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A state-of-the-art review on topology and differential geometry-based robotic path planning—part II: planning under dynamic constraints

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Abstract

Path planning is an intrinsic component of autonomous robotics, be it industrial, research or consumer robotics. Such avenues experience constraints around which paths must be planned. While the choice of an appropriate algorithm is application-dependent, the starting point of an ideal path planning algorithm is the review of past work. Historically, algorithms were classified based on the three tenets of autonomous robotics which are the ability to avoid different constraints (static/dynamic), knowledge of the environment (known/unknown) and knowledge of the robot (general/model specific). This division in literature however, is not comprehensive, especially with respect to dynamics constraints. Therefore, to remedy this issue, we propose a new taxonomy, based on the fundamental tenet of characterizing space, i.e., as a set of distinct, unrelated points or as a set of points that share a relationship. We show that this taxonomy is effective in addressing important parameters of path planning such as connectivity and partitioning of spaces. Therefore, path planning spaces may now be viewed either as a set of points or, as a space with structure. The former relies heavily on robot models, since the mathematical structure of the environment is not considered. Thus, the approaches used are variants of optimization algorithms and specific variants of model-based methods that are tailored to counteract effects of dynamic constraints. The latter depicts spaces as points with inter-connecting relationships, such as surfaces or manifolds. These structures allow for unique characterizations of paths using homotopy-based methods. The goals of this work, viewed specifically in light with dynamic constraints, are therefore as follows: First, we propose an all-encompassing taxonomy for robotic path planning literature that considers an underlying structure of the space. Second, we provide a detailed accumulation of works that do focus on the characterization of paths in spaces formulated to show underlying structure. This work accomplishes the goals by doing the following: It highlights existing classifications of path planning literature, identifies gaps in common classifications, proposes a new taxonomy based on the mathematical nature of the path planning space (topological properties), and provides an extensive conglomeration of literature that is encompassed by this new proposed taxonomy.

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Abbreviations

APF :

Artificial potential field

CDGT :

Cell decomposition and graph traversal

DC :

Dynamic constraint

EA :

Evolutionary algorithm

\(HA^{*}\) :

Homotopic A*

HB :

Homotopic bug

HBM :

Homotopy based method

HCM :

Homotopy continuation methods

HRRT :

Homotopic RRT

LAG :

L-augmented graph

MBM :

Model based methods

MPC :

Model predictive control

NAES :

Non-linear algebraic equation system

NF :

Navigation functions

OA :

Optimization algorithm

PPM :

Path planning manifold

PPP :

Path planning problem

PPS :

Path planning space

PRM :

Probabilistic road map

RRT :

Rapidly exploring random tree

SA :

Sampling algorithm

SC :

Static constraint

SHIO :

Single homotopy inducing obstacle

VOS :

Velocity obstacle sets

\(H-signature\) :

Unique measure associated to a homotopic class

\({{\textbf {p}}^{\text {start}}}{\in \mathcal {P}}\) :

Starting point in \({\mathcal {P}}\)

\({{\textbf {p}}^{\text {goal}}}{\in \mathcal {P}}\) :

Destination point in \({\mathcal {P}}\)

References

  • Agirrebeitia, J., Avilés, R., de Bustos, I.F., Ajuria, G.: A new APF strategy for path planning in environments with obstacles. Mech. Mach. Theory 40(6), 645–658 (2005)

    Article  MathSciNet  Google Scholar 

  • Akbaripour, H., Akbaripour, H., Masehian, E., Masehian, E.: Semi-lazy probabilistic roadmap: a parameter-tuned, resilient and robust path planning method for manipulator robots. Int. J. Adv. Manuf. Technol. 89(5), 1401–1430 (2017)

    Article  Google Scholar 

  • Ataka, A., Lam, H.-K., Althoefer, K.: Reactive magnetic-field-inspired navigation method for robots in unknown convex 3-D environments. IEEE Robot. Autom. Lett. 3(4), 3583–3590 (2018)

    Article  Google Scholar 

  • Atramentov, A., LaValle, S.M.: Efficient nearest neighbor searching for motion planning. In: Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), vol. 1, pp. 632–6371 (2002). https://doi.org/10.1109/ROBOT.2002.1013429

