2018

Journal Papers

  • F. Z. Saberifar, S. Ghasemlou, D. A. Shell, and J. M. O'Kane, "Toward a language-theoretic foundation for planning and filtering", International Journal of Robotics Research, accepted to appear, 2018. (arXiv) (Preprint: PDF)
  • Y. Zhang and D. A. Shell, "Complete characterization of a class of privacy-preserving tracking problems", International Journal of Robotics Research, accepted to appear, 2018. (arXiv) (Preprint: PDF)
  • Y.-H Kim and D. A. Shell, "Bound to help: cooperative manipulation of objects via compliant, unactuated tails", accepted to appear as part of the Autonomous Robots (Special Issue on Distributed Robotics: From Fundamentals to Applications), February 2018. (Preprint: PDF)
  • T. Alam, L. Bobadilla, and D. A. Shell, "Space-efficient filters for mobile robot localization from discrete limit cycles", IEEE Robotics and Automation Letters, 3(1):257–264, January 2018. (Preprint: PDF). Also presented at IEEE IROS'17 in Vancouver, Canada, September 2017.

Conference Papers

  • Y. Zhang, D. A. Shell, and J. M. O'Kane, "Finding plans subject to stipulations on what information they divulge" accepted to appear in Workshop on the Algorithmic Foundations of Robotics (WAFR-XIII), Mérida, México, December 2018. (arXiv) [Acceptance Rate was 56.8%]
  • F. Z. Saberifar, J. M. O'Kane, and D. A. Shell, "The hardness of minimizing design cost subject to planning problems" accepted to appear in Workshop on the Algorithmic Foundations of Robotics (WAFR-XIII), Mérida, México, December 2018. [Acceptance Rate was 56.8%]
  • S. Ghasemlou, J. M. O'Kane, and D. A. Shell, "Delineating boundaries of feasibility between robot designs", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, October 2018. (PDF) [Acceptance Rate was 46.7%]

Other Papers

  • Y. Zhang, D. A. Shell, and J. M. O'Kane, "What does my knowing your plans tell me?" in IEEE/RSJ IROS Workshop—Towards Intelligent Social Robots: From Naive Robots to Robot Sapiens, Madrid, Spain, October 2018. (arXiv) (PDF) [Acceptance Rate was 60%]
  • Y.-C. Hsu, S. Gopalswamy, S. Saripalli, D. A. Shell, "An MDP Model of Vehicle-Pedestrian Interaction at an Unsignalized Intersection" a workshop paper appearing in IEEE Vehicular Technology Conference (VTC), Chicago, Illinois, August 2018. (PDF) [Acceptance rate unknown]
  • A. Q. Nilles, D. A. Shell, J. M. O'Kane, "Robot Design: Formalisms, Representations, and the Role of the Designer" in IEEE ICRA Workshop on Autonomous Robot Design, Brisbane, Australia, May 2018. (arXiv) (PDF) [Acceptance rate unknown]

2017

Journal Papers

  • J. M. O'Kane and D. A. Shell, "Concise planning and filtering: hardness and algorithms", IEEE Transactions on Automation Science and Engineering (T-ASE), 14(4):1666–1681, October 2017. (Preprint: PDF)
  • P. Ivanov and D. A. Shell, "Hark! Who goes there? Concurrent Association of Communication Channels for Multiple Mobile Robots", Autonomous Robots, 41(4):811–829, April 2017. (Preprint: PDF)
  • Y.-H Kim and D. A. Shell, "Using a compliant, unactuated tail to manipulate objects", IEEE Robotics and Automation Letters, 2(1):223–230, January 2017. (Preprint: PDF) (Video). Featured in IEEE Spectrum and by Digital Trends.
  • C. Nam and D. A. Shell, "Analyzing the sensitivity of the optimal assignment in probabilistic multi-robot task allocation", IEEE Robotics and Automation Letters, 2(1):193–200, January 2017. (Preprint: PDF). Also presented at IEEE CASE'16 in Fort Worth, Texas, August 2016.

