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Generalizing the dubins and reeds-shepp cars: Fastest paths for bounded-velocity mobile robots

Andrei A. Furtuna, Devin J. Balkcom, Hamidreza Chitsaz, Paritosh Kavathekar
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nytnrt3gtzbixld5r6a4talbky" style="color: black;">2008 IEEE International Conference on Robotics and Automation</a> </i> &nbsp;
The answer to this fundamental question is only known analytically for a few planar mobile robots: the Dubins and Reeds-Shepp steered cars, the differential drive, and a particular omnidirectional robot  ...  What is the shortest or fastest path a mobile robot can follow between two configurations in the unobstructed plane?  ...  The optimal paths are only known analytically for four ground vehicles: Dubins and Reeds-Shepp steered cars, the differential-drive, and the symmetric three-wheeled omnidirectional vehicle.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/robot.2008.4543594">doi:10.1109/robot.2008.4543594</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icra/FurtunaBCK08.html">dblp:conf/icra/FurtunaBCK08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bkejsv7q4rfwzclr2jolyrok2e">fatcat:bkejsv7q4rfwzclr2jolyrok2e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401064821/http://www.cs.dartmouth.edu/~robotics/papers/aaf-icra08.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/56/c7/56c7e768517a69034cba18b6e3b5a30c5ee18501.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/robot.2008.4543594"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Minimum-time trajectories for kinematic mobile robots and other planar rigid bodies with finite control sets

Andrei A. Furtuna, Wenyu Lu, Weifu Wang, Devin J. Balkcom
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dmucnarmarh2fj6syg5jyqs7ny" style="color: black;">2011 IEEE/RSJ International Conference on Intelligent Robots and Systems</a> </i> &nbsp;
This paper presents first attempts at a method for searching for time-optimal trajectories for a general model of mobile robots that includes Dubins and Reeds-Shepp cars, differential-drive robots, and  ...  This search is not formally guaranteed to find a nearoptimal trajectory if the sampling of the search space is not fine enough, but comparison to existing analytical results for specific systems, and a  ...  For the Dubins and Reeds-Shepp cars and the diff-drive, we generated q 0 from the range With the exception of the Reeds-Shepp car (for which whirl trajectories may be optimal), for each starting configuration  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2011.6094923">doi:10.1109/iros.2011.6094923</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iros/FurtunaLWB11.html">dblp:conf/iros/FurtunaLWB11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gopvya4tpjd77eaedmlhaxjcui">fatcat:gopvya4tpjd77eaedmlhaxjcui</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150301104754/http://cs.dartmouth.edu:80/~harrisonwfw/iros_2011.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/26/eb/26eb551a6b6070d1800a0c0ae9b1dc3f681d64de.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2011.6094923"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Minimum-time trajectories for kinematic mobile robots and other planar rigid bodies with finite control sets

A. A. Furtuna, Wenyu Lu, Weifu Wang, D. J. Balkcom
<span title="">2011</span> <i title="IEEE"> 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems </i> &nbsp;
This paper presents first attempts at a method for searching for time-optimal trajectories for a general model of mobile robots that includes Dubins and Reeds-Shepp cars, differential-drive robots, and  ...  This search is not formally guaranteed to find a nearoptimal trajectory if the sampling of the search space is not fine enough, but comparison to existing analytical results for specific systems, and a  ...  For the Dubins and Reeds-Shepp cars and the diff-drive, we generated q 0 from the range With the exception of the Reeds-Shepp car (for which whirl trajectories may be optimal), for each starting configuration  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2011.6048592">doi:10.1109/iros.2011.6048592</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/erjdnoygubd4pdwpmubgd2tx34">fatcat:erjdnoygubd4pdwpmubgd2tx34</a> </span>
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Generalizing Dubins Curves: Minimum-time Sequences of Body-fixed Rotations and Translations in the Plane

Andrei A. Furtuna, Devin J. Balkcom
<span title="2010-03-17">2010</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uhsvnr5ecvb4die3422lvgaz6q" style="color: black;">The international journal of robotics research</a> </i> &nbsp;
These trajectories are a generalization of the well-known Dubins and Reeds-Shepp curves, which describe the shortest paths for steered cars in the plane.  ...  The configuration of the body is its position and orientation, given by (x, y, θ) coordinates, and the rotations and translations are velocities (ẋ,ẏ,θ) that are constant in the frame of the robot.  ...  Rgeodesics are of particular interest in robotics because they describe the shortest paths for a simple model of a car with bounded steering angle and velocity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0278364910365093">doi:10.1177/0278364910365093</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u5jivo5wcnehlo4u47xqd37nnu">fatcat:u5jivo5wcnehlo4u47xqd37nnu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20141014100442/http://www.cs.dartmouth.edu:80/~devin/papers/aaf-ijrr2010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/80/80/8080ab2b568698734aee8de4f6ec5ebe4a59c28c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0278364910365093"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> sagepub.com </button> </a>

