Factor Graphs in Optimization-Based Robotic Control—A Tutorial and Review

constrained factor graphs; Factor graphs; graph optimization; least squares optimization; model predictive control; robotic control; robotic perception; situational awareness; slam; Constrained factor graph; Graph optimization; Least square optimization; Model-predictive control; Robotic controls; Robotic perception; Simultaneous localization and mapping; Situational awareness; Computer Science (all); Materials Science (all); Engineering (all); Robots; Optimization; Probabilistic logic; Optimal control; Uncertainty; Tutorials; Reviews; Probability distribution; Heuristic algorithms

Résumé :

[en] Factor graphs, initially developed as probabilistic graphical models, have been widely employed for solving large-scale inference problems in robotics, particularly in tasks such as pose estimation, Structure from Motion (SfM), or Simultaneous Localization and Mapping (SLAM). Their capability to efficiently model uncertainty and the locality of sensor data has made them crucial for robotic perception and situational awareness. Recently, factor graphs have evolved beyond their probabilistic origins and are also being applied to deterministic optimization problems, such as robotic planning and control. This paper first aims to provide a comprehensive tutorial on factor graphs and the formulation and solution of the related optimization problems within the context of robotics perception. In addition, we undertake a thorough review of approaches that extend factor graphs—traditionally solved by unconstrained optimization—to optimal control tasks, emphasizing how they handle the constraints intrinsic to control problems. Finally, we analyze the potential of factor graphs for the seamless integration of robotic situational awareness, planning, and control, which remains one of the most critical challenges in achieving fully autonomous robot operations in complex environments.

Disciplines :

Ingénierie électrique & électronique

Auteur, co-auteur :

ABDELKARIM, Anas ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Automation ; RPTU University of Kaiserslautern-Landau, Department of Electrical and Computer Engineering, Kaiserslautern, Germany

VOOS, Holger ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Automation

Gorges, Daniel ; RPTU University of Kaiserslautern-Landau, Department of Electrical and Computer Engineering, Kaiserslautern, Germany

Co-auteurs externes :

yes

Langue du document :

Anglais

Titre :

Factor Graphs in Optimization-Based Robotic Control—A Tutorial and Review

Date de publication/diffusion :

2025

Titre du périodique :

IEEE Access

ISSN :

2169-3536

Maison d'édition :

Institute of Electrical and Electronics Engineers Inc.

Volume/Tome :

Pagination :

28315 - 28334

Peer reviewed :

Peer reviewed vérifié par ORBi

URL complémentaire :

http://xplorestaging.ieee.org/ielx8/6287639/10820123/10855417.pdf?arnumber=10855417

Projet FnR :

FNR17041397 - MOCCA - Multi-objective Adaptive Cruise Control Of Battery Electric Vehicles With Advanced Situational Awareness, 2022 (01/02/2023-31/01/2027) - Anas Abdelkarim

Organisme subsidiant :

Fonds National de la Recherche Luxembourg

Subventionnement (détails) :

This research was funded in whole, or in part, by the Luxembourg National Research Fund (FNR), MOCCA Project, ref. 17041397. For the purpose of open access, and in fulfilment of the obligations arising from the grant agreement, the author has applied a Creative Commons Attribution 4.0 International (CC BY 4.0) license to any Author Accepted Manuscript version arising from this submission.

Disponible sur ORBilu :

depuis le 15 avril 2025

Statistiques

Nombre de vues

147 (dont 3 Unilu)

Nombre de téléchargements

232 (dont 8 Unilu)