Conference Papers

  • A. Tamjidi, R. Oftadeh, S. Chakravorty, and D. A. Shell, "Efficient Distributed State Estimation of Hidden Markov Models over Unreliable Networks", in Proceedings of the International Symposium on Multi-Robot and Multi-Agent Systems (MRS), Los Angeles, California, December 2017. (PDF) [Acceptance Rate was 24%]
  • F. Z. Saberifar, J. O'Kane, and D. A. Shell, "Inconsequential improprieties: Filter reduction in probabilistic worlds", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, Canada, September 2017. (PDF) [Acceptance Rate was 45%]
  • K. Qin and D. A. Shell, "Robots going round the bend—a comparative study of estimators for anticipating river meanders", in Proceedings of IEEEInternational Conference on Robotics and Automation (ICRA), Singapore, May 2017. (PDF , and supporting technical report: PDF) [Acceptance Rate was 41%]
  • T. Alam, L. Bobadilla, and D. A. Shell, "Minimalist Robot Navigation and Coverage using a Dynamical System Approach", in Proceedings of IEEE International Conference on Robotic Computing (IRC), Taiwan, April 2017. (PDF) [Acceptance rate unknown]

2016

Journal Papers

  • S. Janpuangtong and D. A. Shell, "Helping Novices Avoid the Hazards of Data: Leveraging Ontologies to Improve Model Generalization Automatically with Online Data Sources" in AI Magazine, 37(2):19–32, Summer 2016. (Preprint: PDF)

Conference Papers

  • S. Ghasemlou, F. Z. Saberifar, J. M. O'Kane, D. A. Shell. , "Beyond the planning potpourri: reasoning about label transformations on procrustean graphs", in Workshop on the Algorithmic Foundations of Robotics (WAFR-XII), San Francisco, California, December 2016. (PDF) [Acceptance Rate was 25%]
  • Y. Zhang and D. A. Shell, "You can't save all the pandas: impossibility results for privacy-preserving tracking", in Workshop on the Algorithmic Foundations of Robotics (WAFR-XII), San Francisco, California, December 2016. (PDF) [Acceptance Rate was 25%]
  • C. Nam and D. A. Shell, "Bundling policies for sequential stochastic tasks in multi-robot systems", in Proceedings of International Symposium on Distributed Autonomous Robotic Systems (DARS), London, U.K., November 2016. (PDF, and supporting technical report: PDF) [Acceptance Rate was 39%]
  • A. Tamjidi, S. Chakravorty and D. A. Shell, "Unifying Consensus and Covariance Intersection for Decentralized State Estimation", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Deajeon, South Korea, October 2016. (PDF) [Acceptance Rate was 48%]
    Note: Since the appearance of this paper, we have discovered that we ought to have been aware of the 2014 paper entitled "Consensus-Based Linear and Nonlinear Filtering" by G. Battistelli, L. Chisci, G. Mugnai, A. Farina, and A. Graziano. Their work has a near identical approach, though our work specifically examines networks which undergo partition.
  • F. Z. Saberifar, S. Ghasemlou, J. M. O'Kane, and D. A. Shell, "Set-labelled filters and sensor transformations", in Robotics Science and Systems (RSS-2016), Ann Arbor, Michigan, June 2016. (PDF) [Acceptance Rate was 21%]
  • R. Hosseini Teshnizi and D. A. Shell, "Planning motions for a planar robot attached to a stiff tether", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 2016. (PDF) [Acceptance Rate was 35%]

Other Papers

  • R. R. Orduño, N. Winard, S. Bierwagen, D. A. Shell, N. Kalantar, A. Borhani, and E. Akleman, "A Mathematical Approach to Obtain Isoperimetric Shapes for D-Form Construction" in Bridges: Mathematics, Music, Art, Architecture, Education, Culture, Jyväskylä, Finland, August 2016. (PDF) [Acceptance rate unknown]
  • R. Hosseini Teshnizi and D. A. Shell, "Some progress toward tethered pairs" in the ICRA Workshop on Emerging Topological Techniques in Robotics, Stockholm, Sweden, May 2016. (PDF) [Acceptance rate unknown]