Time-optimal Trajectories for an Omni-directional Vehicle

Devin J. Balkcom, Paritosh A. Kavathekar, Matthew T. Mason
<span title="">2006</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uhsvnr5ecvb4die3422lvgaz6q" style="color: black;">The international journal of robotics research</a> </i> &nbsp;
Unlike a steered car, a vehicle with this design can move in any direction without needing to rotate first, and can spin as it does so. The shortest paths for this vehicle are straight lines.  ...  A common mobile robot design consists of three 'omniwheels' arranged at the vertices of an equilateral triangle, with wheel axles aligned with the rays from the center of the triangle to each wheel.  ...  The authors would like to thank Steven LaValle, Hamid Chitsaz, Jean-Paul Laumond, Bruce Donald, the members of the CMU Center for the Foundations of Robotics, and the members of the Dartmouth Robotics  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0278364906069166">doi:10.1177/0278364906069166</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7jihpl3amjbave3h45o3igki5m">fatcat:7jihpl3amjbave3h45o3igki5m</a> </span>
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A genetic algorithm for nonholonomic motion planning

Gorkem Erinc, Stefano Carpin
<span title="">2007</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rytolcxr5rgw3dx2hhx2tlpo6q" style="color: black;">Engineering of Complex Computer Systems (ICECCS), Proceedings of the IEEE International Conference on</a> </i> &nbsp;
Mainly focusing on mobile robots, the algorithm uses present randomized algorithms to come up with suboptimal paths and iteratively optimizes them according to a fitness function which includes domain  ...  The paper presents a genetic algorithm to find and optimize solutions for nonholonomic motion planning problems.  ...  1} and u φ ∈ {φ max , φ min } we obtain the famous Reeds and Shepp car.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/robot.2007.363590">doi:10.1109/robot.2007.363590</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icra/ErincC07.html">dblp:conf/icra/ErincC07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x5tzgb5cgbdsxjacy75solfg6u">fatcat:x5tzgb5cgbdsxjacy75solfg6u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100614201425/https://robotics.ucmerced.edu/Robotics/papers/paperfinal.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/10/33/1033a991a47d59103b49b805cff13dad79a759b8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/robot.2007.363590"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Sampling Extremal Trajectories for Planar Rigid Bodies [chapter]

Weifu Wang, Devin Balkcom
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lirc5icuifhy7ln5rynpn4ak2e" style="color: black;">Springer Tracts in Advanced Robotics</a> </i> &nbsp;
This paper presents an approach to finding the time-optimal trajectories for a simple rigid-body model of a mobile robot in an obstacle-free plane.  ...  The main contribution of this paper is a method for sampling the extremal trajectories sufficiently densely to guarantee that for any pair of start and goal configurations, a trajectory can be found that  ...  This rigid body might represent a simple model of a mobile robot (for example, the steered cars studied by Dubins, Reeds and Shepp, and others [4, 16, 18, 11, 19] , differential drives [2] , omnidirectional  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-36279-8_20">doi:10.1007/978-3-642-36279-8_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qa3qdtn4fnbeljluhf3s3cwqqy">fatcat:qa3qdtn4fnbeljluhf3s3cwqqy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20121114215305/http://cs.dartmouth.edu/~harrisonwfw/wafr_2012.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/c9/a4c93292045b7113ec8903b091b5bcc28ea3f6da.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-36279-8_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Time-optimal trajectories with bounded curvature in anisotropic media

Irina S Dolinskaya, Alvaro Maggiar
<span title="2012-09-11">2012</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uhsvnr5ecvb4die3422lvgaz6q" style="color: black;">The international journal of robotics research</a> </i> &nbsp;
The presented work is a generalization of the Dubins car problem, which considers fastest paths with bounded curvature while assuming constant speed and minimum turning radius.  ...  We relax this assumption and discuss fastest-path finding problems for the generalized direction-dependent speed and minimum turning radius functions, to account for the effects of waves, winds and slope  ...  Acknowledgment The first author would like to thank Elmer G. Gilbert and Robert L. Smith from the University of Michigan for their helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0278364912458464">doi:10.1177/0278364912458464</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tc6vwmuzpjerxcurpg65kwg2ae">fatcat:tc6vwmuzpjerxcurpg65kwg2ae</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321041502/http://users.iems.northwestern.edu/~ama132/docs/dolinskaya-maggiar-12-02.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/18/e3/18e397fd127f9121429551096ad2f8e06dd4b7b0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/0278364912458464"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> sagepub.com </button> </a>

A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles [article]

Brian Paden, Michal Cap, Sze Zheng Yong, Dmitry Yershov, Emilio Frazzoli
<span title="2016-04-25">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements.  ...  Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation.  ...  Another notable variation is the Reeds-Shepp car for which minimum length paths are known when v r takes a single forward and reverse speed [58] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1604.07446v1">arXiv:1604.07446v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ajwztawbwra6tpw2zf67uncevm">fatcat:ajwztawbwra6tpw2zf67uncevm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200901203708/https://arxiv.org/pdf/1604.07446v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d4/90/d4900f6facbdc6da1bd73cab03bbc7c0320bd23e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1604.07446v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Construction of Fastest Curvature-Constrained Paths in Direction-Dependent Media