Voir plus de statistiques

citations Scopus^®

citations Scopus^®
sans auto-citations

OpenCitations

citations OpenAlex

citations WoS^™

Bibliographie

F. Dellaert and M. Kaess, ‘‘Factor graphs for robot perception,’’ Found. Trends Robot., vol. 6, nos. 1–2, pp. 1–139, 2017.
F. Dellaert, ‘‘Factor graphs: Exploiting structure in robotics,’’ Annu. Rev. Control, Robot., Auto. Syst., vol. 4, no. 1, pp. 141–166, May 2021.
R. Kümmerle, G. Grisetti, H. Strasdat, K. Konolige, and W. Burgard, ‘‘G2o: A general framework for graph optimization,’’ in Proc. IEEE Int. Conf. Robot. Autom., May 2011, pp. 3607–3613.
S. Thrun, ‘‘Probabilistic robotics,’’ Commun. ACM, vol. 45, no. 3, pp. 52–57, 2002.
G. Grisetti, R. Kümmerle, C. Stachniss, and W. Burgard, ‘‘A tutorial on graph-based SLAM,’’ IEEE Intell. Transp. Syst. Mag., vol. 2, no. 4, pp. 31–43, Winter 2010.
F. Dellaert, ‘‘Factor graphs and GTSAM: A hands-on introduction,’’ Georgia Inst. Technol., Atlanta, GA, USA, Tech. Rep. GT-RIM-CP&R-2012-002, 2012, vol. 2, p. 4.
H. Bavle, J. L. Sanchez-Lopez, M. Shaheer, J. Civera, and H. Voos, ‘‘S-Graphs+: Real-time localization and mapping leveraging hierarchical representations,’’ IEEE Robot. Autom. Lett., vol. 8, no. 8, pp. 4927–4934, Aug. 2023.
A. Tourani, H. Bavle, D. I. Avsar, J. L. Sanchez-Lopez, R. Munoz-Salinas, and H. Voos, ‘‘Vision-based situational graphs exploiting fiducial markers for the integration of semantic entities,’’ Robotics, vol. 13, p. 106, 2024.
G. Grisetti, T. Guadagnino, I. Aloise, M. Colosi, B. D. Corte, and D. Schlegel, ‘‘Least squares optimization: From theory to practice,’’ Robotics, vol. 9, no. 3, p. 51, Jul. 2020.
B. Alsadik and S. Karam, ‘‘The simultaneous localization and mapping (SLAM)—An overview,’’ J. Appl. Sci. Technol. Trends, vol. 2, no. 2, pp. 147–158, Nov. 2021.
S. Agarwal and K. Mierle. (Oct. 2023). Ceres Solver. [Online]. Available: https://github.com/ceres-solver/ceres-solver
A. Wächter and L. T. Biegler, ‘‘On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,’’ Math. Program., vol. 106, no. 1, pp. 25–57, Mar. 2006.
X. Wu, B. Xiao, C. Wu, Y. Guo, and L. Li, ‘‘Factor graph based navigation and positioning for control system design: A review,’’ Chin. J. Aeronaut., vol. 35, no. 5, pp. 25–39, May 2022.
C. Cadena, L. Carlone, H. Carrillo, Y. Latif, D. Scaramuzza, J. Neira, I. Reid, and J. J. Leonard, ‘‘Past, present, and future of simultaneous localization and mapping: Toward the robust-perception age,’’ IEEE Trans. Robot., vol. 32, no. 6, pp. 1309–1332, Dec. 2016.
A. Tourani, H. Bavle, J. L. Sanchez-Lopez, and H. Voos, ‘‘Visual SLAM: What are the current trends and what to expect?’’ Sensors, vol. 22, no. 23, p. 9297, Nov. 2022.
H. Bavle, J. L. Sanchez-Lopez, C. Cimarelli, A. Tourani, and H. Voos, ‘‘From SLAM to situational awareness: Challenges and survey,’’ Sensors, vol. 23, no. 10, p. 4849, May 2023.
R. M. Neal, ‘‘Probabilistic inference using Markov chain Monte Carlo methods,’’ Dept. Comput. Sci., Univ. Toronto, Toronto, ON, Canada, Tech. Rep. CRGT-TR-93-1, 1993.
P. Alevizos, ‘‘Factor graphs: Theory and applications,’’ Ph.D. dissertation, Dept. Electron. Comput. Eng., Tech. Univ. Crete, Chania, Greece, 2012.
S. Levine, ‘‘Reinforcement learning and control as probabilistic inference: Tutorial and review,’’ 2018, arXiv:1805.00909.
T. Brüdigam, ‘‘(Stochastic) model predictive control—A simulation example,’’ 2021, arXiv:2101.12020.
M. Wick, A. McCallum, and G. Miklau, ‘‘Scalable probabilistic databases with factor graphs and MCMC,’’ 2010, arXiv:1005.1934.
M. Fernandez-Cortizas, H. Bavle, D. Perez-Saura, J. Luis Sanchez-Lopez, P. Campoy, and H. Voos, ‘‘Multi S-graphs: An efficient distributed semantic-relational collaborative SLAM,’’ 2024, arXiv:2401.05152.
D. Koller and N. Friedman, Probabilistic Graphical Models: Principles and Techniques. Cambridge, MA, USA: MIT Press, 2009.