2015

Journal Papers

  • L. Liu, N. Michael, and D. A. Shell, "Communication Constrained Task Allocation with Optimized Local Task Swaps", Autonomous Robots, 39(3):429–444, October 2015. (Preprint: PDF)
  • C. Nam and D. A. Shell, "Assignment Algorithms for Modeling Resource Contention in Multi-Robot Task Allocation", IEEE Transactions on Automation Science and Engineering (T-ASE) — Special Issue on Networked Cooperative Autonomous Systems, 12(3):889–900, July 2015. (Preprint: PDF)

Conference Papers

  • G. A. Wilde, R. R. Murphy, D. A. Shell, and C. M. Marianno. "A man-packable unmanned surface vehicle for radiation localization and forensics", in Proceedings of IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), West Lafayette, Indiana, October 2015. (PDF) [Acceptance rate unknown]
  • J. O'Kane and D. A. Shell, "Automatic Design of Discreet Discrete Filters", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Seattle, Washington, May 2015. (PDF) [Acceptance Rate was 41%]
  • J-H Kim and D. A. Shell, "A New Model for Self-Organized Robotic Clustering: Understanding Boundary Induced Densities and Cluster Compactness", in Proceedings of IEEEInternational Conference on Robotics and Automation (ICRA), Seattle, Washington, May 2015. (PDF) [Acceptance Rate was 41%]
  • C. Nam and D. A. Shell, "When to Do Your Own Thing: Analysis of Cost Uncertainties in Multi-Robot Task Allocation at Run-Time", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Seattle, Washington, May 2015. (PDF, and supporting technical report: PDF) [Acceptance Rate was 41%]
  • S. Janpuangtong and D. A. Shell, "Leveraging Ontologies to Improve Model Generalization Automatically with Online Data Sources", in Proceedings of Conference on Innovative Applications of Artificial Intelligence (IAAI), Austin, TX, January 2015. (PDF) [Acceptance rate unknown]

Other Papers

  • T. Alam, M. Edwards, L. Bobadilla, and D. A. Shell, "Distributed Multi-Robot Area Patrolling in Adversarial Environments" in the International Workshop on Robotic Sensor Networks (RSN), Seattle, Washington, April 2015. (PDF) [Acceptance rate unknown]

2014

Journal Papers

  • L. Liu, D. A. Shell, and N. Michael. "From Selfish Auctioning to Incentivized Marketing", Autonomous Robots, 37(4):417–430, December 2014. (Preprint: PDF)

Conference Papers

  • P. Ivanov and D. A. Shell, "Associating Nearby Robots to their Voices", in Proceedings of International Conference on the Synthesis and Simulation of Living Systems (ALife), New-York, NY, August 2014. (PDF) [Acceptance rate unknown]
  • L. Liu, N. Michael, and D. A. Shell, "Fully Decentralized Task Swaps with Optimized Local Searching", in Robotics Science and Systems (RSS-2014), July 2014, Berkeley, CA. (PDF) [Acceptance Rate was 32%]
  • Y.-H. Kim and D. A. Shell, "Distributed Robotic Sampling of Non-Homogeneous Spatio-Temporal Fields Via Recursive Geometric Sub-Division", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Hong-Kong, China, May 2014. (PDF) [Acceptance Rate was 48%]
  • C. Nam and D. A. Shell, "Assignment Algorithms for Modeling Resource Contention and Interference in Multi-Robot Task-Allocation", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Hong-Kong, China, May 2014. (PDF) [Acceptance Rate was 48%]
  • R. Hosseini Teshnizi and D. A. Shell, "Computing Cell-Based Decompositions Dynamically for Planning Motions of Tethered Robots", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Hong-Kong, China, May 2014. (PDF) [Acceptance Rate was 48%]

