Time-Robust Path Planning with Piece-Wise Linear Trajectory for Signal Temporal Logic Specifications (2403.10735v1)
Abstract: Real-world scenarios are characterized by timing uncertainties, e.g., delays, and disturbances. Algorithms with temporal robustness are crucial in guaranteeing the successful execution of tasks and missions in such scenarios. We study time-robust path planning for synthesizing robots' trajectories that adhere to spatial-temporal specifications expressed in Signal Temporal Logic (STL). In contrast to prior approaches that rely on {discretize}d trajectories with fixed time steps, we leverage Piece-Wise Linear (PWL) signals for the synthesis. PWL signals represent a trajectory through a sequence of time-stamped waypoints. This allows us to encode the STL formula into a Mixed-Integer Linear Program (MILP) with fewer variables. This reduction is more pronounced for specifications with a long planning horizon. To that end, we define time-robustness for PWL signals. Subsequently, we propose quantitative semantics for PWL signals according to the recursive syntax of STL and prove their soundness. We then propose an encoding strategy to transform our semantics into a MILP. Our simulations showcase the soundness and the performance of our algorithm.
- O. Maler and D. Nickovic, “Monitoring temporal properties of continuous signals,” in FORMATS/FTRTFT, 2004.
- V. Raman, A. Donzé, D. Sadigh, R. M. Murray, and S. A. Seshia, “Reactive synthesis from signal temporal logic specifications,” Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, 2015.
- Y. V. Pant, H. Abbas, and R. Mangharam, “Smooth operator: Control using the smooth robustness of temporal logic,” in 2017 IEEE Conference on Control Technology and Applications (CCTA), 2017, pp. 1235–1240.
- L. Lindemann and D. V. Dimarogonas, “Control barrier functions for signal temporal logic tasks,” IEEE Control Systems Letters, vol. 3, pp. 96–101, 2019.
- A. Donzé and O. Maler, “Robust satisfaction of temporal logic over real-valued signals,” in Proceedings of the 8th International Conference on Formal Modeling and Analysis of Timed Systems, ser. FORMATS’10. Berlin, Heidelberg: Springer-Verlag, 2010, p. 92–106.
- T. Akazaki and I. Hasuo, “Time robustness in mtl and expressivity in hybrid system falsification (extended version),” 2015.
- A. Rodionova, L. Lindemann, M. Morari, and G. J. Pappas, “Time-robust control for stl specifications,” in 2021 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 572–579.
- A. Rodionova, L. Lindemann, M. Morari, and G. Pappas, “Temporal robustness of temporal logic specifications: Analysis and control design,” ACM Trans. Embed. Comput. Syst., vol. 22, no. 1, oct 2022. [Online]. Available: https://doi.org/10.1145/3550072
- S. Karaman, R. G. Sanfelice, and E. Frazzoli, “Optimal control of mixed logical dynamical systems with ltl specifications,” 2008 47th IEEE Conference on Decision and Control, pp. 2117–2122, 2008.
- K. Leung, N. Aréchiga, and M. Pavone, “Back-propagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods,” ArXiv, vol. abs/2008.00097, 2020.
- Z. Zhang and S. Haesaert, “Modularized control synthesis for complex signal temporal logic specifications,” 2023.
- C. Fan, K. Miller, and S. Mitra, “Fast and guaranteed safe controller synthesis for nonlinear vehicle models,” Computer Aided Verification - 32nd International Conference, CAV 2020, Los Angeles, CA, USA, July 21-24, 2020, Proceedings, Part I, vol. 12224. [Online]. Available: https://par.nsf.gov/biblio/10180137
- D. Sun, J. Chen, S. Mitra, and C. Fan, “Multi-agent motion planning from signal temporal logic specifications,” IEEE Robotics and Automation Letters, vol. 7, no. 2, p. 3451 – 3458, 2022, cited by: 2; All Open Access, Green Open Access, Hybrid Gold Open Access.
- Y. V. Pant, H. Abbas, R. A. Quaye, and R. Mangharam, “Fly-by-logic: Control of multi-drone fleets with temporal logic objectives,” in 2018 ACM/IEEE 9th International Conference on Cyber-Physical Systems (ICCPS), 2018, pp. 186–197.
- Y. Zhou, D. Maity, and J. S. Baras, “Optimal mission planner with timed temporal logic constraints,” in 2015 European Control Conference (ECC), 2015, pp. 759–764.