C. Zhang and C. Ré, ‘‘Towards high-throughput Gibbs sampling at scale: A study across storage managers,’’ in Proc. ACM SIGMOD Int. Conf. Manage. Data, Jun. 2013, pp. 397–408.
J. Winn and C. Bishop, ‘‘Variational message passing,’’ J. Mach. Learn. Res., vol. 6, no. 23, pp. 661–694, Dec. 2005.
B. J. Frey, F. R. Kschischang, and H. A. Loeliger, ‘‘Factor graphs and algorithms,’’ in Proc. Annu. Allerton Conf. Commun. Control Comput., Jan. 2008, pp. 666–680.
R. Santana, A. Mendiburu, and J. A. Lozano, ‘‘A review of message passing algorithms in estimation of distribution algorithms,’’ Natural Comput., vol. 15, no. 1, pp. 165–180, Mar. 2016.
F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, ‘‘Factor graphs and the sum-product algorithm,’’ IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb. 2001.
J. Coughlan, ‘‘A tutorial introduction to belief propagation,’’ Kettlewell Eye Res. Inst., San Francisco, CA, USA, Tech. Rep., 2009.
K. Tanaka, H. Shouno, M. Okada, and D. M. Titterington, ‘‘Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing,’’ J. Phys. A, Math. Gen., vol. 37, no. 36, pp. 8675–8695, Sep. 2004.
J. S. Yedidia, W. T. Freeman, and Y. Weiss, ‘‘Constructing free-energy approximations and generalized belief propagation algorithms,’’ IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2282–2312, Jul. 2005.
K. Murphy, Y. Weiss, and M. I. Jordan, ‘‘Loopy belief propagation for approximate inference: An empirical study,’’ 2013, arXiv:1301.6725.
B. J. Frey and D. Dueck, ‘‘Clustering by passing messages between data points,’’ Science, vol. 315, no. 5814, pp. 972–976, Feb. 2007.
M. Toussaint, ‘‘Robot trajectory optimization using approximate inference,’’ in Proc. 26th Annu. Int. Conf. Mach. Learn., Jun. 2009, pp. 1049–1056.
H. J. Kappen, V. Gómez, and M. Opper, ‘‘Optimal control as a graphical model inference problem,’’ Mach. Learn., vol. 87, no. 2, pp. 159–182, May 2012.
I. Sugiarto and J. Conradt, ‘‘A model-based approach to robot kinematics and control using discrete factor graphs with belief propagation,’’ Robot. Auto. Syst., vol. 91, pp. 234–246, May 2017.
C. Hoffmann and P. Rostalski, ‘‘Linear optimal control on factor graphs—A message passing perspective,’’ IFAC-PapersOnLine, vol. 50, no. 1, pp. 6314–6319, Jul. 2017.
C. Herzog né Hoffmann, E. Petersen, and P. Rostalski, ‘‘Iterative approximate nonlinear inference via Gaussian message passing on factor graphs,’’ IEEE Control Syst. Lett., vol. 3, no. 4, pp. 978–983, Oct. 2019.
J. Watson, H. Abdulsamad, and J. Peters, ‘‘Stochastic optimal control as approximate input inference,’’ in Proc. Conf. Robot Learn., Jan. 2019, pp. 697–716.
C. Herzog Né Hoffmann, F. Vollmer, J. Gruner, and P. Rostalski, ‘‘Teaching estimation and control via probabilistic graphical models—An intuitive and problem-based approach,’’ IFAC-PapersOnLine, vol. 55, no. 17, pp. 206–211, 2022.
F. Dellaert. (2022). Borglab/GTSAM. Accessed: Jun. 13, 2024. [Online]. Available: https://github.com/borglab/gtsam
R. Kümmerle, G. Grisetti, H. Strasdat, K. Konolige, and W. Burgard. (2023). Rainerkuemmerle, G2O. Accessed: Jun. 13, 2024. [Online]. Available: https://github.com/RainerKuemmerle/g2o
D. M. Rosen, L. Carlone, A. S. Bandeira, and J. J. Leonard, ‘‘SE-sync: A certifiably correct algorithm for synchronization over the special Euclidean group,’’ Int. J. Robot. Res., vol. 38, nos. 2–3, pp. 95–125, Mar. 2019.
V. Ila, L. Polok, M. Solony, and P. Svoboda, ‘‘SLAM++—A highly efficient and temporally scalable incremental SLAM framework,’’ Int. J. Robot. Res., vol. 36, no. 2, pp. 210–230, Feb. 2017.
A. Juric, F. Kendeš, I. Markovic, and I. Petrovic, ‘‘A comparison of graph optimization approaches for pose estimation in SLAM,’’ in Proc. 44th Int. Conv. Inf., Commun. Electron. Technol. (MIPRO), Sep. 2021, pp. 1113–1118.
A. Abdelkarim, ‘‘Development of numerical solvers for online optimization with application to MPC-based energy-optimal adaptive cruise control,’’ Master thesis, Dept. Elect. Comput. Eng., Technische Universität Kaiserslautern, Kaiserslautern, Germany, 2020.