2013

Journal Papers

  • L. Liu and D. A. Shell, "Physically Routing Robots through a Multi-robot Network: Flexibility through a Three Dimensional Matching Graph", International Journal of Robotics Research, 32(12): 1475–1494, September 2013. (Preprint: PDF)
  • L. Liu and D. A. Shell, "An Anytime Assignment Algorithm: From Local Task Swapping to Global Optimality", Autonomous Robots, 35(4):271–286, November 2013. (Preprint: PDF)
  • B. Fine and D. A. Shell, "Unifying Microscopic Flocking Motion Models for Virtual, Robotic, and Biological Flock Members", Autonomous Robots, 35(2–3):195–219, October 2013. (Preprint: PDF)

Conference Papers

  • L. Liu and D. A. Shell, "Optimal Market-based Multi-Robot Task Allocation via Strategic Pricing", in Robotics Science and Systems (RSS-2013), June 2013, Berlin, Germany. (PDF) [Acceptance Rate was 30%]
  • J. O'Kane and D. A. Shell, "Finding concise plans: Hardness and algorithms", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, November 2013. (PDF) [Acceptance Rate was 43%]
  • J-H Kim and D. A. Shell, "Improving the performance of self-organized robotic clustering: modeling and planning sequential changes to the division of labor", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, November 2013. (PDF) [Acceptance Rate was 43%]
  • B. Fine and D. A. Shell, "Eliciting Collective Behaviors through Automatically Generated Environments", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, November 2013. (PDF) [Acceptance Rate was 43%]
  • A. Ghoshal and D. A. Shell, "Covering space with simple robots: from chains to random trees", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 2013. (PDF) [Acceptance Rate was 39%]
  • J. O'Kane and D. A. Shell, "Automatic Reduction of Combinatorial Filters", in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 2013. (PDF) [Acceptance Rate was 39%]

2012

Journal Papers

  • L. Liu and D. A. Shell, "Large-Scale Multi-Robot Task Allocation via Dynamic Partitioning and Distribution", Autonomous Robots, 33(3): 291–307, October 2012. (Preprint: PDF)

Conference Papers

  • E. Drumwright and D. A. Shell, "Extensive analysis of Linear Complementarity Problem (LCP) solver performance on randomly generated rigid body contact problems" in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5034–5039, Algarve, Portugal, October 2012. (PDF) [Acceptance Rate was 45%]
  • S. Kristek and D. A. Shell, "Orienting deformable polygonal parts without sensors" in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 973–979, Algarve, Portugal, October 2012. (PDF) [Acceptance Rate was 45%]
  • L. Liu and D. A. Shell, "An Efficient Distributed Topo-Geometric Spatial Density Estimation Method for Multi-Robot Systems" in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 828–833, Algarve, Portugal, October 2012. (PDF) [Acceptance Rate was 45%]
  • L. Liu and D. A. Shell, "A Distributable and Computation-flexible Assignment Algorithm: From Local Task Swapping to Global Optimality" in Robotics Science and Systems (RSS-2012), Sydney Australia, July 2012. (PDF) [Acceptance Rate was 33%]
  • L. Liu and D. A. Shell, "Tunable Routing Solutions for Multi-Robot Navigation via the Assignment Problem: A 3D Representation of the Matching Graph" in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages 4800–4805, St. Paul, MN, USA, May 2012. (PDF) [Acceptance Rate was 40%]

