Abstract
Motion planning is one of the core problems in a wide range of robotic applications. We discuss the use of temporal logics to include complex objectives, constraints, and preferences in motion planning algorithms and focus on three topics: the first one addresses computational tractability of Linear Temporal Logic (LTL) motion planning in systems with uncertain non-holonomic dynamics, i.e. systems whose ability to move in space is constrained. We introduce feedback motion primitives and heuristics to guide motion planning and demonstrate its use on a rover in 2D and a fixed-wing drone in 3D. Second, we introduce combined motion planning and hybrid feedback control design in order to find and follow trajectories under Metric Interval Temporal Logic (MITL) specifications. Our solution creates a path to be tracked, a sequence of obstacle-free polytopes and time stamps, and a controller that tracks the path while staying in the polytopes. Third, we focus on motion planning with spatio-temporal preferences expressed in a fragment of Signal Temporal Logic (STL). We introduce a cost function for a of a path reflecting the satisfaction/violation of the preferences based on the notion of STL spatial and temporal robustness. We integrate the cost into anytime asymptotically optimal motion planning algorithm RRT\(^\star \) and we show the use of the algorithm in integration with an autonomous exploration planner on a UAV.
This work was partially supported by the Swedish Research Council (VR), and the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knutand Alice Wallenberg Foundation. The authors are with the Division of Robotics, Perception, and Learning at KTH, and also affiliated with Digital Futures.
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References
Andersson, S., Nikou, A., Dimarogonas, D.V.: Control synthesis for multi-agent systems under metric interval temporal logic specifications. IFAC-PapersOnLine 50(1), 2397–2402 (2017)
Barbosa, F.S., Duberg, D., Jensfelt, P., Tumova, J.: Guiding autonomous exploration with signal temporal logic. IEEE Robot. Autom. Lett. 4(4), 3332–3339 (2019)
Barbosa, F.S., Lindemann, L., Dimarogonas, D.V., Tumova, J.: Integrated motion planning and control under metric interval temporal logic specifications. In: 2019 18th European Control Conference (ECC), pp. 2042–2049. IEEE (2019)
Bhatia, A., Kavraki, L.E., Vardi, M.Y.: Sampling-based motion planning with temporal goals. In: 2010 IEEE International Conference on Robotics and Automation, pp. 2689–2696. IEEE (2010)
Bircher, A., Kamel, M., Alexis, K., Oleynikova, H., Siegwart, R.: Receding horizon “next-best-view" planner for 3D exploration. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 1462–1468. IEEE (2016)
Castro, L.I.R., Chaudhari, P., Tumova, J., Karaman, S., Frazzoli, E., Rus, D.: Incremental sampling-based algorithm for minimum-violation motion planning. In: 52nd IEEE Conference on Decision and Control, pp. 3217–3224. IEEE (2013)
Herbert, S.L., Chen, M., Han, S., Bansal, S., Fisac, J.F., Tomlin, C.J.: FaSTrack: a modular framework for fast and guaranteed safe motion planning. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 1517–1522. IEEE (2017)
Hoxha, B., Fainekos, G.: Planning in dynamic environments through temporal logic monitoring. In: Workshops at the Thirtieth AAAI Conference on Artificial Intelligence (2016)
Karaman, S., Frazzoli, E.: Sampling-based motion planning with deterministic \(\mu \)-calculus specifications. In: Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp. 2222–2229. IEEE (2009)
Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30(7), 846–894 (2011)
Karlsson, J., Barbosa, F.S., Tumova, J.: Sampling-based motion planning with temporal logic missions and spatial preferences. IFAC-PapersOnLine 53(2), 15537–15543 (2020)
Karlsson, J., Vasile, C.I., Tumova, J., Karaman, S., Rus, D.: Multi-vehicle motion planning for social optimal mobility-on-demand. In: 2018 IEEE International Conference on Robotics and Automation (ICRA), pp. 7298–7305. IEEE (2018)
Kloetzer, M., Belta, C.: A fully automated framework for control of linear systems from temporal logic specifications. IEEE Trans. Autom. Control 53(1), 287–297 (2008)
Kress-Gazit, H., Fainekos, G.E., Pappas, G.J.: Temporal-logic-based reactive mission and motion planning. IEEE Trans. Robot. 25(6), 1370–1381 (2009)
Kress-Gazit, H., Lahijanian, M., Raman, V.: Synthesis for robots: guarantees and feedback for robot behavior. Annu. Rev. Control Robot. Auton. Syst. 1, 211–236 (2018)
LaValle, S.M.: Planning Algorithms. Cambridge University Press (2006)
Lindemann, L., Dimarogonas, D.V.: Control barrier functions for signal temporal logic tasks. IEEE Control Syst. Lett. 3(1), 96–101 (2019)
Luo, X., Kantaros, Y., Zavlanos, M.M.: An abstraction-free method for multirobot temporal logic optimal control synthesis. IEEE Trans. Robot. (2021)
Majumdar, A., Tedrake, R.: Funnel libraries for real-time robust feedback motion planning. Int. J. Robot. Res. 36(8), 947–982 (2017)
Montana, F.J., Liu, J., Dodd, T.J.: Sampling-based reactive motion planning with temporal logic constraints and imperfect state information. In: Critical Systems: Formal Methods and Automated Verification, pp. 134–149. Springer (2017). https://doi.org/10.1007/978-3-319-67113-0_9
Selin, M., Tiger, M., Duberg, D., Heintz, F., Jensfelt, P.: Efficient autonomous exploration planning of large-scale 3-D environments. IEEE Robot. Autom. Lett. 4(2), 1699–1706 (2019)
Singh, S., Majumdar, A., Slotine, J.J., Pavone, M.: Robust online motion planning via contraction theory and convex optimization. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 5883–5890. IEEE (2017)
Tajvar, P., Barbosa, F.S., Tumova, J.: Safe motion planning for an uncertain non-holonomic system with temporal logic specification. In: 2020 IEEE 16th International Conference on Automation Science and Engineering (CASE), pp. 349–354. IEEE (2020)
Tedrake, R., Manchester, I.R., Tobenkin, M., Roberts, J.W.: LQR-trees: feedback motion planning via sums-of-squares verification. Int. J. Robot. Res. 29(8), 1038–1052 (2010)
Vasile, C.I., Li, X., Belta, C.: Reactive sampling-based path planning with temporal logic specifications. Int. J. Robot. Res. 39(8), 1002–1028 (2020)
Vasile, C.I., Raman, V., Karaman, S.: Sampling-based synthesis of maximally-satisfying controllers for temporal logic specifications. In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3840–3847. IEEE (2017)
Vasile, C.I., Tumova, J., Karaman, S., Belta, C., Rus, D.: Minimum-violation scltl motion planning for mobility-on-demand. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 1481–1488. IEEE (2017)
Zhou, Y., Maity, D., Baras, J.S.: Timed automata approach for motion planning using metric interval temporal logic. In: 2016 European Control Conference (ECC), pp. 690–695. IEEE (2016)
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Barbosa, F.S., Karlsson, J., Tajvar, P., Tumova, J. (2021). Formal Methods for Robot Motion Planning with Time and Space Constraints (Extended Abstract). In: Dima, C., Shirmohammadi, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2021. Lecture Notes in Computer Science(), vol 12860. Springer, Cham. https://doi.org/10.1007/978-3-030-85037-1_1
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