S. P. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
J. Nocedal and S. J. Wright, Numerical Optimization. New York, USA: Springer, 2006.
A. Cauchy, ‘‘Méthode générale pour la résolution des systemes d’équations simultanées,’’ Comp. Rend. Sci. Paris, vol. 25, no. 1847, pp. 536–538, 1847.
S. Ruder, ‘‘An overview of gradient descent optimization algorithms,’’ 2016, arXiv:1609.04747.
S. H. Haji and A. M. Abdulazeez, ‘‘Comparison of optimization techniques based on gradient descent algorithm: A review,’’ PalArch’s J. Archaeol. Egypt/Egyptol., vol. 18, no. 4, pp. 2715–2743, 2021.
J. A. Nelder and R. Mead, ‘‘A simplex method for function minimization,’’ Comput. J., vol. 7, no. 4, pp. 308–313, Jan. 1965.
M. Mitchell, An Introduction to Genetic Algorithms. Cambridge, MA, USA: MIT Press, 1998.
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, ‘‘Optimization by simulated annealing,’’ Science, vol. 220, no. 4598, pp. 671–680, May 1983.
H. A. Jaafar, C.-H. Kao, and S. Saeedi, ‘‘MR.CAP: Multi-robot joint control and planning for object transport,’’ IEEE Control Syst. Lett., vol. 8, pp. 139–144, 2024.
M. Kaess, H. Johannsson, R. Roberts, V. Ila, J. J. Leonard, and F. Dellaert, ‘‘ISAM2: Incremental smoothing and mapping using the Bayes tree,’’ Int. J. Robot. Res., vol. 31, no. 2, pp. 216–235, Feb. 2012.
P. Sodhi, S. Choudhury, J. G. Mangelson, and M. Kaess, ‘‘ICS: Incremental constrained smoothing for state estimation,’’ in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 2020, pp. 279–285.
M. Qadri, P. Sodhi, J. G. Mangelson, F. Dellaert, and M. Kaess, ‘‘InCOpt: Incremental constrained optimization using the Bayes tree,’’ in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Oct. 2022, pp. 6381–6388.
B. Bazzana, T. Guadagnino, and G. Grisetti, ‘‘Handling constrained optimization in factor graphs for autonomous navigation,’’ IEEE Robot. Autom. Lett., vol. 8, no. 1, pp. 432–439, Jan. 2023.
B. Bazzana, H. Andreasson, and G. Grisetti, ‘‘How-to augmented Lagrangian on factor graphs,’’ IEEE Robot. Autom. Lett., vol. 9, no. 3, pp. 2806–2813, Mar. 2024.
K. Levenberg, ‘‘A method for the solution of certain non-linear problems in least squares,’’ Quart. Appl. Math., vol. 2, no. 2, pp. 164–168, Jul. 1944.
D. W. Marquardt, ‘‘An algorithm for least-squares estimation of nonlinear parameters,’’ J. Soc. Ind. Appl. Math., vol. 11, no. 2, pp. 431–441, Jun. 1963.
M. J. Powell, ‘‘A new algorithm for unconstrained optimization,’’ in Nonlinear Programming. Amsterdam, The Netherlands: Elsevier, 1970, pp. 31–65.
R. H. Byrd, R. B. Schnabel, and G. A. Shultz, ‘‘Approximate solution of the trust region problem by minimization over two-dimensional subspaces,’’ Math. Program., vols. 40–40, nos. 1–3, pp. 247–263, Jan. 1988.
T. Ando, ‘‘Generalized Schur complements,’’ Linear Algebra Its Appl., vol. 27, pp. 173–186, Oct. 1979.
F. Zhang, The Schur Complement and Its Applications, vol. 4. Cham, Switzerland: Springer, 2006.
G. H. Golub, ‘‘Numerical methods for solving linear least squares problems,’’ Appl. Math., vol. 10, no. 3, pp. 213–216, 1965.
G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD, USA: JHU Press, 2013.
Y. Saad, Iterative Methods for Sparse Linear Systems. Philadelphia, PA, USA: SIAM, 2003.
D. Dereniowski and M. Kubale, ‘‘Cholesky factorization of matrices in parallel and ranking of graphs,’’ in Proc. 5th Int. Conf. Parallel Process. Appl. Math., Czestochowa, Poland. Cham, Switzerland: Springer, Jan. 2004, pp. 985–992.
N. J. Higham, ‘‘Cholesky factorization,’’ Wiley Interdiscipl. Rev., Comput. Statist., vol. 1, no. 2, pp. 251–254, Jun. 2009.
W. Gander, ‘‘Algorithms for the QR decomposition,’’ Res. Rep, vol. 80, no. 2, pp. 1251–1268, 1980.