Other Papers

  • L. Liu and D. A. Shell, "Tackling Task Allocation Uncertainty via a Combinatorial Method" in the IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), College Station, Texas, November 2012. (PDF) [Acceptance rate unknown]
  • L. Liu and D. A. Shell, "Multi-robot Formation Morphing through a Graph Matching Problem", in Proceedings of International Symposium on Distributed Autonomous Robotic Systems (DARS). Baltimore, MD. Nov 2012. Best Student Paper Runner-up Award. (PDF) [Acceptance rate unknown]
  • L. Liu and D. A. Shell, "Distribute the Task Swapping Assignment Method under Communication Constraints", in Symposium on Emerging Topics in Control and Modeling: Networked Systems (CMNS). Urbana-Champaign, IL. Oct 2012. (PDF) [Acceptance rate unknown]
  • B. Fine and D. A. Shell, "Flocking Motions: Examination of Information Requirements", in the 2012 Symposium on Emerging Topics in Control and Modeling: Networked Systems (CMNS). Urbana-Champaign, IL. Oct 2012. (PDF) [Acceptance rate unknown]
  • T. Ahmed and D. A. Shell, "Quantifying Uncertainty in Networked Robotic Systems", in the 2012 Symposium on Emerging Topics in Control and Modeling: Networked Systems (CMNS). Urbana-Champaign, IL. Oct 2012. [Acceptance rate unknown]
  • Y. Song, J.-H. Kim, and D. A. Shell, "Self-organized Clustering of Square Objects by Multiple Robots", in Proceedings of the International Conference on Swarm Intelligence (ANTS), pages 308–315, Brussels, Belgium, September 2012. (PDF) [Acceptance rate unknown]
  • B. Fine and D. A. Shell, "Examining the Information Requirements for Flocking Motion", in Proceedings of the International Conference on Simulation of Adaptive Behavior (SAB), pages 442–452, Odense, Denmark, August 2012. (PDF) [Acceptance rate unknown]
  • T. Mitra and D. A. Shell, "Cost, Precision, and Task Structure in Aggression-Based Arbitration for Minimalist Robot Cooperation", in Proceedings of the International Conference on Simulation of Adaptive Behavior (SAB), pages 431–441, Odense, Denmark, August 2012. (PDF) [Acceptance rate unknown]
  • Y.-H. Kim, D. A. Shell, C. Ho, and S. Saripalli, "Spatial Interpolation for Robotic Sampling: Uncertainty with two Models of Variance", in Proceedings of the International Symposium on Experimental Robotics (ISER), Québec City, Canada, June 2012. (PDF) [Acceptance rate unknown]
  • R. Leontie, E. Drumwright, D. A. Shell, and R. Simha, "Load Equalization on a Two-Armed Robot via Proprioceptive Sensing", in Proceedings of the International Symposium on Experimental Robotics (ISER), Québec City, Canada, June 2012. (PDF) [Acceptance rate unknown]
  • D. A. Shell, R. Murphy, A. Guerin, and A. Casey, "Artistic Elements and Practical Challenges in A Midsummer Night's Dream with Unmanned Vehicles", in the IEEE International Conference on Robotics and Automation (ICRA) Workshop on Robotics and Performing Arts: Reciprocal influences, St. Paul, Minnesota, USA, May, 14th 2012. (PDF) [Acceptance rate unknown]

2011

Journal Papers

  • L. Liu and D. A. Shell, "Assessing Optimal Assignment under Uncertainty: An Interval-based Algorithm." International Journal of Robotics Research, 30(7):936–953, June 2011. (Preprint: PDF)
  • Y.-H. Kim, S.-W. Lee, H. Yang, and D. A. Shell, "Toward Autonomous Robotic Containment Booms: Visual Servoing for Robust Inter-vehicle Docking of Surface Vehicles", Journal of Intelligent Service Robotics, 5(1): 1–18, September 2011. (Preprint: PDF)
  • R. Murphy, D. A. Shell, A. Hopper, B. Duncan, B. Fine, K. Pratt, T. Zourntos, "A Midsummer Night's Dream (with Flying Robots)", Autonomous Robots, Vol. 30, No. 2, February 2011. (Preprint: PDF)