  • Barraquand, J., Latombe, J.-C.: Robot motion planning: a distributed representation approach. Int. J. Robot. Res. 10(6), 628–649 (2016)

    Article  Google Scholar 

  • Belkhouche, F.: Reactive path planning in a dynamic environment. IEEE Trans. Robot. 25(4), 902–911 (2009)

    Article  Google Scholar 

  • Belkhouche, F., Bendjilali, B.: Reactive path planning for 3-D autonomous vehicles. IEEE Trans. Control Syst. Technol. 20(1), 249–256 (2012)

    Google Scholar 

  • Bevilacqua, P., Frego, M., Fontanelli, D., Palopoli, L.: Reactive planning for assistive robots. IEEE Robot. Autom. Lett. 3(2), 1276–1283 (2018)

    Article  Google Scholar 

  • Bhattacharya, S., Kumar, V., Likhachev, M.: Search-based path planning with homotopy class constraints. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. AAAI’10, pp. 1230–1237. AAAI Press, Atlanta (2010)

  • Bhattacharya, S., Likhachev, M., Kumar, V.: Identification and representation of homotopy classes of trajectories for search-based path planning in 3D. In: Robotics. MIT Press, Cambridge (2012a)

  • Bhattacharya, S., Likhachev, M., Kumar, V.: Search-based path planning with homotopy class constraints in 3D. In: Invited Paper for Sub-area Spotlights Track on ’Best-paper Talks’, Proceedings of Twenty-Sixth Conference on Artificial Intelligence (AAAI-12) (2012b)

  • Bloch, A., Camarinha, M., Colombo, L.J.: Dynamic interpolation for obstacle avoidance on Riemannian manifolds. Int. J. Control 94(3), 588–600 (2021)

    Article  MathSciNet  Google Scholar 

  • Bohlin, R., Kavraki, L.E.: Path planning using lazy PRM. In: Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), vol. 1, pp. 521–5281 (2000). https://doi.org/10.1109/ROBOT.2000.844107

  • Cabello, S., Liu, Y., Mantler, A., Snoeyink, J.: Testing homotopy for paths in the plane. Discrete Comput. Geom. 31(1), 61–81 (2004)

    Article  MathSciNet  Google Scholar 

  • Cockayne, E.J., Hall, G.W.C.: Plane motion of a particle subject to curvature constraints. SIAM J. Control 13(1), 197–220 (1975)

    Article  MathSciNet  Google Scholar 

  • Cui, P., Yan, W., Wang, Y.: Reactive path planning approach for docking robots in unknown environment. J. Adv. Transport. 2017, 1–11 (2017)

    Article  Google Scholar 

  • Dale, L.K., Amato, N.M.: Probabilistic roadmaps-putting it all together. In: Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), vol. 2, pp. 1940–19472 (2001). https://doi.org/10.1109/ROBOT.2001.932892

  • De Filippis, L., Guglieri, G., Quagliotti, F.: Path planning strategies for UAVs in 3D environments. J. Intell. Robot. Syst. 65(1), 247–264 (2012)

    Article  Google Scholar 

  • Diankov, R., Kuffner, J.: Randomized statistical path planning. In: 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1–6 (2007). https://doi.org/10.1109/IROS.2007.4399557

  • Diaz-Arango, G., Sarmiento-Reyes, A., Hernandez-Martinez, L., Vazquez-Leal, H., Lopez-Hernandez, D.D., Marin-Hernandez, A.: Path optimization for terrestrial robots using homotopy path planning method. In: 2015 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2824–2827. IEEE, Lisbon (2015)

  • Diaz-Arango, G., Vazquez-Leal, H., Hernandez-Martinez, L., Manuel Jimenez-Fernandez, V., Heredia-Jimenez, A., Ambrosio, R.C., Huerta-Chua, J., De Cos-Cholula, H., Hernandez-Mendez, S.: Multiple-target homotopic quasi-complete path planning method for mobile robot using a piecewise linear approach. Sensors (Basel, Switzerland) 20(11), 3265 (2020)

    Article  Google Scholar 

  • Diéguez, A.R., Sanz, R., López, J.: Deliberative on-line local path planning for autonomous mobile robots. J. Intell. Robot. Syst. 37(1), 1–19 (2003)