M. Kaess, V. Ila, R. Roberts, and F. Dellaert, ‘‘The Bayes tree: An algorithmic foundation for probabilistic robot mapping,’’ in Proc. 9th Int. Workshop Algorithmic Found. Robot. Cham, Switzerland: Springer, Jan. 2010, pp. 157–173.
Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, ‘‘Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate,’’ ACM Trans. Math. Softw., vol. 35, no. 3, pp. 1–14, Oct. 2008.
T. A. Davis, Direct Methods for Sparse Linear Systems. Philadelphia, PA, USA: SIAM, 2006.
T. A. Davis, ‘‘Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization,’’ ACM Trans. Math. Softw., vol. 38, no. 1, pp. 1–22, Nov. 2011.
G. Guennebaud and B. Jacob. (2010). Eigen. [Online]. Available: http://eigen.tuxfamily.org
J. Demmel, ‘‘LAPACK: A portable linear algebra library for high-performance computers,’’ Concurrency, Pract. Exper., vol. 3, no. 6, pp. 655–666, Dec. 1991.
T. A. Davis, S. Rajamanickam, and W. M. Sid-Lakhdar, ‘‘A survey of direct methods for sparse linear systems,’’ Acta Numerica, vol. 25, pp. 383–566, May 2016.
F. Dellaert and M. Kaess, ‘‘Square root SAM: Simultaneous localization and mapping via square root information smoothing,’’ Int. J. Robot. Res., vol. 25, no. 12, pp. 1181–1203, Dec. 2006.
M. Kaess, A. Ranganathan, and F. Dellaert, ‘‘Fast incremental square root information smoothing,’’ in Proc. IJCAI, Jan. 2007, pp. 2129–2134.
M. Kaess, A. Ranganathan, and F. Dellaert, ‘‘ISAM: Incremental smoothing and mapping,’’ IEEE Trans. Robot., vol. 24, no. 6, pp. 1365–1378, Dec. 2008.
M. Kaess, H. Johannsson, R. Roberts, V. Ila, J. Leonard, and F. Dellaert, ‘‘ISAM2: Incremental smoothing and mapping with fluid relinearization and incremental variable reordering,’’ in Proc. IEEE Int. Conf. Robot. Autom., May 2011, pp. 3281–3288.
C. C. de Wit, B. Siciliano, and G. Bastin, Theory of Robot Control. Cham, Switzerland: Springer, 2012.
S. B. Niku, Introduction to Robotics: Analysis, Control, Applications. Hoboken, NJ, USA: Wiley, 2020.
B. Hernández and E. Giraldo, ‘‘A review of path planning and control for autonomous robots,’’ in Proc. IEEE 2nd Colombian Conf. Robot. Autom. (CCRA), Nov. 2018, pp. 1–6.
A. Abdelkarim, Y. Jia, and D. Görges, ‘‘An accelerated interior-point method for convex optimization leveraging backtracking mitigation,’’ in Proc. 49th Annu. Conf. IEEE Ind. Electron. Soc., Oct. 2023, pp. 1–6.
A. R. Mehrabian, C. Lucas, and J. Roshanian, ‘‘Aerospace launch vehicle control: An intelligent adaptive approach,’’ Aerosp. Sci. Technol., vol. 10, no. 2, pp. 149–155, Mar. 2006.
U. Eren, A. Prach, B. B. Koçer, S. V. Raković, E. Kayacan, and B. Açükmeşe, ‘‘Model predictive control in aerospace systems: Current state and opportunities,’’ J. Guid., Control, Dyn., vol. 40, no. 7, pp. 1541–1566, Jul. 2017.
R. Chai, A. Tsourdos, A. Savvaris, S. Chai, Y. Xia, and C. L. P. Chen, ‘‘Review of advanced guidance and control algorithms for space/aerospace vehicles,’’ Prog. Aerosp. Sci., vol. 122, Apr. 2021, Art. no. 100696.
A. Mahfouz, G. Gaias, D. M. K. K. Venkateswara Rao, and H. Voos, ‘‘Autonomous optimal absolute orbit keeping through formation flying techniques,’’ Aerospace, vol. 10, no. 11, p. 959, Nov. 2023.
G. Stephanopoulos, Chemical Process Control, vol. 2. Upper Saddle River, NJ, USA: Prentice-Hall, 1984.
B. W. Bequette, ‘‘Nonlinear control of chemical processes: A review,’’ Ind. Eng. Chem. Res., vol. 30, no. 7, pp. 1391–1413, Jul. 1991.
R. S. Gesser, R. Sartori, T. P. Damo, C. M. Vettorazzo, L. B. Becker, D. M. Lima, M. L. de Lima, L. D. Ribeiro, M. C. M. M. Campos, and J. E. Normey-Rico, ‘‘Advanced control applied to a gas compression system of an offshore platform: From modeling to related system infrastructure,’’ J. Petroleum Sci. Eng., vol. 208, Jan. 2022, Art. no. 109428.
H. L. Trentelman, A. A. Stoorvogel, and M. Hautus, ‘‘Control theory for linear systems,’’ Appl. Mech. Rev., vol. 55, no. 5, p. B87, Jan. 2002.
H. K. Khalil, Control of Nonlinear Systems. New York, NY, USA: Prentice-Hall, 2002.
