A Neural Network Approach for High-Dimensional Optimal Control Applied to Multiagent Path Finding

Onken, Derek; Nurbekyan, Levon; Li, Xingjian; Fung, Samy Wu; Osher, Stanley; Ruthotto, Lars

doi:10.1109/tcst.2022.3172872

A Neural Network Approach for High-Dimensional Optimal Control Applied to Multiagent Path Finding

Journal Article · 01 January 2023 · IEEE Transactions on Control Systems Technology

DOI:https://doi.org/10.1109/tcst.2022.3172872· OSTI ID:2424683

^[1]; ^[2]; Li, Xingjian ^[3]; ^[4]; ^[2]; Ruthotto, Lars ^[3]

Department of Computer Science, Emory University, Atlanta, GA, USA
Department of Mathematics, University of California at Los Angeles (UCLA), Los Angeles, CA, USA
Department of Mathematics, Emory University, Atlanta, GA, USA
Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, USA

Not provided.

Research Organization:: US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Advanced Scientific Computing Research (ASCR)

Sponsoring Organization:: USDOE

OSTI ID:: 2424683

Journal Information:: IEEE Transactions on Control Systems Technology, Journal Name: IEEE Transactions on Control Systems Technology Journal Issue: 1 Vol. 31; ISSN 1063-6536

Publisher:: IEEE

Country of Publication:: United States

Language:: English

References (53)

