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2008 | OriginalPaper | Chapter

5. Motion Planning

Authors : Lydia E. Kavraki, Prof, Steven M. LaValle, Prof

Published in: Springer Handbook of Robotics

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter first provides a formulation of the geometric path planning problem in Sect. 5.1 and then introduces sampling-based planning in Sect. 5.2. Sampling-based planners are general techniques applicable to a wide set of problems and have been successful in dealing with hard planning instances. For specific, often simpler, planning instances, alternative approaches exist and are presented in Sect. 5.3. These approaches provide theoretical guarantees and for simple planning instances they outperform sampling-based planners. Section 5.4 considers problems that involve differential constraints, while Sect. 5.5 overviews several other extensions of the basic problem formulation and proposed solutions. Finally, Sect. 5.7 addresses some important and more advanced topics related to motion planning.

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Literature
5.1.
go back to reference J.H. Reif: Complexity of the moverʼs problem and generalizations, IEEE Symp. Found. Comput. Sci. (1979) pp. 421–427 J.H. Reif: Complexity of the moverʼs problem and generalizations, IEEE Symp. Found. Comput. Sci. (1979) pp. 421–427
5.2.
go back to reference H.H. Gonzalez-Banos, D. Hsu, J.C. Latombe: Motion planning: Recent developments. In: Automous Mobile Robots: Sensing, Control, Decision-Making and Applications, ed. by S.S. Ge, F.L. Lewis (CRC, Boca Raton 2006) H.H. Gonzalez-Banos, D. Hsu, J.C. Latombe: Motion planning: Recent developments. In: Automous Mobile Robots: Sensing, Control, Decision-Making and Applications, ed. by S.S. Ge, F.L. Lewis (CRC, Boca Raton 2006)
5.3.
go back to reference S.R. Lindemann, S.M. LaValle: Current issues in sampling-based motion planning. In: Robotics Research: The Eleventh International Symposium, ed. by P. Dario, R. Chatila (Springer, Berlin 2005) pp. 36–54 S.R. Lindemann, S.M. LaValle: Current issues in sampling-based motion planning. In: Robotics Research: The Eleventh International Symposium, ed. by P. Dario, R. Chatila (Springer, Berlin 2005) pp. 36–54
5.4.
go back to reference J.T. Schwartz, M. Sharir: A survey of motion planning and related geometric algorithms, Artif. Intell. J. 37, 157–169 (1988)CrossRefMATHMathSciNet J.T. Schwartz, M. Sharir: A survey of motion planning and related geometric algorithms, Artif. Intell. J. 37, 157–169 (1988)CrossRefMATHMathSciNet
5.5.
go back to reference H. Choset, K.M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L.E. Kavraki, S. Thrun: Principles of Robot Motion: Theory, Algorithms, and Implementations (MIT Press, Cambridge 2005)MATH H. Choset, K.M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L.E. Kavraki, S. Thrun: Principles of Robot Motion: Theory, Algorithms, and Implementations (MIT Press, Cambridge 2005)MATH
5.6.
go back to reference J.C. Latombe: Robot Motion Planning (Kluwer, Boston 1991) J.C. Latombe: Robot Motion Planning (Kluwer, Boston 1991)
5.7.
5.8.
go back to reference S. Udupa: Collision detection and avoidance in computer controlled manipulators. Ph.D. Thesis (Dept. of Electical Engineering, California Institute of Technology 1977) S. Udupa: Collision detection and avoidance in computer controlled manipulators. Ph.D. Thesis (Dept. of Electical Engineering, California Institute of Technology 1977)
5.9.
go back to reference T. Lozano-Pérez: Spatial planning: A configuration space approach, IEEE Trans. Comput. C-32(2), 108–120 (1983)CrossRef T. Lozano-Pérez: Spatial planning: A configuration space approach, IEEE Trans. Comput. C-32(2), 108–120 (1983)CrossRef
5.10.
go back to reference J.T. Schwartz, M. Sharir: On the piano moversʼ problem: III. Coordinating the motion of several independent bodies, Int. J. Robot. Res. 2(3), 97–140 (1983)CrossRefMathSciNet J.T. Schwartz, M. Sharir: On the piano moversʼ problem: III. Coordinating the motion of several independent bodies, Int. J. Robot. Res. 2(3), 97–140 (1983)CrossRefMathSciNet
5.11.