O. Katsuhiko, Modern Control Engineering. Miami, FL, USA: Félix Varela, 2009.
S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design. Hoboken, NJ, USA: Wiley, 2005.
F. L. Lewis, D. Vrabie, and V. L. Syrmos, Optimal Control. Hoboken, NJ, USA: Wiley, 2012.
R. P. Borase, D. K. Maghade, S. Y. Sondkar, and S. N. Pawar, ‘‘A review of PID control, tuning methods and applications,’’ Int. J. Dyn. Control, vol. 9, no. 2, pp. 818–827, Jun. 2021.
H. R. Nohooji, A. Zaraki, and H. Voos, ‘‘Actor–critic learning based PID control for robotic manipulators,’’ Appl. Soft Comput., vol. 151, Dec. 2023, Art. no. 111153.
O. A. Somefun, K. Akingbade, and F. Dahunsi, ‘‘The dilemma of PID tuning,’’ Annu. Rev. Control, vol. 52, pp. 65–74, Jan. 2021.
D. E. Kirk, Optimal Control Theory: An Introduction. Courier Corporation, 2004.
D. Bertsekas, Dynamic Programming and Optimal Control, vol. 4. Belmont, MA, USA: Athena Scientific, 2012.
R. E. Kopp, ‘‘Pontryagin maximum principle,’’ in Mathematics in Science and Engineering, vol. 5. Amsterdam, The Netherlands: Elsevier, 1962, pp. 255–279.
A. D. Lewis, ‘‘The maximum principle of pontryagin in control and in optimal control,’’ Dept. Math. Statist., Queen’s Univ., Kingston, Canada, 2006.
R. Bellman, ‘‘Dynamic programming,’’ Science, vol. 153, no. 3731, pp. 34–37, 1966.
J. T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Philadelphia, PA, USA: SIAM, 2010.
D. P. Bertsekas, ‘‘Nonlinear programming,’’ J. Oper. Res. Soc., vol. 48, no. 3, p. 334, 1997.
C. R. Hargraves and S. W. Paris, ‘‘Direct trajectory optimization using nonlinear programming and collocation,’’ J. Guid., Control, Dyn., vol. 10, no. 4, pp. 338–342, Jul. 1987.
M. Kelly, ‘‘An introduction to trajectory optimization: How to do your own direct collocation,’’ SIAM Rev., vol. 59, no. 4, pp. 849–904, Jan. 2017.
M. Gerdts, Optimal Control of ODEs and DAEs. Walter de Gruyter GmbH & Co KG, 2023.
R. Tedrake. (2023). Underactuated Robotics. [Online]. Available: https://underactuated.csail.mit.edu
D.-N. Ta, M. Kobilarov, and F. Dellaert, ‘‘A factor graph approach to estimation and model predictive control on unmanned aerial vehicles,’’ in Proc. Int. Conf. Unmanned Aircr. Syst. (ICUAS), May 2014, pp. 181–188.
G. Chen and F. Zhang, and Y. Dellaert. (2019). LQR Control Using Factor Graphs. Accessed: Jun. 15, 2024. [Online]. Available: https://gtsam.org/2019/11/07/lqr-control.html
Y. Hao, B. Yu, Q. Liu, and S.-S. Liu, ‘‘FGLQR: Factor graph accelerator of LQR control for autonomous machines,’’ 2023, arXiv:2308.02768.
S. Yang, G. Chen, Y. Zhang, H. Choset, and F. Dellaert, ‘‘Equality constrained linear optimal control with factor graphs,’’ in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 2021, pp. 9717–9723.
F. Borrelli, A. Bemporad, and M. Morari, Predictive Control for Linear and Hybrid Systems. Cambridge, U.K.: Cambridge Univ. Press, 2017.
D. Q. Mayne, ‘‘Model predictive control: Recent developments and future promise,’’ Automatica, vol. 50, no. 12, pp. 2967–2986, Dec. 2014.
J. A. Rossiter, Model-Based Predictive Control: A Practical Approach. Boca Raton, FL, USA: CRC Press, 2017.
J. B. Rawlings, D. Q. Mayne, and M. Diehl, Model Predictive Control: Theory, Computation, and Design, vol. 2. Madison, WI, USA: Nob Hill Publishing, 2017.
S. Yu, M. Reble, H. Chen, and F. Allgöwer, ‘‘Inherent robustness properties of quasi-infinite horizon nonlinear model predictive control,’’ Automatica, vol. 50, no. 9, pp. 2269–2280, Sep. 2014.
F. Allgöwer, R. Findeisen, and Z. K. Nagy, ‘‘Nonlinear model predictive control: From theory to application,’’ J.-Chin. Inst. Chem. Eng., vol. 35, no. 3, pp. 299–315, May 2004.
L. Grüne, Nonlinear Model Predictive Control. Cham, Switzerland: Springer, 2017.
A. Mesbah, ‘‘Stochastic model predictive control: An overview and perspectives for future research,’’ IEEE Control Syst. Mag., vol. 36, no. 6, pp. 30–44, Dec. 2016.