    Article  Google Scholar 

  • Duchoň, F., Babinec, A., Kajan, M., Beňo, P., Florek, M., Fico, T., Jurišica, L.: Path planning with modified a star algorithm for a mobile robot. Proc. Eng. 96, 59–69 (2014)

    Article  Google Scholar 

  • Eduardo De Cos-Cholula, H., Ulises Diaz-Arango, G., Hernandez-Martinez, L., Vazquez-Leal, H., Sarmiento-Reyes, A., Teresa Sanz-Pascual, M., Leobardo Herrera-May, A., Castaneda-Sheissa, R.: FPGA implementation of homotopic path planning method with automatic assignment of repulsion parameter. Energies (Basel) 13(10), 2623 (2020)

  • Elbanhawi, M., Simic, M.: Sampling-based robot motion planning: a review. IEEE Access 2, 56–77 (2014). https://doi.org/10.1109/ACCESS.2014.2302442

    Article  Google Scholar 

  • Faverjon, B., Tournassoud, P.: A local based approach for path planning of manipulators with a high number of degrees of freedom. In: Proceedings. 1987 IEEE International Conference on Robotics and Automation, vol. 4, pp. 1152–1159 (1987). https://doi.org/10.1109/ROBOT.1987.1087982

  • Ferguson, D., Stentz, A.: Anytime RRTs. In: 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5369–5375 (2006). https://doi.org/10.1109/IROS.2006.282100

  • Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using velocity obstacles. Int. J. Robot. Res. 17(7), 760–772 (1998)

    Article  Google Scholar 

  • Ginesi, M., Meli, D., Roberti, A., Sansonetto, N., Fiorini, P.: Dynamic movement primitives: volumetric obstacle avoidance using dynamic potential functions. J. Intell. Robot. Syst. 101(4), 1–20 (2021)

    Article  Google Scholar 

  • Gregoire, J., Čáp, M., Frazzoli, E.: Locally-optimal multi-robot navigation under delaying disturbances using homotopy constraints. Auton. Robots 42(4), 895–907 (2018)

    Article  Google Scholar 

  • Hernandez, E., Carreras, M., Ridao, P., Antich, J., Ortiz, A.: A search-based path planning algorithm with topological constraints. application to an AUV. IFAC Proc. Vol. 44(1), 13654–13659 (2011)

  • Hernández, E., Carreras, M., Ridao, P.: A bug-based path planner guided with homotopy classes. In: ICINCO 2012—Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics, vol. 2, pp. 123–131 (2012)

  • Hernández, E., Carreras, M., Ridao, P.: A path planning algorithm for an AUV guided with homotopy classes. In: Proceedings of the Twenty-First International Conference on Automated Planning and Scheduling, vol. 21 (2011)

  • Hernandez, E., Carreras, M., Ridao, P.: A comparison of homotopic path planning algorithms for robotic applications. Robot. Auton. Syst. 64, 44–58 (2015)

    Article  Google Scholar 

  • Hildebrandt, A.-C., Klischat, M., Wahrmann, D., Wittmann, R., Sygulla, F., Seiwald, P., Rixen, D., Buschmann, T.: Real-time path planning in unknown environments for bipedal robots. IEEE Robot. Autom. Lett. 2(4), 1856–1863 (2017)

    Article  Google Scholar 

  • Hossain, M.A., Ferdous, I.: Autonomous robot path planning in dynamic environment using a new optimization technique inspired by bacterial foraging technique. Robot. Auton. Syst. 64, 137–141 (2015)

    Article  Google Scholar 

  • Hsu, D., Zheng, S.: Adaptively combining multiple sampling strategies for probabilistic roadmap planning. In: IEEE Conference on Robotics, Automation and Mechatronics, 2004, vol. 2, pp. 774–7792 (2004). https://doi.org/10.1109/RAMECH.2004.1438016

  • Hughes, K., Tokuta, A., Ranganathan, N.: Trulla: an algorithm for path planning among weighted regions by localized propagations. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 1, pp. 469–476 (1992). https://doi.org/10.1109/IROS.1992.587377

  • Jaillet, L., Cortés, J., Siméon, T.: Sampling-based path planning on configuration-space costmaps. IEEE Trans. Robot. 26(4), 635–646 (2010)