go back to reference J.T. Schwartz, M. Sharir: On the piano moversʼ problem: V. The case of a rod moving in three-dimensional space amidst polyhedral obstacles, Commun. Pure Appl. Math. 37, 815–848 (1984)CrossRefMATHMathSciNet J.T. Schwartz, M. Sharir: On the piano moversʼ problem: V. The case of a rod moving in three-dimensional space amidst polyhedral obstacles, Commun. Pure Appl. Math. 37, 815–848 (1984)CrossRefMATHMathSciNet
5.12.
go back to reference J.F. Canny: The Complexity of Robot Motion Planning (MIT Press, Cambridge 1988) J.F. Canny: The Complexity of Robot Motion Planning (MIT Press, Cambridge 1988)
5.13.
go back to reference D. Halperin, M. Sharir: A near-quadratic algorithm for planning the motion of a polygon in a polygonal environment, Discrete Comput. Geom. 16, 121–134 (1996)CrossRefMATHMathSciNet D. Halperin, M. Sharir: A near-quadratic algorithm for planning the motion of a polygon in a polygonal environment, Discrete Comput. Geom. 16, 121–134 (1996)CrossRefMATHMathSciNet
5.14.
go back to reference J.E. Hopcroft, J.T. Schwartz, M. Sharir: On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the warehousemanʼs problem, Int. J. Robot. Res. 3(4), 76–88 (1984)CrossRef J.E. Hopcroft, J.T. Schwartz, M. Sharir: On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the warehousemanʼs problem, Int. J. Robot. Res. 3(4), 76–88 (1984)CrossRef
5.15.
go back to reference J. Canny, J. Reif: New lower bound techniques for robot motion planning problems, IEEE Symp. Found. Comput. Sci. (1987) pp. 49–60 J. Canny, J. Reif: New lower bound techniques for robot motion planning problems, IEEE Symp. Found. Comput. Sci. (1987) pp. 49–60
5.16.
go back to reference M.C. Lin, J.F. Canny: Efficient algorithms for incremental distance computation, IEEE Int. Conf. Robot. Autom. (1991) M.C. Lin, J.F. Canny: Efficient algorithms for incremental distance computation, IEEE Int. Conf. Robot. Autom. (1991)
5.17.
go back to reference P. Jiménez, F. Thomas, C. Torras: Collision detection algorithms for motion planning. In: Robot Motion Planning and Control, ed. by J.P. Laumond (Springer, Berlin 1998) pp. 1–53 P. Jiménez, F. Thomas, C. Torras: Collision detection algorithms for motion planning. In: Robot Motion Planning and Control, ed. by J.P. Laumond (Springer, Berlin 1998) pp. 1–53
5.18.
go back to reference M.C. Lin, D. Manocha: Collision and proximity queries. In: Handbook of Discrete and Computational Geometry, 2nd Ed, ed. by J.E. Goodman, J. OʼRourke (Chapman Hall/CRC, New York 2004) pp. 787–807 M.C. Lin, D. Manocha: Collision and proximity queries. In: Handbook of Discrete and Computational Geometry, 2nd Ed, ed. by J.E. Goodman, J. OʼRourke (Chapman Hall/CRC, New York 2004) pp. 787–807
5.19.
go back to reference L.E. Kavraki, P. Svestka, J.C. Latombe, M.H. Overmars: Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Trans. Robot. Autom. 12(4), 566–580 (1996)CrossRef L.E. Kavraki, P. Svestka, J.C. Latombe, M.H. Overmars: Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Trans. Robot. Autom. 12(4), 566–580 (1996)CrossRef
5.20.
go back to reference N.M. Amato, O.B. Bayazit, L.K. Dale, C. Jones, D. Vallejo: OBPRM: an obstacle-based PRM for 3D workspaces, Workshop Algorith. Found. Robot. (1998) pp. 155–168 N.M. Amato, O.B. Bayazit, L.K. Dale, C. Jones, D. Vallejo: OBPRM: an obstacle-based PRM for 3D workspaces, Workshop Algorith. Found. Robot. (1998) pp. 155–168
5.21.
go back to reference V. Boor, M.H. Overmars, A.F. van der Stappen: The Gaussian sampling strategy for probabilistic roadmap planners, IEEE Int. Conf. Robot. Autom. (1999) pp. 1018–1023 V. Boor, M.H. Overmars, A.F. van der Stappen: The Gaussian sampling strategy for probabilistic roadmap planners, IEEE Int. Conf. Robot. Autom. (1999) pp. 1018–1023
5.22.
go back to reference C. Holleman, L.E. Kavraki: A framework for using the workspace medial axis in PRM planners, IEEE Int. Conf. Robot. Autom. (2000) pp. 1408–1413 C. Holleman, L.E. Kavraki: A framework for using the workspace medial axis in PRM planners, IEEE Int. Conf. Robot. Autom. (2000) pp. 1408–1413
5.23.
go back to reference J.M. Lien, S.L. Thomas, N.M. Amato: A general framework for sampling on the medial axis of the free space, IEEE Int. Conf. Robot. Autom. (2003) J.M. Lien, S.L. Thomas, N.M. Amato: A general framework for sampling on the medial axis of the free space, IEEE Int. Conf. Robot. Autom. (2003)
5.24.
