Structure-exploiting Newton-type method for optimal control of switched systems

References

• Amestoy, P., Duff, I. S., L'Excellent, J. Y., & Koster, J. (2001). A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications, 23(1), 15–41. https://doi.org/10.1137/S0895479899358194
   Web of Science ®Google Scholar
• Andersson, J. A. E., Gillis, J., Horn, G., Rawlings, J. B., & Diehl, M. (2019). CasADi – a software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1), 1–36. https://doi.org/10.1007/s12532-018-0139-4
   Web of Science ®Google Scholar
• Belotti, P., Kirches, C., Leyffer, S., Linderoth, J., Luedtke, J., & Mahajan, A. (2013). Mixed-integer nonlinear optimization. Acta Numerica, 22, 1–131. https://doi.org/10.1017/S0962492913000032
   Web of Science ®Google Scholar
• Bertsekas, D. P. (2005). Dynamic programming and optimal control (3rd ed.). Athena Scientific.
   Google Scholar
• Betts, J. T. (2010). Practical methods for optimal control and estimation using nonlinear programming (2nd ed.). Cambridge University Press.
   Google Scholar
• Bock, H., & Plitt, K. (1984). A multiple shooting algorithm for direct solution of optimal control problem. 9th IFAC World Congress, 17(2), 1603–1608. https://doi.org/10.1016/S1474-6670(17)61205-9
   Google Scholar
• Bryson, A. E., & Ho, Y. C. (1975). Applied optimal control: optimization, estimation, and control. CRC Press.
   Google Scholar
• Bürger, A., Zeile, C., Altmann-Dieses, A., Sager, S., & Diehl, M. (2019). Design, implementation and simulation of an MPC algorithm for switched nonlinear systems under combinatorial constraints. Journal of Process Control, 81, 15–30. https://doi.org/10.1016/j.jprocont.2019.05.016
   Web of Science ®Google Scholar
• Carpentier, J., & Mansard, N. (2018). Analytical derivatives of rigid body dynamics algorithms. In Robotics: science and systems (RSS 2018) (p. hal-01790971v2f).
   Google Scholar
• Carpentier, J., Saurel, G., Buondonno, G., Mirabel, J., Lamiraux, F., Stasse, O., & Mansard, N. (2019). The Pinocchio C++ library – a fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives The Pinocchio C++ library – A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives. In International symposium on system integration (SII) (pp. 614–619).
   Google Scholar
• Dagum, L., & Menon, R. (1998). OpenMP: an industry-standard API for shared-memory programming. IEEE Computational Science & Engineering, 5(1), 46–55. https://doi.org/10.1109/99.660313
   Web of Science ®Google Scholar
• Di Carlo, J., Wensing, P. M., Katz, B., Bledt, G., & Kim, S. (2018). Dynamic locomotion in the MIT cheetah 3 through convex model-predictive control. In 2018 IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 1–9).
   Google Scholar
• Diehl, M., Bock, H. G., & Schlöder, J. P. (2005). A real-time iteration scheme for nonlinear optimization in optimal feedback control. SIAM Journal on Control and Optimization, 43(5), 1714–1736. https://doi.org/10.1137/S0363012902400713
   Web of Science ®Google Scholar
• Farshidian, F., Jelavic, E., Satapathy, A., Giftthaler, M., & Buchli, J (2017). Real-time motion planning of legged robots: a model predictive control approach. In 2017 IEEE-RAS 17th international conference on humanoid robotics (Humanoids) (pp. 577–584).
   Google Scholar
• Farshidian, F., Kamgarpour, M., Pardo, D., & Buchli, J. (2017). Sequential linear quadratic optimal control for nonlinear switched systems. IFAC-PapersOnLine, 50(1), 1463–1469. https://doi.org/10.1016/j.ifacol.2017.08.29120th IFAC World Congress.
   Google Scholar
• Featherstone, R. (2008). Rigid body dynamics algorithms. Springer.
   Google Scholar
• Ferreau, H. J., Kirches, C., Potschka, A., Bock, H. G., & Diehl, M. (2014). qpOASES: a parametric active-set algorithm for quadratic programming. Mathematical Programming Computation, 6(4), 327–363. https://doi.org/10.1007/s12532-014-0071-1
   Google Scholar
• Fu, J., & Zhang, C. (2021). Optimal control of path-constrained switched systems with guaranteed feasibility. IEEE Transactions on Automatic Control, 67(3), 1342–1355. https://doi.org/10.1109/TAC.2021.3071035
   Web of Science ®Google Scholar
• Grandia, R., Taylor, A. J., Ames, A. D., & Hutter, M. (2021). Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control. In 2021 IEEE international conference on robotics and automation (ICRA) (pp. 8352–8358).
