Papers
Topics
Authors
Recent
Search
2000 character limit reached

Optimization with Temporal and Logical Specifications via Generalized Mean-based Smooth Robustness Measures

Published 16 May 2024 in math.OC | (2405.10996v1)

Abstract: This paper introduces a generalized mean-based C1-smooth robustness measure over discrete-time signals (D-GMSR) for signal temporal logic (STL) specifications. In conjunction with its C1-smoothness, D-GMSR is proven to be both sound and complete. Furthermore, it demonstrates favorable gradient properties and addresses locality and masking problems, which are critical for numerical optimization. The C1-smoothness of the proposed formulations enables the implementation of robust and efficient numerical optimization algorithms to solve problems with STL specifications while preserving their theoretical guarantees. The practical utility of the proposed robustness measure is demonstrated on two real-world trajectory optimization problems: i) quadrotor flight, and ii) autonomous rocket landing. A sequential convex programming (SCP) framework, incorporating a convergence-guaranteed optimization algorithm (the prox-linear method) is used to solve inherently non-convex trajectory optimization problems with STL specifications. The implementation is available at https://github.com/UW-ACL/D-GMSR

Definition Search Book Streamline Icon: https://streamlinehq.com
References (65)
  1. Principles of Model Checking. MIT press, 2008. URL: https://mitpress.mit.edu/9780262026499/principles-of-model-checking/.
  2. Autonomous vehicle decision-making and monitoring based on signal temporal logic and mixed-integer programming. In 2020 American Control Conference (ACC), pages 454–459. IEEE, 2020. URL: https://doi.org/10.23919/ACC45564.2020.9147917.
  3. Trajectory optimization for high-dimensional nonlinear systems under STL specifications. IEEE Control Systems Letters, 5(4):1429–1434, 2020. URL: https://doi.org/10.1109/LCSYS.2020.3038640.
  4. Probabilistic control of heterogeneous swarms subject to graph temporal logic specifications: A decentralized and scalable approach. IEEE Transactions on Automatic Control, 68(4):2245–2260, 2022. URL: https://doi.org/10.1109/TAC.2022.3176797.
  5. Multirobot coordination with counting temporal logics. IEEE Transactions on Robotics, 36(4):1189–1206, 2019. URL: https://doi.org/10.1109/TRO.2019.2957669.
  6. Planning of heterogeneous multi-agent systems under signal temporal logic specifications with integral predicates. IEEE Robotics and Automation Letters, 6(2):1375–1382, 2021. URL: https://doi.org/10.1109/LRA.2021.3057049.
  7. Fly-by-logic: Control of multi-drone fleets with temporal logic objectives. In 2018 ACM/IEEE 9th International Conference on Cyber-Physical Systems (ICCPS), pages 186–197. IEEE, 2018. URL: https://doi.org/10.1109/ICCPS.2018.00026.
  8. Mission planning and control of multi-aircraft systems with signal temporal logic specifications. IEEE Access, 7:155941–155950, 2019. URL: https://doi.org/10.1109/ACCESS.2019.2949426.
  9. STLnet: Signal temporal logic enforced multivariate recurrent neural networks. Advances in Neural Information Processing Systems, 33:14604–14614, 2020. URL: https://dl.acm.org/doi/abs/10.5555/3495724.3496948.
  10. Q-learning for robust satisfaction of signal temporal logic specifications. In 2016 IEEE 55th Conference on Decision and Control (CDC), pages 6565–6570. IEEE, 2016. URL: https://doi.org/10.1109/CDC.2016.7799279.
  11. Safe reinforcement learning via shielding. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 32, 2018. URL: https://doi.org/10.1609/AAAI.V32I1.11797.
  12. Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods. The International Journal of Robotics Research, 42(6):356–370, 2023. URL: https://doi.org/10.1177/02783649221082115.
  13. Amir Pnueli. The temporal logic of programs. In 18th Annual Symposium on Foundations of Computer Science (SFCS 1977), pages 46–57. IEEE, 1977. URL: https://doi.org/10.1109/SFCS.1977.32.
  14. A theory of timed automata. Theoretical Computer Science, 126(2):183–235, 1994. URL: https://doi.org/10.1016/0304-3975(94)90010-8.
  15. Receding horizon temporal logic planning. IEEE Transactions on Automatic Control, 57(11):2817–2830, 2012. URL: https://doi.org/10.1109/TAC.2012.2195811.
  16. TuLiP: a software toolbox for receding horizon temporal logic planning. In Proceedings of the 14th International Conference on Hybrid Systems: Computation and Control, pages 313–314, 2011. URL: https://doi.org/10.1145/1967701.1967747.
  17. Optimal control of mixed logical dynamical systems with linear temporal logic specifications. In 2008 47th IEEE Conference on Decision and Control, pages 2117–2122. IEEE, 2008. URL: https://doi.org/10.1109/CDC.2008.4739370.