A. Mesbah, ‘‘Stochastic model predictive control with active uncertainty learning: A survey on dual control,’’ Annu. Rev. Control, vol. 45, pp. 107–117, Jan. 2018.
T. A. N. Heirung, J. A. Paulson, J. O’Leary, and A. Mesbah, ‘‘Stochastic model predictive control—How does it work?’’ Comput. Chem. Eng., vol. 114, pp. 158–170, Jun. 2018.
E. F. Camacho, D. R. Ramirez, D. Limon, D. Muñoz de la Peña, and T. Alamo, ‘‘Model predictive control techniques for hybrid systems,’’ Annu. Rev. Control, vol. 34, no. 1, pp. 21–31, Apr. 2010.
A. Abdelkarim and P. Zhang, ‘‘Optimal scheduling of preventive maintenance for safety instrumented systems based on mixed-integer programming,’’ in Proc. 7th Int. Symp. Model-Based Saf. Assessment, Lisbon, Portugal. Cham, Switzerland: Springer, Jan. 2020, pp. 83–96.
P. D. Christofides, R. Scattolini, D. Muñoz de la Peña, and J. Liu, ‘‘Distributed model predictive control: A tutorial review and future research directions,’’ Comput. Chem. Eng., vol. 51, pp. 21–41, Apr. 2013.
Z. Ajanović, M. Stolz, and M. Horn, ‘‘Energy-efficient driving in dynamic environment: Globally optimal MPC-like motion planning framework,’’ in Advanced Microsystems for Automotive Applications 2017: Smart Systems Transforming the Automobile. Cham, Switzerland: Springer, 2018, pp. 111–122.
G. F. Usieto, ‘‘Trajectory generation for autonomous highway driving using model predictive control,’’ Master’s thesis, Universitat Politècnica de Catalunya, Barcelona, Spain, 2017.
D. M. K. K. Venkateswara Rao, H. Habibi, J. L. Sanchez-Lopez, and H. Voos, ‘‘An integrated real-time UAV trajectory optimization and potential field approach for dynamic collision avoidance,’’ in Proc. Int. Conf. Unmanned Aircr. Syst. (ICUAS), Jun. 2023, pp. 79–86.
P. Kremer, H. Rahimi Nohooji, and H. Voos, ‘‘Constrained trajectory optimization and force control for UAVs with universal jamming grippers,’’ Sci. Rep., vol. 14, no. 1, p. 11968, May 2024.
E. L. Haseltine and J. B. Rawlings, ‘‘Critical evaluation of extended Kalman filtering and moving-horizon estimation,’’ Ind. Eng. Chem. Res., vol. 44, no. 8, pp. 2451–2460, Apr. 2005.
D. A. Allan and J. B. Rawlings, ‘‘Moving horizon estimation,’’ in Handbook of Model Predictive Control, 2019, pp. 99–124.
A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, ‘‘The explicit linear quadratic regulator for constrained systems,’’ Automatica, vol. 38, no. 1, pp. 3–20, Jan. 2002.
A. Alessio and A. Bemporad, ‘‘A survey on explicit model predictive control,’’ in Nonlinear Model Predictive Control: Towards New Challenging Applications, 2009, pp. 345–369.
A. Bemporad, ‘‘Model predictive control design: New trends and tools,’’ in Proc. 45th IEEE Conf. Decis. Control, Sep. 2006, pp. 6678–6683.
J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, ‘‘CasADi: A software framework for nonlinear optimization and optimal control,’’ Math. Program. Comput., vol. 11, no. 1, pp. 1–36, Mar. 2019.
A. Abdelkarim, Y. Jia, and D. Gorges, ‘‘Optimization of vehicle-to-grid profiles for peak shaving in microgrids considering battery health,’’ in Proc. 49th Annu. Conf. IEEE Ind. Electron. Soc., Oct. 2023, pp. 1–6.
D. T. Agi, K. D. Jones, M. J. Watson, H. G. Lynch, M. Dougher, X. Chen, M. N. Carlozo, and A. W. Dowling, ‘‘Computational toolkits for model-based design and optimization,’’ Current Opinion Chem. Eng., vol. 43, Mar. 2024, Art. no. 100994.
S. Boyd, ‘‘Distributed optimization and statistical learning via the alternating direction method of multipliers,’’ Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1–122, 2010.
D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. New York, NY, USA: Academic, 2014.
R. Darnley, ‘‘Flow control of wireless mesh networks using LQR and factor graphs,’’ Master thesis, Carnegie Mellon Univ., Pittsburgh, PA, USA, 2021.
R. Darnley and M. Travers, ‘‘Flow control of wireless mesh networks using LQR and factor graphs,’’ in Proc. Amer. Control Conf. (ACC), Mar. 2022, pp. 2295–2302.
