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Iterative methods for efficient sampling-based optimal motion planning of nonlinear systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper extends the RRT* algorithm, a recently developed but widely used sampling based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often leads to difficulties in choosing an appropriate distance metric and in computing optimized trajectory segments in tree construction. To tackle these two difficulties, this work adopts the affine quadratic regulator-based pseudo-metric as the distance measure and utilizes iterative two-point boundary value problem solvers to compute the optimized segments. The proposed extension then preserves the inherent asymptotic optimality of the RRT* framework, while efficiently handling a variety of kinodynamic constraints. Three numerical case studies validate the applicability of the proposed method.
Rocznik
Strony
155--168
Opis fizyczny
Bibliogr. 27 poz., rys., tab., wykr.
Twórcy
autor
  • Mechanical Engineering Research Institute, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong, Deajeon 34141, Republic of Korea
autor
  • Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong, Deajeon 34141, Republic of Korea
autor
  • nuTonomy Inc., 1 Broadway, Cambridge, MA 02142, USA
Bibliografia
  • [1] Arslan, O. and Tsiotras, P. (2013). Use of relaxation methods in sampling-based algorithms for optimal motion planning, IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, pp. 2421–2428.
  • [2] García-Rodríguez, R., Segovia-Palacios, V., Parra-Vega, V. and Villalva-Lucio, M. (2016). Dynamic optimal grasping of a circular object with gravity using robotic soft-fingertips, International Journal of Applied Mathematics and Computer Science 26(2): 309–323, DOI: 10.1515/amcs-2016-0022.
  • [3] Glassman, E. and Tedrake, R. (2010). A quadratic regulator-based heuristic for rapidly exploring state space, IEEE International Conference on Robotics and Automation, Anchorage, AK, USA, pp. 5021–5028.
  • [4] Goretkin, G., Perez, A., Platt, R. and Konidaris, G. (2013). Optimal sampling-based planning for linear-quadratic kinodynamic systems, IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, pp. 2429–2436.
  • [5] Ha, J.-S., Lee, J.-J. and Choi, H.-L. (2013). A successive approximation-based approach for optimal kinodynamic motion planning with nonlinear differential constraints, IEEE Conference on Decision and Control, Florence, Italy, pp. 3623–3628.
  • [6] Huynh, V.A., Karaman, S. and Frazzoli, E. (2012). An incremental sampling-based algorithm for stochastic optimal control, IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, pp. 2865–2872.
  • [7] Huynh, V.A., Kogan, L. and Frazzoli, E. (2014). A Martingale approach and time-consistent sampling-based algorithms for risk management in stochastic optimal control, IEEE Conference on Decision and Control, Los Angeles, CA, USA, pp. 1858–1865.
  • [8] Janson, L., Schmerling, E., Clark, A. and Pavone, M. (2015). Fast marching tree: A fast marching sampling-based method for optimal motion planning in many dimensions, The International Journal of Robotics Research 34(7): 883–921.
  • [9] Jeon, J., Karaman, S. and Frazzoli, E. (2011). Anytime computation of time-optimal off-road vehicle maneuvers using the RRT*, IEEE Conference on Decision and Control, Orlando, FL, USA, pp. 3276–3282.
  • [10] Jeon, J., Karaman, S. and Frazzoli, E. (2015). Optimal sampling-based feedback motion trees among obstacles for controllable linear systems with linear constraints, IEEE International Conference on Robotics and Automation, Seattle, WA, USA, pp. 4195–4201.
  • [11] Karaman, S. and Frazzoli, E. (2010). Optimal kinodynamic motion planning using incremental sampling-based methods, IEEE Conference on Decision and Control, Atlanta, GA, USA, pp. 7681–7687.
  • [12] Karaman, S. and Frazzoli, E. (2011a). Incremental sampling-based algorithms for a class of pursuit-evasion games, in D. Hsu et al. (Eds.), Algorithmic Foundations of Robotics IX, Springer, Berlin/Heidelberg, pp. 71–87.
  • [13] Karaman, S. and Frazzoli, E. (2011b). Sampling-based algorithms for optimal motion planning, International Journal of Robotics Research 30(7): 846–894.
  • [14] Karaman, S. and Frazzoli, E. (2013). Sampling-based optimal motion planning for non-holonomic dynamical systems, IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, pp. 5041–5047.
  • [15] Karaman, S., Walter, M.R., Perez, A., Frazzoli, E. and Teller, S. (2011). Anytime motion planning using the RRT*, IEEE International Conference on Robotics and Automation, Shanghai, China, pp. 1478–1483.
  • [16] Kirk, D.E. (2012). Optimal Control Theory: An Introduction, Courier Corporation, Dover Publications, Inc. Mineola, NY.
  • [17] Klaučo, M., Blažek, S. and Kvasnica, M. (2016). An optimal path planning problem for heterogeneous multi-vehicle systems, International Journal of Applied Mathematics and Computer Science 26(2): 297–308, DOI: 10.1515/amcs-2016-0021.
  • [18] LaValle, S.M. (1998). Rapidly-exploring random trees: A new tool for path planning, Technical Report 98-11, Iowa State University, Ames, IO.
  • [19] LaValle, S.M. (2011). Motion planning, IEEE Robotics & Automation Magazine 18(1): 79–89.
  • [20] Lewis, F.L., Vrabie, D. and Syrmos, V.L. (1995). Optimal Control, John Wiley & Sons, New York, NY.
  • [21] Pepy, R., Kieffer, M. and Walter, E. (2009). Reliable robust path planning with application to mobile robots, International Journal of Applied Mathematics and Computer Science 19(3): 413–424, DOI: 10.2478/v10006-009-0034-2.
  • [22] Perez, A., Platt, R., Konidaris, G., Kaelbling, L. and Lozano-Perez, T. (2012). LQR-RRT*: Optimal sampling-based motion planning with automatically derived extension heuristics, IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA, pp. 2537–2542.
  • [23] Rodríguez-Liñán, M.C., Mendoza, M., Bonilla, I. and Chávez-Olivares, C.A. (2017). Saturating stiffness control of robot manipulators with bounded inputs, International Journal of Applied Mathematics and Computer Science 27(1): 79–90, DOI: 10.1515/amcs-2017-0006.
  • [24] Szynkiewicz, W. and Błaszczyk, J. (2011). Optimization-based approach to path planning for closed chain robot systems, International Journal of Applied Mathematics and Computer Science 21(4): 659–670, DOI: 10.2478/v10006-011-0052-8.
  • [25] Tang, G. (2005). Suboptimal control for nonlinear systems: A successive approximation approach, Systems & Control Letters 54(5): 429–434.
  • [26] Tedrake, R. (2009). Underactuated robotics: Learning, planning, and control for efficient and agile machines, Course Notes for MIT 6.832, MIT, Cambridge, MA, http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-832-underactuated-robotics-spring-2009/.
  • [27] Webb, D.J. and van den Berg, J. (2013). Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics, 2013 IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, pp. 5054–5061.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-963c6f20-af6a-4922-8a19-0f0523864282
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