  18. Ron Koymans. Specifying real-time properties with metric temporal logic. Real-Time Systems, 2(4):255–299, 1990. URL: https://doi.org/10.1007/BF01995674.
  19. The benefits of relaxing punctuality. Journal of the ACM (JACM), 43(1):116–146, 1996. URL: https://doi.org/10.1145/227595.227602.
  20. Monitoring temporal properties of continuous signals. In International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, pages 152–166. Springer, 2004. URL: https://doi.org/10.1007/978-3-540-30206-3_12.
  21. Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science, 410(42):4262–4291, 2009. URL: https://doi.org/10.1016/j.tcs.2009.06.021.
  22. Robust satisfaction of temporal logic over real-valued signals. In International Conference on Formal Modeling and Analysis of Timed Systems, pages 92–106. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-15297-9_9.
  23. Control barrier functions for signal temporal logic tasks. IEEE Control Systems Letters, 3(1):96–101, 2018. URL: https://doi.org/10.1109/LCSYS.2018.2853182.
  24. Formal methods for control synthesis: An optimization perspective. Annual Review of Control, Robotics, and Autonomous Systems, 2:115–140, 2019. URL: https://doi.org/10.1146/annurev-control-053018-023717.
  25. Model predictive control with signal temporal logic specifications. In 53rd IEEE Conference on Decision and Control, pages 81–87. IEEE, 2014. URL: https://doi.org/10.1109/CDC.2014.7039363.
  26. Robust temporal logic model predictive control. In 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 772–779. IEEE, 2015. URL: https://doi.org/10.1109/ALLERTON.2015.7447084.
  27. Time-robust control for STL specifications. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 572–579. IEEE, 2021. URL: https://doi.org/10.1109/CDC45484.2021.9683477.
  28. Combined left and right temporal robustness for control under STL specifications. IEEE Control Systems Letters, 7:619–624, 2022. URL: https://doi.org/10.1109/LCSYS.2022.3209928.
  29. Smooth operator: Control using the smooth robustness of temporal logic. In 2017 IEEE Conference on Control Technology and Applications (CCTA), pages 1235–1240. IEEE, 2017. URL: https://doi.org/10.1109/CCTA.2017.8062628.
  30. Control from signal temporal logic specifications with smooth cumulative quantitative semantics. In 2019 IEEE 58th Conference on Decision and Control (CDC), pages 4361–4366. IEEE, 2019. URL: https://doi.org/10.1109/CDC40024.2019.9029429.
  31. A smooth robustness measure of signal temporal logic for symbolic control. IEEE Control Systems Letters, 5(1):241–246, 2020. URL: https://doi.org/10.1109/LCSYS.2020.3001875.
  32. Successive convexification for optimal control with signal temporal logic specifications. In Proceedings of the 25th ACM International Conference on Hybrid Systems: Computation and Control, pages 1–7, 2022. URL: https://doi.org/10.1145/3501710.3519518.
  33. Robust control for signal temporal logic specifications using discrete average space robustness. Automatica, 101:377–387, 2019. URL: https://doi.org/10.1016/j.automatica.2018.12.022.
  34. Arithmetic-geometric mean robustness for control from signal temporal logic specifications. In 2019 American Control Conference (ACC), pages 1690–1695. IEEE, 2019. URL: https://doi.org/10.23919/ACC.2019.8814487.
  35. Specifying user preferences using weighted signal temporal logic. IEEE Control Systems Letters, 5(6):2006–2011, 2020. URL: https://doi.org/10.1109/LCSYS.2020.3047362.
  36. Average-based robustness for continuous-time signal temporal logic. In 2019 IEEE 58th Conference on Decision and Control (CDC), pages 5312–5317. IEEE, 2019. URL: https://doi.org/10.1109/CDC40024.2019.9029989.
  37. Time robustness in MTL and expressivity in hybrid system falsification. In International Conference on Computer Aided Verification, pages 356–374. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21668-3_21.
  38. Successive convexification of non-convex optimal control problems and its convergence properties. In 2016 IEEE 55th Conference on Decision and Control (CDC), pages 3636–3641. IEEE, 2016. URL: https://doi.org/10.1109/CDC.2016.7798816.
  39. Advances in trajectory optimization for space vehicle control. Annual Reviews in Control, 52:282–315, 2021. URL: https://doi.org/10.1016/j.arcontrol.2021.04.013.
  40. Convex optimization for trajectory generation: A tutorial on generating dynamically feasible trajectories reliably and efficiently. IEEE Control Systems Magazine, 42(5):40–113, 2022. URL: https://doi.org/10.1109/MCS.2022.3187542.