   Google Scholar
• Guennebaud, G., & Jacob, B. (2010). Eigen v3. http://eigen.tuxfamily.org.
   Google Scholar
• Hutter, M., Gehring, C., Lauber, A., Gunther, F., Bellicoso, C. D., Tsounis, V., Fankhauser, P., Diethelm, R., Bachmann, S., Bloesch, M., Kolvenbach, H., Bjelonic, M., Isler, L., & Meyer, K. (2017). ANYmal – toward legged robots for harsh environments. Advanced Robotics, 31(17), 918–931. https://doi.org/10.1080/01691864.2017.1378591
   Web of Science ®Google Scholar
• Jenelten, F., Miki, T., Vijayan, A. E., Bjelonic, M., & Hutter, M. (2020). Perceptive locomotion in rough terrain – online foothold optimization. IEEE Robotics and Automation Letters, 5, 5370–5376. https://doi.org/10.1109/LSP.2016.
   Web of Science ®Google Scholar
• Johnson, E. R., & T. D. Murphey (2011). Second-Order switching time optimization for nonlinear time-varying dynamic systems. IEEE Transactions on Automatic Control, 56(8), 1953–1957. https://doi.org/10.1109/TAC.2011.2150310
   Web of Science ®Google Scholar
• Jung, M. N., Kirches, C., & Sager, S. (2013). On perspective functions and vanishing constraints in mixed-integer nonlinear optimal control. In G. R. M. Jünger (Ed.), Facets of combinatorial optimization (pp. 387–417). Springer.
   Google Scholar
• Katayama, S. (2020). robotoc. https://github.com/mayataka/robotoc.
   Google Scholar
• Katayama, S., Doi, M., & Ohtsuka, T (2020). A moving switching sequence approach for nonlinear model predictive control of switched systems with state-dependent switches and state jumps. International Journal of Robust and Nonlinear Control, 30(2), 719–740. https://doi.org/10.1002/rnc.v30.2
   Web of Science ®Google Scholar
• Katayama, S., & Ohtsuka, T. (2021a). Efficient Riccati recursion for optimal control problems with pure-state equality constraints. arXiv:2102.09731.
   Google Scholar
• Katayama, S., & Ohtsuka, T. (2021b). Lifted contact dynamics for efficient direct optimal control of rigid body systems with contacts. arXiv:2108.01781.
   Google Scholar
• Katayama, S., & Ohtsuka, T. (2021c). Riccati recursion for optimal control problems of nonlinear switched systems. In Proceedings of the 7th IFAC conference on nonlinear model predictive control 2021 (NMPC) (p. 18).
   Google Scholar
• Kuindersma, S., Deits, R., Fallon, M., Valenzuela, A., Dai, H., Permenter, F., Koolen, T., Marion, P., & Tedrake, R. (2016). Optimization-based locomotion planning, estimation, and control design for the Atlas humanoid robot. Autonomous Robots, 40, 429–455. https://doi.org/10.1007/s10514-015-9479-3
   Web of Science ®Google Scholar
• Li, H., & Wensing, P. M. (2020). Hybrid systems differential dynamic programming for whole-body motion planning of legged robots. IEEE Robotics and Automation Letters, 5(4), 5448–5455. https://doi.org/10.1109/LSP.2016.
   Web of Science ®Google Scholar
• Mastalli, C., Havoutis, I., Focchi, M., Caldwell, D. G., & Semini, C. (2020). Motion planning for quadrupedal locomotion: coupled planning, terrain mapping, and whole-body control. IEEE Transactions on Robotics, 36(6), 1635–1648. https://doi.org/10.1109/TRO.8860
   Web of Science ®Google Scholar
• Messerer, F., Baumgärtner, K., & Diehl, M. (2021). Survey of sequential convex programming and generalised Gauss-Newton methods. Citation: ESAIM: Proceedings and Surveys, 71(1), 64–88. https://doi.org/10.1051/proc/202171107
   Google Scholar
• Nocedal, J., & Wright, S. J. (2006). Numerical optimization (2nd ed.). Springer.
   Google Scholar
• Nurkanović, A., Albrecht, S., & Diehl, M. (2020). Limits of MPCC formulations in direct optimal control with nonsmooth differential equations. In 2020 European control conference (ECC) (pp. 2015–2020).
