embodiment, the implicit function representation may be used to quickly determine points on candidate surfaces which may be obstructed from view. In an embodiment, the parametric representation may be used to provide ray-surface intersection solutions enabling visualization of the boundary surface of the obstruction region.
Analytical Graphics Inc. | Date: 2013-12-20
A device and method for presenting augmented image data. An image capture device captures an image together with information about the image. Alternatively a data logger may capture additional information about a particular image. The image and additional information is sent to a database where a server analyzes the augmented image and relates the augmented image to other images in the database. A subsequent user may query the database for all images and augmented information for a particular area, location, or object and retrieve that collected information for subsequent analysis.
Analytical Graphics Inc. | Date: 2013-02-28
A device and method for displaying data simultaneously in two-dimensional and three-dimensional formats. A user selects data to be represented in multiple formats simultaneously. A data rendition server retrieves the data and determines the three-dimensional representations that are possible. The user then selects the three-dimensional representation desired, and the server renders the data to the user in both two-dimensional and three-dimensional formats. The data may be rendered together with static data such as digital terrain data and other static data types. Data representations may be rotated and morphed as desired by the user.
Analytical Graphics Inc. | Date: 2014-10-22
A computing device may detect that a space object has undergone a maneuver and may attempt to calculate a solution to that maneuver based in part on start and stop times and thrust uncertainties associated with the detected maneuver. However, the computing device may sometimes be unable to calculate an acceptable solution for a detected maneuver given these initial start and stop times and thrust uncertainties. Thus, the various embodiments provide for a computing device and methods implemented by a processor executing on the device for identifying and calculating a recovery maneuver of a space object when an acceptable solution for a detected maneuver cannot be determined. In the various embodiments, a computing device processor may generate a recovery maneuver based on the detected maneuver, and the processor may adjust the start and stop times and the uncertainty values of the recovery maneuver until an acceptable solution is found.
News Article | March 30, 2015
Zappos CEO Tony Hsieh offered his nearly 4,000 employees an ultimatum last week: accept Holacracy or leave. While the word may conjur images of a new-age cult, Holacracy is an alternative organizational structure that has been adopted by companies around the world—including Medium, the alt-publishing platform from Twitter cofounder Ev Williams, and the David Allen Company, the productivity consultants. It sheds traditional hierarchies for self-governing teams that get work done through tactical meetings. Zappos is the largest company to have adopted the system, and the transition hasn't been entirely smooth. By multiple reports and now an admission in an internal memo, first posted by Quartz and obtained by Fast Company, people don't love the idea of relinquishing their manager titles. Nevertheless, Hsieh is anxious to fully embrace Holacracy, and is going all-in on the new structure by offering three months severance to people who don't want to adapt. "We've been operating partially under Holacracy and partially under the legacy management hierarchy in parallel for over a year now," Hsieh writes in the memo. "Having one foot in one world while having the other foot in the other world has slowed down our transformation towards self-management and self-organization." Adopting Holacracy isn't cheap or easy. The system has its own set of rules and lingo, and is complicated to implement. The Holacracy parent company, HolacracyOne, helps companies transition by offering consulting services that run from $50,000 to $500,000, depending on how long it takes to achieve self-sufficiency. Even for much smaller companies, like Medium, which implemented Holacracy when it was just a couple dozen people in 2012, the journey takes multiple years and has a steep learning curve. Holacracy was invented by Brian Robertson, a 35-year-old former programmer with barely any management experience. He created Holacracy in 2007 because he had a "burning sense that there has to be a better way to work together," he said in an interview with Fast Company. Robertson, who describes himself as a coding savant, says he taught himself to program at age 6. By the time he was 13, he says he was charging $25 an hour for software development through the Sierra Network, an early competitor to AOL. "They had no idea how old I was" Robertson said. "I didn’t even know enough to name my business." After dropping out of the Stevens Institute of Technology, 17-year-old Robertson managed to get a job at Analytical Graphics, an aerospace company known for its perk-laced work culture. "You couldn’t beat the benefits, the environment, the culture. From a conventional view, they were really cool" he said. They had free meals, a gym, and a game room. Robertson had a great boss, who