  41. Successive convexification for trajectory optimization with continuous-time constraint satisfaction. arXiv preprint arXiv:2404.16826, 2024. URL: https://doi.org/10.48550/arXiv.2404.16826.
  42. Fast homotopy for spacecraft rendezvous trajectory optimization with discrete logic. Journal of Guidance, Control, and Dynamics, 46(7):1262–1279, 2023. URL: https://doi.org/10.2514/1.G006295.
  43. Harold Shniad. On the convexity of mean value functions. Bulletin of the American Mathematical Society, 54:770–776, 1948. URL: https://doi.org/10.1090/S0002-9904-1948-09077-2.
  44. Fuel-optimal low-thrust trajectory optimization using indirect method and successive convex programming. IEEE Transactions on Aerospace and Electronic Systems, 54(4):2053–2066, 2018. URL: https://doi.org/10.1109/TAES.2018.2803558.
  45. Direct–indirect hybrid strategy for optimal powered descent and landing. Journal of Spacecraft and Rockets, 60(6):1787–1804, 2023. URL: https://doi.org/10.2514/1.A35650.
  46. A customized first-order solver for real-time powered-descent guidance. In AIAA SciTech 2022 Forum. American Institute of Aeronautics and Astronautics, January 2022. URL: https://doi.org/10.2514/6.2022-0951.
  47. Customized real-time first-order methods for onboard dual quaternion-based 6-DoF powered-descent guidance. In AIAA SciTech 2023 Forum. American Institute of Aeronautics and Astronautics, January 2023. URL: https://doi.org/10.2514/6.2023-2003.
  48. Real-time quad-rotor path planning using convex optimization and compound state-triggered constraints. In 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 7666–7673. IEEE, 2019. URL: https://doi.org/10.1109/IROS40897.2019.8967706.
  49. Successive convexification for real-time six-degree-of-freedom powered descent guidance with state-triggered constraints. Journal of Guidance, Control, and Dynamics, 43(8):1399–1413, 2020. URL: https://doi.org/10.2514/1.G004549.
  50. Dual quaternion-based powered descent guidance with state-triggered constraints. Journal of Guidance, Control, and Dynamics, 43(9):1584–1599, 2020. URL: https://doi.org/10.2514/1.G004536.
  51. A multiple shooting algorithm for direct solution of optimal control problems. IFAC proceedings volumes, 17(2):1603–1608, July 1984. URL: https://doi.org/10.1016/s1474-6670(17)61205-9.
  52. Multiple shooting in a microsecond. In Multiple Shooting and Time Domain Decomposition Methods: MuS-TDD, Heidelberg, May 6-8, 2013, pages 183–201. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-23321-5_7.
  53. Numerical Optimization. Springer, 2 edition, July 2006. URL: https://doi.org/10.1007/978-0-387-40065-5.
  54. Efficiency of minimizing compositions of convex functions and smooth maps. Mathematical Programming, 178:503–558, 2019. URL: https://doi.org/10.1007/s10107-018-1311-3.
  55. CVXPY: A python-embedded modeling language for convex optimization. Journal of Machine Learning Research, 17(83):1–5, 2016. URL: https://www.cvxpy.org/.
  56. ECOS: An SOCP solver for embedded systems. In 2013 European control conference (ECC), pages 3071–3076. IEEE, 2013. URL: https://doi.org/10.23919/ECC.2013.6669541.
  57. Mosek ApS. Mosek optimization toolbox for matlab. User’s Guide and Reference Manual, Version, 4(1), 2019. URL: https://docs.mosek.com/10.1/toolbox.pdf.
  58. Proportional–integral projected gradient method for conic optimization. Automatica, 142:110359, 2022. URL: https://doi.org/10.1016/j.automatica.2022.110359.
  59. Extrapolated proportional-integral projected gradient method for conic optimization. IEEE Control Systems Letters, 7:73–78, 2022. URL: https://doi.org/10.1109/LCSYS.2022.3186647.
  60. On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. SIAM Journal on Optimization, 21(4):1721–1739, 2011. URL: https://doi.org/10.1137/11082381X.
  61. Fast monte carlo analysis for 6-DoF powered-descent guidance via GPU-accelerated sequential convex programming. In AIAA SciTech 2024 Forum. AIAA, 2024. URL: https://doi.org/10.2514/6.2024-1762.
  62. Successive convexification for nonlinear model predictive control with continuous-time constraint satisfaction. In 8th IFAC Conference on Nonlinear Model Predictive Control, Kyoto, Japan, August 2024. URL: https://doi.org/10.48550/arXiv.2405.00061.
  63. Approach and landing trajectory optimization for a 6-dof aircraft with a runway alignment constraint, 2024.
  64. Real-time sequential conic optimization for multi-phase rocket landing guidance. IFAC-PapersOnLine, 56(2):3118–3125, 2023. URL: https://doi.org/10.1016/j.ifacol.2023.10.1444.
  65. Austin DeSisto. Starship and its belly flop maneuver, 2021. URL: https://everydayastronaut.com/starships-belly-flop-maneuver.

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free