   Google Scholar
• Ohtsuka, T. (2004). A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica, 40(4), 563–574. https://doi.org/10.1016/j.automatica.2003.11.005
   Web of Science ®Google Scholar
• Patterson, M. A., & Rao, A. V. (2014). GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-Adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Transactions on Mathematical Software, 41(1), 1–37. https://doi.org/10.1145/2558904
   Web of Science ®Google Scholar
• Posa, M., Cantu, C., & Tedrake, R. (2014). A direct method for trajectory optimization of rigid bodies through contact. The International Journal of Robotics Research, 33(1), 69–81. https://doi.org/10.1177/0278364913506757
   Web of Science ®Google Scholar
• Quirynen, R., Houska, B., Vallerio, M., Telen, D., Logist, F., Van Impe, J., & Diehl, M. (2014). Symmetric algorithmic differentiation based exact Hessian SQP method and software for Economic MPC. In 53rd IEEE conference on decision and control (CDC) (pp. 2752–2757).
   Google Scholar
• Rao, C., Wright, S. J., & Rawlings, J. B. (1998). Application of interior-point methods to model predictive control. Journal of Optimization Theory and Applications, 99(3), 723–757. https://doi.org/10.1023/A:1021711402723
   Web of Science ®Google Scholar
• Rawlings, K., Mayne, D. Q., & Diehl, M. (2017). Model predictive control: theory, computation, and design. Nob Hill Publishing, LCC.
   Google Scholar
• Robuschi, N., Zeile, C., Sager, S., & Braghin, F. (2021). Multiphase mixed-integer nonlinear optimal control of hybrid electric vehicles. Automatica, 123, 109325. https://doi.org/10.1016/j.automatica.2020.109325
   Web of Science ®Google Scholar
• Sager, S., Jung, M. N., & Kirches, C. (2011). Combinatorial integral approximation. Mathematical Methods of Operations Research, 73, 363–380. https://doi.org/10.1007/s00186-011-0355-4
   Web of Science ®Google Scholar
• Schultz, G., & Mombaur, K. (2010). Modeling and optimal control of human-like running. IEEE/ASME Transactions on Mechatronics, 15(5), 783–792. https://doi.org/10.1109/TMECH.2009.2035112
   Web of Science ®Google Scholar
• Sideris, A., & Rodriguez, L. A. (2011). A Riccati approach for constrained linear quadratic optimal control. International Journal of Control, 84(2), 370–380. https://doi.org/10.1080/00207179.2011.555883
   Web of Science ®Google Scholar
• Stellato, B., Banjac, G., Goulart, P., Bemporad, A., & Boyd, S. (2020). OSQP: an operator splitting solver for quadratic programs. Mathematical Programming Computation, 12(4), 637–672. https://doi.org/10.1007/s12532-020-00179-2
   Web of Science ®Google Scholar
• Stellato, B., Ober-Blöbaum, S., & Goulart, P. J. (2017). Second-order switching time optimization for switched dynamical systems. IEEE Transactions on Automatic Control, 62(10), 5407–5414. https://doi.org/10.1109/TAC.2017.2697681
   Web of Science ®Google Scholar
• Wächter, A., & Biegler, L. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 106, 25–57. https://doi.org/10.1007/s10107-004-0559-y
   Web of Science ®Google Scholar
• Wang, Y., & Boyd, S. (2010). Fast model predictive control using online optimization. IEEE Transactions on Control Systems Technology, 18(2), 267–278. https://doi.org/10.1109/TCST.2009.2017934
   Web of Science ®Google Scholar
• Xu, X., & Antsaklis, P. J. (2002). Optimal control of switched systems via non-linear optimization based on direct differentiations of value functions. International Journal of Control, 75(16-17), 1406–1426. https://doi.org/10.1080/0020717021000023825
   Web of Science ®Google Scholar
• Xu, X., & Antsaklis, P. J. (2004). Optimal control of switched systems based on parameterization of the switching instants. IEEE Transactions on Automatic Control, 49(1), 2–16. https://doi.org/10.1109/TAC.2003.821417
   Web of Science ®Google Scholar
• Yunt, K. (2011). An augmented lagrangian based shooting method for the optimal trajectory generation of switching lagrangian systems. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 18(5), 615–645. https://www.researchgate.net/profile/Kerim-Yunt/publication/255621657_An_augmented_Lagrangian_based_shooting_method_for_the_optimal_trajectory_generation_of_switching_Lagrangian_systems/links/56c9960908ae5488f0d904e7/Anaugmented-Lagrangian-based-shooting-method-for-the-optimal-trajectory-generation-of-switching-Lagrangian-systems.pdf
   Google Scholar
• Zanelli, A., Domahidi, A., Jerez, J., & Morari, M. (2020). FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs. International Journal of Control, 93(1), 13–29. https://doi.org/10.1080/00207179.2017.1316017
   Web of Science ®Google Scholar