    Article  Google Scholar 

  • Jenkins, K.D.: The shortest path problem in the plane with obstacles: a graph modeling approach to producing finite search lists of homotopy classes. Master’s thesis, Naval Postgraduate School Monterey California (1991)

  • Kala, R.: Homotopy conscious roadmap construction by fast sampling of narrow corridors. Appl. Intell. (Dordrecht, Netherlands) 45(4), 1089–1102 (2016)

    Google Scholar 

  • Kala, R.: Homotopic roadmap generation for robot motion planning. J. Intell. Robot. Syst. 82(3), 555–575 (2016)

    Article  MathSciNet  Google Scholar 

  • Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. Int. J. Robot. Res. 30(7), 846–894 (2011)

    Article  Google Scholar 

  • Kavraki, L.E., Svestka, P., Latombe, J.-C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566–580 (1996). https://doi.org/10.1109/70.508439

    Article  Google Scholar 

  • Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90–98 (1986)

    Article  Google Scholar 

  • Khosla, P., Volpe, R.: Superquadric artificial potentials for obstacle avoidance and approach. In: Proceedings. 1988 IEEE International Conference on Robotics and Automation, pp. 1778–17843 (1988). https://doi.org/10.1109/ROBOT.1988.12323

  • Kim, D., Kang, M., Yoon, S.-E.: Volumetric tree: adaptive sparse graph for effective exploration of homotopy classes. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1496–1503. IEEE, Macau (2019)

  • Kim, S., Sreenath, K., Bhattacharya, S., Kumar, V.: Trajectory planning for systems with homotopy class constraints. In: Latest Advances in Robot Kinematics (ARK), Innsbruck, pp. 83–90 (2012)

  • Koditschek, D.: Exact robot navigation by means of potential functions: Some topological considerations. In: Proceedings. 1987 IEEE International Conference on Robotics and Automation, vol. 4, pp. 1–6 (1987). https://doi.org/10.1109/ROBOT.1987.1088038

  • Koditschek, D.E., Rimon, E.: Robot navigation functions on manifolds with boundary. Adv. Appl. Math. 11(4), 412–442 (1990)

    Article  MathSciNet  Google Scholar 

  • Kolur, K., Chintalapudi, S., Boots, B., Mukadam, M.: Online motion planning over multiple homotopy classes with gaussian process inference. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2358–2364. IEEE, Macau (2019)

  • Kowalczyk, W.: Rapid navigation function control for two-wheeled mobile robots. J. Intell. Robot. Syst. 93(3–4), 687–697 (2018)

    Google Scholar 

  • Kowalczyk, W., Kowalczyk, W., Przybyla, M., Przybyla, M., Kozlowski, K., Kozlowski, K.: Set-point control of mobile robot with obstacle detection and avoidance using navigation function—experimental verification. J. Intell. Robot. Syst. 85(3), 539–552 (2017)

    Article  Google Scholar 

  • Kuffner, J.J., LaValle, S.M.: RRT-connect: an efficient approach to single-query path planning. In: Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065), vol. 2, pp. 995–10012 (2000). https://doi.org/10.1109/ROBOT.2000.844730

  • Kuwata, Y., Teo, J., Karaman, S., Fiore, G., Frazzoli, E., How, J.: Motion planning in complex environments using closed-loop prediction. In: AIAA Guidance, Navigation and Control Conference and Exhibit (2008). https://doi.org/10.2514/6.2008-7166. AIAA

  • Lamiraux, F., Bonnafous, D., Lefebvre, O.: Reactive path deformation for nonholonomic mobile robots. IEEE Trans. Robot. 20(6), 967–977 (2004)

    Article  Google Scholar 

  • M.LaValle, S.: Rapidly-exploring random trees: a new tool for path planning. Technical report, Iowa State University, Ames (1998)

  • LaValle, S.M., Kuffner, J.J.: Randomized kinodynamic planning. Int. J. Robot. Res. 20(5), 378–400 (2001)

    Article  Google Scholar 

  • LaValle, S.M., Branicky, M.S., Lindemann, S.R.: On the relationship between classical grid search and probabilistic roadmaps. Int. J. Robot. Res. 23(7–8), 673–692 (2004)

    Article  Google Scholar 

  • Lee, J., Pippin, C., Balch, T.: Cost based planning with RRT in outdoor environments. In: 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 684–689 (2008). https://doi.org/10.1109/IROS.2008.4651052