S. Kim, D. K. Jha, D. Romeres, P. Patre, and A. Rodriguez, ‘‘Simultaneous tactile estimation and control of extrinsic contact,’’ in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 2023, pp. 12563–12569.
S. Kim, A. Bronars, P. Patre, and A. Rodriguez, ‘‘TEXterity—Tactile extrinsic deXterity: Simultaneous tactile estimation and control for extrinsic dexterity,’’ 2024, arXiv:2403.00049.
G. Chen, S. Baek, J.-D. Florez, W. Qian, S.-W. Leigh, S. Hutchinson, and F. Dellaert, ‘‘GTGraffiti: Spray painting graffiti art from human painting motions with a cable driven parallel robot,’’ in Proc. Int. Conf. Robot. Autom. (ICRA), May 2022, pp. 4065–4072.
G. Chen, S. Hutchinson, and F. Dellaert, ‘‘Locally optimal estimation and control of cable driven parallel robots using time varying linear quadratic Gaussian control,’’ in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Oct. 2022, pp. 7367–7374.
G. Chen, H. Muriki, A. Sharkey, C. Pradalier, Y. Chen, and F. Dellaert, ‘‘A hybrid cable-driven robot for non-destructive leafy plant monitoring and mass estimation using structure from motion,’’ in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 2023, pp. 11809–11816.
G. Chen, T. Al-Haddad, F. Dellaert, and S. Hutchinson, ‘‘Architectural-scale artistic brush painting with a hybrid cable robot,’’ 2024, arXiv:2403.12214.
M. Xie, A. Escontrela, and F. Dellaert, ‘‘A factor-graph approach for optimization problems with dynamics constraints,’’ 2020, arXiv:2011.06194.
M. King–Smith, P. Tsiotras, and F. Dellaert, ‘‘Simultaneous control and trajectory estimation for collision avoidance of autonomous robotic spacecraft systems,’’ in Proc. Int. Conf. Robot. Autom. (ICRA), May 2022, pp. 257–264.
P. Yang and W. Wen, ‘‘Tightly joining positioning and control for trustworthy unmanned aerial vehicles based on factor graph optimization in urban transportation,’’ in Proc. IEEE 26th Int. Conf. Intell. Transp. Syst. (ITSC), Sep. 2023, pp. 3589–3596.
P. Yang, W. Wen, S. Bai, and L.-T. Hsu, ‘‘Tightly joined positioning and control model for unmanned aerial vehicles based on factor graph optimization,’’ 2024, arXiv:2404.14724.
J. Dong, M. Mukadam, F. Dellaert, and B. Boots, ‘‘Motion planning as probabilistic inference using Gaussian processes and factor graphs,’’ in Proc. Robot., Sci. Syst., 2016, vol. 12, no. 4.
M. Mukadam, J. Dong, X. Yan, F. Dellaert, and B. Boots, ‘‘Continuous-time Gaussian process motion planning via probabilistic inference,’’ Int. J. Robot. Res., vol. 37, no. 11, pp. 1319–1340, Sep. 2018.
M. Mukadam, J. Dong, F. Dellaert, and B. Boots, ‘‘STEAP: Simultaneous trajectory estimation and planning,’’ Auto. Robots, vol. 43, no. 2, pp. 415–434, Feb. 2019.
M. Mukadam, ‘‘Structured learning and inference for robot motion generation,’’ Ph.D. dissertation, Georgia Inst. Technol., Atlanta, GA, USA, 2019.
P. Sodhi, ‘‘Learning and inference in factor graphs with applications to tactile perception,’’ Ph.D. dissertation, Carnegie Mellon Univ., Pittsburgh, PA, USA, 2022.
F. Laine and C. Tomlin, ‘‘Efficient computation of feedback control for equality-constrained LQR,’’ in Proc. Int. Conf. Robot. Autom. (ICRA), May 2019, pp. 6748–6754.
G. Williams, P. Drews, B. Goldfain, J. M. Rehg, and E. A. Theodorou, ‘‘Aggressive driving with model predictive path integral control,’’ in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), May 2016, pp. 1433–1440.
A. Carron, E. Arcari, M. Wermelinger, L. Hewing, M. Hutter, and M. N. Zeilinger, ‘‘Data-driven model predictive control for trajectory tracking with a robotic arm,’’ IEEE Robot. Autom. Lett., vol. 4, no. 4, pp. 3758–3765, Oct. 2019.
F. Cursi, W. Bai, E. M. Yeatman, and P. Kormushev, ‘‘Task accuracy enhancement for a surgical macro-micro manipulator with probabilistic neural networks and uncertainty minimization,’’ IEEE Trans. Autom. Sci. Eng., vol. 21, no. 1, pp. 241–256, Jan. 2022.