he still considers a friend and mentor. Analytical Graphics even won an award for being one of the best small companies to work for in the U.S. by the Great Place to Work Institute. "The bureaucracy seemed to be set up in a way that people couldn't use their gifts, their talents," Robertson said. In 2001, he started his own company to figure out a better way to run one. Robertson certainly isn't alone in his disdain for top-down order. Holacracy comes out of and operates within a milieu of unconventional ways to work that have become more popular in the last decade as younger and more visionary CEOs eschew tradition and seek out a new way of working. Among the options are sociocracy, Freedom at Work, the Morning Star Self Management System, and the Results Only Work Environment (ROWE). Each of those systems, including Holacracy, has a distinct approach to the same general problem. "The industrial age operating system is no longer compatible," said Traci Fenton, the founder and CEO of WorldBlu, which preaches the Freedom at Work method used by hundreds of companies worldwide, including Zappos before it adopted Holacracy. (Zappos still uses WorldBlu's services, which aren't incompatible with Holacracy.*) "You have to move into the new age to realize we've outgrown the clothes." The hierarchical organization dates back to the industrial revolution, when companies wanted to preserve accountability while employing large numbers of people. "It was a way of organizing labor such that the division of labor would be more productive and would be able to do tasks better repeatedly in a predictable way," says Ethan Bernstein, who studies organizational behavior at Harvard Business School. As the American workforce moved away from the assembly line and into the cubicle, work no longer required people to repeatedly complete specific tasks. The information economy prizes ideas, creativity, and collaboration—all of which gets stifled by hierarchy. One Stanford study that looked at 80 different teams, both real world and lab simulated, found that hierarchy led to conflict at higher levels of management. "I found they didn’t reach as good of a collective or a group solution," says Lindred Greer, who studies hierarchy at the Stanford School of Business. As a result, the relationship between manager and employee has organically shifted over the last few decades. Almost half of the CEOs interviewed for a 2015 report by the London brand consultancy Wolff Olins said they had structured their companies to give employees more autonomy. The modern company is more of a conversation than a mandate. But while the hierarchy may be flattening in many companies, the latest wave of non-traditional structures argue for more radical changes. The video game maker Valve, perhaps the most extreme example, forgoes titles and managers altogether. In an ideal Holacracy, it's impossible to tell who the CEO is. Robertson spent six years exploring these different alternative organizational systems, picking and choosing the aspects he liked best—and trying them out on the 12 employees who he hired to build software products. He borrowed theories from the agile software movement and David Allen's Getting Things Done. By 2007, Robertson took the "early embryo" of Holacracy and along with his business partner Tom Thomison, a former management consultant, founded HolacracyOne, the Pennsylvania based organization that acts as a kind of consulting firm for companies that want to adopt the system. Along with the personal consulting services, HolacracyOne offers seminars that can cost up to $4,000 a seat, and it sells an organizational software application called GlassFrog that runs $500 a month. The software is optional, but both Medium and Zappos use it. HolacracyOne also has a healthy business training third-party coaches. Robertson is writing a book slated to come out this summer. Unlike some of its contemporaries, Holacracy doesn't advocate for a flat organization. Holacracy organizes work (and people) around circles within circles within circles. People within those circles have "roles" that give certain team members complete control over their domains. Someone at Medium, for example, is in charge of fonts and makes all font-related decisions. Contrary to headlines (including one on this website), Medium still has managers, because each circle has a leader. But unlike a traditional manager, not all decisions have to go through that one person, and that person can change—the structure of a Holacracy is very fluid. That's why people don't have titles, they have roles that often do change. The main objective is to distribute authority throughout an organization. Fewer decisions bottleneck through a boss, meaning faster decision making and in theory faster innovation. All of that makes Holacracy particularly appealing to companies that want to retain the benefits of fast-moving startups as they grow. "Holacracy is not going to take a bad business idea and make it succeed. It’s not going to take a team that doesn’t have the skills and make it brilliant," Robertson said. "It's more of an accelerant," he said. He likens Holacracy to getting a new computer. Generally, self-management systems promise happier employees, healthier workforces, and as a result a more successful company. Hsieh is so eager to ditch hierarchy because he wants his company to operate with the efficiency of a bustling