  • Lengyel, J., Reichert, M., Donald, B.R., Greenberg, D.P.: Real-time robot motion planning using rasterizing computer graphics hardware. Comput. Graph. (New York, N. Y.) 24(4), 327–335 (1990)

    Google Scholar 

  • Li, X., Zhao, G., Li, B.: Generating optimal path by level set approach for a mobile robot moving in static/dynamic environments. Appl. Math. Model. 85, 210–230 (2020)

    Article  MathSciNet  Google Scholar 

  • Lin, Y., Saripalli, S.: Sampling-based path planning for uav collision avoidance. IEEE Trans. Intell. Transport. Syst. 18(11), 3179–3192 (2017)

    Article  Google Scholar 

  • Liu, Y., Qi, N., Yao, W., Zhao, J., Xu, S.: Cooperative path planning for aerial recovery of a UAV swarm using genetic algorithm and homotopic approach. Appl. Sci. 10(12), 4154 (2020)

    Article  Google Scholar 

  • Liu, Y., Zheng, Z., Qin, F.: Homotopy based optimal configuration space reduction for anytime robotic motion planning. Chin. J. Aeronaut. 34(1), 364–379 (2021)

    Article  Google Scholar 

  • Lumelsky, V.J., Stepanov, A.A.: Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape. Algorithmica 2(1–4), 403–430 (1987)

    Article  MathSciNet  Google Scholar 

  • Masehian, E., Amin-Naseri, M.R.: A Voronoi diagram-visibility graph-potential field compound algorithm for robot path planning. J. Robot. Syst. 21(6), 275–300 (2004)

    Article  Google Scholar 

  • McFetridge, L., Ibrahim, M.Y.: A new methodology of mobile robot navigation: the agoraphilic algorithm. Robot. Comput. Integr. Manuf. 25(3), 545–551 (2009)

    Article  Google Scholar 

  • Mediavilla, M., González, J.L., Fraile, J.C., Ramón Perán, J.: Reactive approach to on-line path planning for robot manipulators in dynamic environments. Robotica 20(4), 375–384 (2002)

    Article  Google Scholar 

  • Molina, C.P., Ortego, R.G., Pérez, F.M.: Perspectives on Technological Developments Applied to Robotics, pp. 59–86. Springer, London (2014). https://doi.org/10.1007/978-1-4471-5358-0_5

  • Montiel, O., Orozco-Rosas, U., Sepúlveda, R.: Path planning for mobile robots using bacterial potential field for avoiding static and dynamic obstacles. Expert Syst. Appl. 42(12), 5177–5191 (2015)

    Article  Google Scholar 

  • Murphy, R.R., Hughes, K., Marzilli, A., Noll, E.: Integrating explicit path planning with reactive control of mobile robots using trulla. Robot. Auton. Syst. 27(4), 225–245 (1999)

    Article  Google Scholar 

  • Noreen, I., Khan, A., Ryu, H., Doh, N.L., Habib, Z.: Optimal path planning in cluttered environment using RRT-AB. Intell. Serv. Robot. 11(1), 41–52 (2017)

    Article  Google Scholar 

  • Park, J., Karumanchi, S., Iagnemma, K.: Homotopy-based divide-and-conquer strategy for optimal trajectory planning via mixed-integer programming. IEEE Trans. Robot. 31(5), 1101–1115 (2015)

    Article  Google Scholar 

  • Qin, L., Yin, Q., Zha, Y., Peng, Y.: Dynamic detection of topological information from grid-based generalized Voronoi diagrams. Math. Probl. Eng. 2013, 1–11 (2013)

    MathSciNet  Google Scholar 

  • Quillen, P., Muñoz, J., Subbarao, K.: Path planning to a reachable state using minimum control effort based navigation functions. J. Astronaut. Sci. 66(4), 554–581 (2019)

    Article  Google Scholar 

  • Radhakrishnan, S., Gueaieb, W.: A state-of-the-art review on topology and differential geometry-based robotic path planning—part I: planning under static constraints. Int. J. Intell. Robot. Appl. (2023)

  • Radhakrishnan, S.: Observable 2D SLAM and Evidential Occupancy Grids. Master’s thesis, Carleton University (2014)