Lax–Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton-Jacobi Equation. Part II: Computational Methods Claudel, Christian G.; Bayen, Alexandre M. IEEE Transactions on Automatic Control, Vol. 55, Issue 5 https://doi.org/10.1109/TAC.2010.2045439	journal	May 2010
A Neural Network Approach Applied to Multi-Agent Optimal Control Onken, Derek; Nurbekyan, Levon; Li, Xingjian 2021 European Control Conference (ECC) https://doi.org/10.23919/ECC54610.2021.9655103	conference	June 2021
Viscosity Solutions of Hamilton-Jacobi Equations Crandall, Michael G.; Lions, Pierre-Louis Transactions of the American Mathematical Society, Vol. 277, Issue 1 https://doi.org/10.2307/1999343	journal	May 1983
The Uncertainty of Autonomous Unmanned Aerial Vehicles’ Energy consumption ElSayed, Mo.; Mohamed, Moataz 2020 IEEE Transportation Electrification Conference & Expo (ITEC) https://doi.org/10.1109/ITEC48692.2020.9161517	conference	June 2020
A splitting method for overcoming the curse of dimensionality in Hamilton–Jacobi equations arising from nonlinear optimal control and differential games with applications to trajectory generation Lin, Alex Tong; Chow, Yat Tin; Osher, Stanley J. Communications in Mathematical Sciences, Vol. 16, Issue 7 https://doi.org/10.4310/CMS.2018.v16.n7.a9	journal	January 2018
Generalized Risk-Sensitive Optimal Control and Hamilton–Jacobi–Bellman Equation Moon, Jun IEEE Transactions on Automatic Control, Vol. 66, Issue 5 https://doi.org/10.1109/TAC.2020.3004717	journal	May 2021
Affine Formation Maneuver Control of Multiagent Systems Zhao, Shiyu IEEE Transactions on Automatic Control, Vol. 63, Issue 12 https://doi.org/10.1109/TAC.2018.2798805	journal	December 2018
Lax–Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton–Jacobi Equation. Part I: Theory Claudel, Christian G.; Bayen, Alexandre M. IEEE Transactions on Automatic Control, Vol. 55, Issue 5 https://doi.org/10.1109/TAC.2010.2041976	journal	May 2010
Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems Jiang, Yu; Jiang, Zhong-Ping IEEE Transactions on Automatic Control, Vol. 60, Issue 11 https://doi.org/10.1109/TAC.2015.2414811	journal	November 2015
OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport Onken, Derek; Wu Fung, Samy; Li, Xingjian Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 35, Issue 10 https://doi.org/10.1609/aaai.v35i10.17113	journal	May 2021
Subdimensional expansion for multirobot path planning Wagner, Glenn; Choset, Howie Artificial Intelligence, Vol. 219 https://doi.org/10.1016/j.artint.2014.11.001	journal	February 2015
Optimal manipulator path planning with obstacles using disjunctive programming Blackmore, L.; Williams, B. 2006 American Control Conference https://doi.org/10.1109/ACC.2006.1657210	conference	January 2006
Trajectory Generation for Aircraft Avoidance Maneuvers Using Online Optimization Patel, Rushen B.; Goulart, Paul J. Journal of Guidance, Control, and Dynamics, Vol. 34, Issue 1 https://doi.org/10.2514/1.49518	journal	January 2011
Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games Lin, Alex Tong; Fung, Samy Wu; Li, Wuchen Proceedings of the National Academy of Sciences, Vol. 118, Issue 31 https://doi.org/10.1073/pnas.2024713118	journal	July 2021
Adaptive Optimal Control for Large-Scale Nonlinear Systems Michailidis, Iakovos; Baldi, Simone; Kosmatopoulos, Elias B. IEEE Transactions on Automatic Control, Vol. 62, Issue 11 https://doi.org/10.1109/TAC.2017.2684458	journal	November 2017
Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions Shi, Guanya; Honig, Wolfgang; Yue, Yisong 2020 IEEE International Conference on Robotics and Automation (ICRA) https://doi.org/10.1109/ICRA40945.2020.9196800	conference	May 2020
Time-Optimal Collaborative Guidance Using the Generalized Hopf Formula Kirchner, Matthew R.; Mar, Robert; Hewer, Gary IEEE Control Systems Letters, Vol. 2, Issue 2 https://doi.org/10.1109/LCSYS.2017.2785357	journal	April 2018
Algorithms for overcoming the curse of dimensionality for certain Hamilton–Jacobi equations arising in control theory and elsewhere Darbon, Jérôme; Osher, Stanley Research in the Mathematical Sciences, Vol. 3, Issue 1 https://doi.org/10.1186/s40687-016-0068-7	journal	September 2016
A machine learning framework for solving high-dimensional mean field game and mean field control problems Ruthotto, Lars; Osher, Stanley J.; Li, Wuchen Proceedings of the National Academy of Sciences, Vol. 117, Issue 17 https://doi.org/10.1073/pnas.1922204117	journal	April 2020
Optimal Path Following for Small Fixed-Wing UAVs Under Wind Disturbances Yang, Jun; Liu, Cunjia; Coombes, Matthew IEEE Transactions on Control Systems Technology, Vol. 29, Issue 3 https://doi.org/10.1109/TCST.2020.2980727	journal	May 2021
Multiagent Flocking With Angle-Based Formation Shape Control Jing, Gangshan; Wang, Long IEEE Transactions on Automatic Control, Vol. 65, Issue 2 https://doi.org/10.1109/TAC.2019.2917143	journal	February 2020
Potential Flow Generator With L ₂ Optimal Transport Regularity for Generative Models Yang, Liu; Karniadakis, George Em IEEE Transactions on Neural Networks and Learning Systems, Vol. 33, Issue 2 https://doi.org/10.1109/TNNLS.2020.3028042	journal	February 2022
Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation Kunisch, Karl; Walter, Daniel ESAIM: Control, Optimisation and Calculus of Variations, Vol. 27 https://doi.org/10.1051/cocv/2021009	journal	January 2021
Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space Nüsken, Nikolas; Richter, Lorenz Partial Differential Equations and Applications, Vol. 2, Issue 4 https://doi.org/10.1007/s42985-021-00102-x	journal	June 2021
M*: A complete multirobot path planning algorithm with performance bounds Wagner, Glenn; Choset, Howie 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems https://doi.org/10.1109/IROS.2011.6095022	conference	September 2011
Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations E., Weinan; Han, Jiequn; Jentzen, Arnulf Communications in Mathematics and Statistics, Vol. 5, Issue 4 https://doi.org/10.1007/s40304-017-0117-6	journal	November 2017