metropolis, not a clunky corporate behemoth. Cities when they double in size get 15% more productive, companies lose productivity as they grow. Completely restructuring a company from the standard org chart tree to circles is one of the reasons the transition to Holacracy tends to be rocky. To create circles and roles requires a very regimented process, called a governance meeting. Then, there's a separate, also very systematic meeting for assigning particular people to particular jobs. Holacracy doesn't have any rules for firing or compensation. Some companies, like Medium, create special circles that handle HR. Another approach is to give people roles that empower them to fire and promote. Companies can spend a lot of time thinking about their structure, rather than doing actual work, especially in the beginning. All of the confusing rules and terminology tend to scare people, but that's intentional. Obscurity, Robertson says, is part of a strategy to hook the right converts. "My sales approach is to try to talk people out of it," he says. The Holacracy website doesn't make it easy to understand what a company might be getting into. The "in plain English" version of the Holacracy Constitution is multiple mouse scrolls long. Robertson likens his method to that of Nigerian email scammers. "They are filtering out all the people that are not ridiculously gullible, only the ones that are really good targets are left. For us, it's the positive version of that." Robertson wants to attract people that get it, like Hsieh and Medium CEO Ev Williams. Of course, just because bosses can overlook the eccentricities of Holacracy for its potential, employees aren't always as open. The name alone is off-putting. When Williams first introduced Holacracy to Medium, multiple employees thought it sounded cultish. "I think it used to be Holawhat? That sounds like a cult," Jean Hsu, an engineer at Medium told me. Accepting Holacracy is like learning a complicated strategy game, like Settlers of Catan, says Robertson. "If you've ever learned to play a complex board game, all you see are a bunch of rules," he says. "That said, if you play the game with people who have played it before they walk you through it, eventually the rules totally fade to the background." Similarly, the best way to learn Holacracy is by playing. For new converts, Holacracy runs a taster week, during which a consultant simulates tactical and governance meetings. Medium, which implemented Holacracy about three years ago, had a rough adjustment phase, too. Governance meetings can take hours. People got stressed about understanding the system, and began neglecting their jobs as a result. "Being bad at something is frustrating," Williams told me. "To do that something else that we're good at actually, we have to do this thing we’re bad at. As a group, we’re going to do this awkward dance. It’s hard and messy and it causes stress, and you’re like, 'why are we doing this?'" The tactical meetings, a replacement for your standard, generally very painful weekly team gathering, won over Medium's staff—and it's easy to see why, they're fast and efficient. This February I sat in on one at Medium's San Francisco headquarters, and while from the outside it looked like a normal meeting, the process was incredibly regimented. An engineer with a clump of curls named Koop facilitated, ensuring that conversations stayed on track. The heart of the tactical meeting is a process called tension processing, where, one by one, team members talk out their "tensions," which in Holacracy land means any issue someone might have. In Medium's case tensions ranged from the design of the site to the circle's name. Because of Koop, the group stayed on track, getting through 20 issues in about 25 minutes. The meeting also moves quickly because "processing a tension" just means deciding on a next step, not coming to a solution. Over half a dozen current and former employees I spoke with—even ones who didn't like Holacracy in general—mentioned the benefits of tactical meetings. Having sat through one at Medium, I can confirm that they are way better than standard team meetings. Stuff gets done, fast. At this point, it's too early to tell if Holacracy is working for either Zappos or Medium, says Robertson. Holacracy, however, uses the David Allen Company as a case study. Although, even CEO Mike Williams considers it "a work in progress." Unlike Zappos, Medium has a less dramatic relationship with Holacracy. Most people I talked to at the company like it. (Although they're very self conscious about how weird it sounds. Questions about Holacracy are often met with awkward laughs.) "We could be organizing a different way, but I kind of couldn't imagine it given what we're trying to do," Kate Lee, a senior editor at Medium, told me. Then again, the company is much smaller (about 80 people), implemented Holacracy early on, and has a few more years practice. Also, Medium isn't successful by the most standard of metrics: it makes no money. "It's [Holacracy] not a complete system. It's not the answer," in and of itself, added Bernstein. By Hsieh's standards, Zappos hasn't reached its potential. The journey takes about five years and chaos at the beginning is expected, says Robertson. "When I see everything that's going on at Zappos, it's all part of the shift." This post has been updated to clarify Zappos on going relationship with WorldBlu.