Alvaro Maggiar, Irina S. Dolinskaya
<span title="">2014</span> <i title="American Institute of Aeronautics and Astronautics (AIAA)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yekwqy6srncl5bew6tynp7vjsq" style="color: black;">Journal of Guidance Control and Dynamics</a> </i> &nbsp;
The problem studied here is a generalization of the classical Dubins car problem, where the vehicle speed and minimumturning radius are assumed to be constant.  ...  This paper is concerned with the extension and implementation of the authors' earlier results that establish the fastest path between two positions in the plane for a Dubins-like vehicle in a (possibly  ...  [1998] carried out this task for the Reeds and Shepp model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2514/1.61778">doi:10.2514/1.61778</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dbfr4lt635addhmlncpgtgf2ye">fatcat:dbfr4lt635addhmlncpgtgf2ye</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706061127/http://users.iems.northwestern.edu/%7Edolira/maggiar-dolinskaya-2013.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8a/c1/8ac11c6e43cdf410d21140c5a904e2d4159cff98.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2514/1.61778"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A harmonic potential field approach for joint planning and control of a rigid, separable nonholonomic, mobile robot

Ahmad A. Masoud
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ncwahgzkgbfljbalytxadcov3u" style="color: black;">Robotics and Autonomous Systems</a> </i> &nbsp;
The main objective of this paper is to provide a tool for performing path planning at the servo level of a mobile robot.  ...  This paper demonstrates the ability of the harmonic potential field (HPF) approach to generate a provably correct, constrained, well behaved trajectory and control signal for a rigid, nonholonomic robot  ...  Acknowledgment: the author acknowledges King Fahd University of Petroleum and Minerals for its support  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.robot.2013.02.007">doi:10.1016/j.robot.2013.02.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qst2psmc4rbwxmjzideyneulfe">fatcat:qst2psmc4rbwxmjzideyneulfe</a> </span>
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Optimal path finding in direction, location, and time dependent environments

Irina S. Dolinskaya
<span title="2012-06-25">2012</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t7lkodpouve6nhkdui2tcdja54" style="color: black;">Naval Research Logistics</a> </i> &nbsp;
Lawrence Seiford, for his support, his advices, and the opportunities that helped me to successfully complete my studies and get a great academic position.  ...  Michael Parsons, thank you for your time and patience while educating me on the concepts of wave propagation, vessel navigation, seakeeping and other topics that helped me to understand the intricate details  ...  Reeds and Shepp [60] study optimal paths with bounded curvature for a car that can move forward and backwards, resulting in paths with cusps. Boissonnat et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/nav.21492">doi:10.1002/nav.21492</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uzcl3nhiifer5o5zkgyfjeoxty">fatcat:uzcl3nhiifer5o5zkgyfjeoxty</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923011945/https://deepblue.lib.umich.edu/bitstream/handle/2027.42/64828/dolira_1.pdf;jsessionid=0A6C2ABAFBAA8C5135E92280DE3522D3?sequence=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/6a/826a6ed8a56bd13d381696e6b7aaa07b44ca9ffa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/nav.21492"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Optimal Gaits for Dynamic Robotic Locomotion

Jorge Cortés, Sonia Martínez, James P. Ostrowski, Kenneth A. McIsaac
<span title="">2001</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uhsvnr5ecvb4die3422lvgaz6q" style="color: black;">The international journal of robotics research</a> </i> &nbsp;
This generates feasible paths that approach the optimal one as the number of basis functions is increased.  ...  We study near-optimal gaits for an underwater eel-like robot, though the tools and analysis can be applied more broadly to a large family of nonlinear control systems with drift.  ...  Acknowledgments The research of J. Cortés and S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/02783640122067624">doi:10.1177/02783640122067624</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pcytsw3ztvezbohhmzmx56dxr4">fatcat:pcytsw3ztvezbohhmzmx56dxr4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100617061153/http://faemino.ucsd.edu/~soniamartinez/papers/data/2001_CoMaOsIs-ijrr.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/86/5e/865e939f547ccb81dfadd2bb7f624cb589b54706.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1177/02783640122067624"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> sagepub.com </button> </a>

The Minimum-Time Trajectories for an Omni-Directional Vehicle [chapter]

Devin J. Balkcom, Paritosh A. Kavathekar, Matthew T. Mason
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lirc5icuifhy7ln5rynpn4ak2e" style="color: black;">Springer Tracts in Advanced Robotics</a> </i> &nbsp;
We show that if there are independent bounds on the speeds of the wheels, the fastest trajectories for this vehicle contain only spins in place, circular arcs, and straight lines parallel to the wheel  ...  One common mobile robot design consists of three 'omniwheels' arranged at the vertices of an equilateral triangle, with wheel axles aligned with the rays from the center of the triangle to each wheel.  ...  Robotics Lab for invaluable advice and guidance in this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-68405-3_22">doi:10.1007/978-3-540-68405-3_22</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/znywj6t5wvgo5alyk7tbbnxdiy">fatcat:znywj6t5wvgo5alyk7tbbnxdiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706040226/https://parasol.tamu.edu/wafr06/papers/p32.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/01/1601e8b5f9d4e7385b8d9734b6b9435dee0a0aee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-68405-3_22"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>