  • Savkin, A.V., Hoy, M.: Reactive and the shortest path navigation of a wheeled mobile robot in cluttered environments. Robotica 31(2), 323–330 (2013)

    Article  Google Scholar 

  • Stentz, A.: Optimal and efficient path planning for partially-known environments. In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation, pp. 3310–33174 (1994). https://doi.org/10.1109/ROBOT.1994.351061

  • Stopp, A., Riethmuller, T.: Fast reactive path planning by 2d and 3d multi-layer spatial grids for mobile robot navigation. In: Proceedings of Tenth International Symposium on Intelligent Control, pp. 545–550. IEEE, Monterey (1995)

  • Suh, J., Gong, J., Oh, S.: Fast sampling-based cost-aware path planning with nonmyopic extensions using cross entropy. IEEE Trans. Robot. 33(6), 1313–1326 (2017)

    Article  Google Scholar 

  • Tao, S., Tan, J.: Path planning with obstacle avoidance based on normalized r-functions. J. Robot. 2018, 1–10 (2018)

    Article  Google Scholar 

  • van den Berg, J., Overmars, M.: Planning time-minimal safe paths amidst unpredictably moving obstacles. Int. J. Robot. Res. 27(11–12), 1274–1294 (2008)

    Article  Google Scholar 

  • Vazquez-Leal, H., Marin-Hernandez, A., Khan, Y., Yıldırım, A., Filobello-Nino, U., Castaneda-Sheissa, R., Jimenez-Fernandez, V.M.: Exploring collision-free path planning by using homotopy continuation methods. Appl. Math. Comput. 219(14), 7514–7532 (2013)

    Article  MathSciNet  Google Scholar 

  • Volpe, R., Khosla, P.: Artificial potentials with elliptical isopotential contours for obstacle avoidance. In: 26th IEEE Conference on Decision and Control, vol. 26, pp. 180–185 (1987). https://doi.org/10.1109/CDC.1987.272738

  • Volpe, R., Khosla, P.: Manipulator control with superquadric artificial potential functions: theory and experiments. IEEE Trans. Syst. Man Cybern. 20(6), 1423–1436 (1990). https://doi.org/10.1109/21.61211

    Article  Google Scholar 

  • Wada, H., Kinugawa, J., Kosuge, K.: Reactive motion planning using time-layered c-spaces for a collaborative robot pady. Adv. Robot. 35(8), 490–503 (2021)

    Article  Google Scholar 

  • Wang, W., Zuo, L., Xu, X.: A learning-based multi-rrt approach for robot path planning in narrow passages. J. Intell. Robot. Syst. 90(1–2), 81–100 (2017)

    Google Scholar 

  • Wang, B., Liu, Z., Li, Q., Prorok, A.: Mobile robot path planning in dynamic environments through globally guided reinforcement learning. IEEE Robot. Autom. Lett. 5(4), 6932–6939 (2020)

    Article  Google Scholar 

  • Wu, A., How, J.P.: Guaranteed infinite horizon avoidance of unpredictable, dynamically constrained obstacles. Auton. Robots 32(3), 227–242 (2012)

    Article  Google Scholar 

  • Yao, W., Qi, N., Zhao, J., Wan, N.: Bounded curvature path planning with expected length for Dubins vehicle entering target manifold. Robot. Auton. Syst. 97, 217–229 (2017)

    Article  Google Scholar 

  • Yi, D., Goodrich, M., Seppi, K.: Homotopy-aware RRT: Toward human-robot topological path-planning. In: The Eleventh ACM/IEEE International Conference on Human Robot Interaction. HRI ’16, pp. 279–286. IEEE Press, Christchurch (2016)

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This work was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Grant RGPIN-2014-06512.

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  1. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Avenue, Ottawa, K1N 6N5, ON, Canada

    Sindhu Radhakrishnan & Wail Gueaieb

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Sindhu Radhakrishnan. The first draft of the manuscript was written by Sindhu Radhakrishnan and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Radhakrishnan, S., Gueaieb, W. A state-of-the-art review on topology and differential geometry-based robotic path planning—part II: planning under dynamic constraints. Int J Intell Robot Appl 8, 455–479 (2024). https://doi.org/10.1007/s41315-024-00331-4

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