A Differential Game Approach to Multi-agent Collision Avoidance Mylvaganam, Thulasi; Sassano, Mario; Astolfi, Alessandro IEEE Transactions on Automatic Control, Vol. 62, Issue 8 https://doi.org/10.1109/TAC.2017.2680602	journal	August 2017
DeepReach: A Deep Learning Approach to High-Dimensional Reachability Bansal, Somil; Tomlin, Claire J. 2021 IEEE International Conference on Robotics and Automation (ICRA) https://doi.org/10.1109/ICRA48506.2021.9561949	conference	May 2021
ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs Gholaminejad, Amir; Keutzer, Kurt; Biros, George Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence https://doi.org/10.24963/ijcai.2019/103	conference	August 2019
On multiple moving objects Erdmann, Michael; Lozano-Pérez, Tomás Algorithmica, Vol. 2, Issue 1-4 https://doi.org/10.1007/BF01840371	journal	November 1987
A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems Kirchner, Matthew R.; Hewer, Gary; Darbon, Jerome 2018 IEEE Conference on Control Technology and Applications (CCTA) https://doi.org/10.1109/CCTA.2018.8511584	conference	August 2018
Algorithm for overcoming the curse of dimensionality for certain non-convex Hamilton–Jacobi equations, projections and differential games Chow, Yat Tin; Darbon, Jérôme; Osher, Stanley Annals of Mathematical Sciences and Applications, Vol. 3, Issue 2 https://doi.org/10.4310/AMSA.2018.v3.n2.a1	journal	January 2018
Aircraft trajectory planning with collision avoidance using mixed integer linear programming Richards, A.; How, J. P. Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301) https://doi.org/10.1109/ACC.2002.1023918	conference	January 2002
Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations Kang, Wei; Wilcox, Lucas C. Computational Optimization and Applications, Vol. 68, Issue 2 https://doi.org/10.1007/s10589-017-9910-0	journal	April 2017
NanoMap: Fast, Uncertainty-Aware Proximity Queries with Lazy Search Over Local 3D Data Florence, Peter R.; Carter, John; Ware, Jake 2018 IEEE International Conference on Robotics and Automation (ICRA) https://doi.org/10.1109/ICRA.2018.8463195	conference	May 2018
High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations Osher, Stanley; Shu, Chi-Wang SIAM Journal on Numerical Analysis, Vol. 28, Issue 4 https://doi.org/10.1137/0728049	journal	August 1991
Trajectory Planning for Quadrotor Swarms Honig, Wolfgang; Preiss, James A.; Kumar, T. K. Satish IEEE Transactions on Robotics, Vol. 34, Issue 4 https://doi.org/10.1109/TRO.2018.2853613	journal	August 2018
GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning With End-to-End Learning Riviere, Benjamin; Honig, Wolfgang; Yue, Yisong IEEE Robotics and Automation Letters, Vol. 5, Issue 3 https://doi.org/10.1109/LRA.2020.2994035	journal	July 2020
Learning Trajectories for Real- Time Optimal Control of Quadrotors Tang, Gao; Sun, Weidong; Hauser, Kris 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) https://doi.org/10.1109/IROS.2018.8593536	conference	October 2018
Deep Residual Learning for Image Recognition He, Kaiming; Zhang, Xiangyu; Ren, Shaoqing 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) https://doi.org/10.1109/CVPR.2016.90	conference	June 2016
Solutions for Multiagent Pursuit-Evasion Games on Communication Graphs: Finite-Time Capture and Asymptotic Behaviors Lopez, Victor G.; Lewis, Frank L.; Wan, Yan IEEE Transactions on Automatic Control, Vol. 65, Issue 5 https://doi.org/10.1109/TAC.2019.2926554	journal	May 2020
Issues in the real-time computation of optimal control Ross, I. Michael; Fahroo, Fariba Mathematical and Computer Modelling, Vol. 43, Issue 9-10 https://doi.org/10.1016/j.mcm.2005.05.021	journal	May 2006
DGM: A deep learning algorithm for solving partial differential equations Sirignano, Justin; Spiliopoulos, Konstantinos Journal of Computational Physics, Vol. 375 https://doi.org/10.1016/j.jcp.2018.08.029	journal	December 2018
Real-Time Optimal Control via Deep Neural Networks: Study on Landing Problems Sánchez-Sánchez, Carlos; Izzo, Dario Journal of Guidance, Control, and Dynamics, Vol. 41, Issue 5 https://doi.org/10.2514/1.G002357	journal	May 2018
Conflict-based search for optimal multi-agent pathfinding Sharon, Guni; Stern, Roni; Felner, Ariel Artificial Intelligence, Vol. 219 https://doi.org/10.1016/j.artint.2014.11.006	journal	February 2015
Optimization-Based Collision Avoidance Zhang, Xiaojing; Liniger, Alexander; Borrelli, Francesco IEEE Transactions on Control Systems Technology, Vol. 29, Issue 3 https://doi.org/10.1109/TCST.2019.2949540	journal	May 2021
Algorithm for overcoming the curse of dimensionality for state-dependent Hamilton-Jacobi equations Chow, Yat Tin; Darbon, Jérôme; Osher, Stanley Journal of Computational Physics, Vol. 387 https://doi.org/10.1016/j.jcp.2019.01.051	journal	June 2019
FaSTrack:A Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking Chen, Mo; Herbert, Sylvia L.; Hu, Haimin IEEE Transactions on Automatic Control, Vol. 66, Issue 12 https://doi.org/10.1109/TAC.2021.3059838	journal	December 2021
Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations Nakamura-Zimmerer, Tenavi; Gong, Qi; Kang, Wei SIAM Journal on Scientific Computing, Vol. 43, Issue 2 https://doi.org/10.1137/19M1288802	journal	January 2021
Solving high-dimensional partial differential equations using deep learning Han, Jiequn; Jentzen, Arnulf; E., Weinan Proceedings of the National Academy of Sciences, Vol. 115, Issue 34 https://doi.org/10.1073/pnas.1718942115	journal	August 2018
Actor-Critic--Type Learning Algorithms for Markov Decision Processes Konda, Vijaymohan R.; Borkar, Vivek S. SIAM Journal on Control and Optimization, Vol. 38, Issue 1 https://doi.org/10.1137/S036301299731669X	journal	January 1999
Survey of Numerical Methods for Trajectory Optimization Betts, John T. Journal of Guidance, Control, and Dynamics, Vol. 21, Issue 2 https://doi.org/10.2514/2.4231	journal	March 1998
A Real-Time Rerouting Method for Drone Flights Under Uncertain Flight Time Kim, Seon Jin; Lim, Gino J. Journal of Intelligent & Robotic Systems, Vol. 100, Issue 3-4 https://doi.org/10.1007/s10846-020-01214-z	journal	June 2020

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