Conference Papers

  • L. Liu and D. A. Shell, "Multi-level Partitioning and Distribution of the Assignment Problem for Large-scale Multi-robot Task Allocation", in Robotics Science and Systems (RSS-2011), Los Angeles, California, July 2011. (PDF) [Acceptance Rate was 25%]
  • B. Fine and D. A. Shell, "Flocking: don't need no stinkin' robot recognition" in Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS), San Francisco, California, September 2011. (PDF) [Acceptance Rate was 32%]
  • L. Liu, B. Fine, D. A. Shell, and A. Klappenecker, "Approximate Characterization of Multi-Robot Swarm 'Shape' in Sublinear-Time", in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 2011. (PDF) [Acceptance Rate was 49%]
  • E. Drumwright and D. A. Shell, "An Evaluation of Methods for Modeling Contact in Multibody Simulation", in Proceedings of the 2011 IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 2011. (PDF) [Acceptance Rate was 49%]

Other Papers

  • M. Buller, P. Cuddihy, E. Davis, P. Doherty, F. Doshi-Velez, E.. Erdem, D. H. Fisher, N. Green, K. Hinkelmann, M. L. Maher, J. McLurkin, R. T. Maheswaran, S. Rubinelli, N. Schurr, D. Scott, D. A. Shell, P. A. Szekely, B. Thönssen, and A. Urken, "Reports of the AAAI 2011 Spring Symposia", AI Magazine, 32(3): 119–127, Fall 2011.

2010

Conference Papers

  • L. Liu and D. A. Shell, "Assessing Optimal Assignment under Uncertainty: An Interval-based Algorithm", in Robotics Science and Systems (RSS-2010), Zaragoza Spain, June 2010. (PDF) [Acceptance Rate was 16%]
  • E. Drumwright and D. A. Shell, "Modeling Contact Friction and Joint Friction in Dynamic Robotic Simulation using the Principle of Maximum Dissipation", in Workshop on the Algorithmic Foundations of Robotics (WAFR-IX), Singapore, December 2010. (PDF) [Acceptance Rate was 40%]
  • E. Drumwright, J. Hsu, N. Koenig, and D. A. Shell, "Extending Open Dynamics Engine for Robotics", in International Conference on Simulation, Modeling and Programming for Autonomous Robots (SIMPAR), Darmstadt, Germany, November 2010. (PDF) [Acceptance Rate was 37%]

Other Papers

  • L. Liu and D. A. Shell, "Task Insertion and Reassignment in Networked Robotics for Topological Morphing", appeared as poster in IEEE ICRA Network Science and Systems workshop, Anchorage, Alaska, May 2010. (PDF) [Reviewed, but Acceptance Rate unknown]
  • J. O'Hollaren and D. A. Shell, "Incremental Multi-Robot Deployment for Line-of-Sight Chains Using on Radio Signal Strength", appeared as poster in IEEE ICRA Network Science and Systems workshop, Anchorage, Alaska, May 2010. (PDF) [Reviewed, but Acceptance Rate unknown]
  • B. Duncan, R. Murphy, D. A. Shell, A. Hopper, "A Midsummer Night's Dream; Social proof in HRI", accepted as a late breaking report for the ACM/IEEE 2010 Conference on Human-Robot Interactions. (PDF) [Acceptance rate for late breaking reports unknown].

2009

Conference Papers

  • D. A. Shell and M. Mataric', "High-fidelity radio communications modeling for multi-robot simulation", in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 3447–3452, St. Louis, Missouri, October 2009. (PDF) [Acceptance Rate was 58%]
  • E. Drumwright and D. A. Shell, "A robust and tractable contact model for dynamic robotic simulation", in Proceedings of the 2009 ACM Symposium on Applied Computing (SAC), pages 1176–1180, Honolulu, Hawaii, March 2009. (PDF) [Acceptance rate unknown: 2008 was 29%]
  • D. A. Shell and E. Drumwright, "Precise generalized contact point and normal determination for rigid body simulation", a poster paper in Proceedings of the 2009 ACM Symposium on Applied Computing (SAC), pages 11762107–2108, Honolulu, Hawaii, March 2009. (PDF) [Acceptance rate unknown]