go back to reference S.M. LaValle, M.S. Branicky, S.R. Lindemann: On the relationship between classical grid search and probabilistic roadmaps, Int. J. Robot. Res. 23(7/8), 673–692 (2004)CrossRef S.M. LaValle, M.S. Branicky, S.R. Lindemann: On the relationship between classical grid search and probabilistic roadmaps, Int. J. Robot. Res. 23(7/8), 673–692 (2004)CrossRef
5.25.
go back to reference T. Siméon, J.-P. Laumond, C. Nissoux: Visibility based probabilistic roadmaps for motion planning, Adv. Robot. 14(6), 477–493 (2000)CrossRef T. Siméon, J.-P. Laumond, C. Nissoux: Visibility based probabilistic roadmaps for motion planning, Adv. Robot. 14(6), 477–493 (2000)CrossRef
5.26.
go back to reference J. Barraquand, L. Kavraki, J.-C. Latombe, T.-Y. Li, R. Motwani, P. Raghavan: A random sampling scheme for robot path planning. In: Proceedings International Symposium on Robotics Research, ed. by G. Giralt, G. Hirzinger (Springer, New York 1996) pp. 249–264 J. Barraquand, L. Kavraki, J.-C. Latombe, T.-Y. Li, R. Motwani, P. Raghavan: A random sampling scheme for robot path planning. In: Proceedings International Symposium on Robotics Research, ed. by G. Giralt, G. Hirzinger (Springer, New York 1996) pp. 249–264
5.27.
go back to reference A. Ladd, L.E. Kavraki: Measure theoretic analysis of probabilistic path planning, IEEE Trans. Robot. Autom. 20(2), 229–242 (2004)CrossRef A. Ladd, L.E. Kavraki: Measure theoretic analysis of probabilistic path planning, IEEE Trans. Robot. Autom. 20(2), 229–242 (2004)CrossRef
5.28.
go back to reference R. Geraerts, M. Overmars: Sampling techniques for probabilistic roadmap planners, Int. Conf. Intell. Auton. Syst. (2004) R. Geraerts, M. Overmars: Sampling techniques for probabilistic roadmap planners, Int. Conf. Intell. Auton. Syst. (2004)
5.29.
go back to reference D. Hsu, T. Jiang, J. Reif, Z. Sun: The bridge test for sampling narrow passages with probabilistic roadmap planners, IEEE Int. Conf. Robot. Autom. (2003) D. Hsu, T. Jiang, J. Reif, Z. Sun: The bridge test for sampling narrow passages with probabilistic roadmap planners, IEEE Int. Conf. Robot. Autom. (2003)
5.30.
go back to reference R. Bohlin, L. Kavraki: Path planning using lazy PRM, IEEE Int. Conf. Robot. Autom. (2000) R. Bohlin, L. Kavraki: Path planning using lazy PRM, IEEE Int. Conf. Robot. Autom. (2000)
5.31.
go back to reference B. Burns, O. Brock: Sampling-based motion planning using predictive models, IEEE/RSJ Int. Conf. Intell. Robot. Autom. (2005) B. Burns, O. Brock: Sampling-based motion planning using predictive models, IEEE/RSJ Int. Conf. Intell. Robot. Autom. (2005)
5.32.
go back to reference P. Isto: Constructing probabilistic roadmaps with powerful local planning and path optimization, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2002) pp. 2323–2328 P. Isto: Constructing probabilistic roadmaps with powerful local planning and path optimization, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2002) pp. 2323–2328
5.33.
go back to reference P. Leven, S.A. Hutchinson: Using manipulability to bias sampling during the construction of probabilistic roadmaps, IEEE Trans. Robot. Autom. 19(6), 1020–1026 (2003)CrossRef P. Leven, S.A. Hutchinson: Using manipulability to bias sampling during the construction of probabilistic roadmaps, IEEE Trans. Robot. Autom. 19(6), 1020–1026 (2003)CrossRef
5.34.
go back to reference D. Nieuwenhuisen, M.H. Overmars: Useful cycles in probabilistic roadmap graphs, IEEE Int. Conf. Robot. Autom. (2004) pp. 446–452 D. Nieuwenhuisen, M.H. Overmars: Useful cycles in probabilistic roadmap graphs, IEEE Int. Conf. Robot. Autom. (2004) pp. 446–452
5.35.
go back to reference S.M. LaValle, J.J. Kuffner: Rapidly-exploring random trees: progress and prospects. In: Algorithmic and Computational Robotics: New Direction, ed. by B.R. Donald, K.M. Lynch, D. Rus (A. K. Peters, Wellesley 2001) pp. 293–308 S.M. LaValle, J.J. Kuffner: Rapidly-exploring random trees: progress and prospects. In: Algorithmic and Computational Robotics: New Direction, ed. by B.R. Donald, K.M. Lynch, D. Rus (A. K. Peters, Wellesley 2001) pp. 293–308
5.36.
go back to reference K.E. Bekris, B.Y. Chen, A. Ladd, E. Plaku, L.E. Kavraki: Multiple query probabilistic roadmap planning using single query primitives, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2003) K.E. Bekris, B.Y. Chen, A. Ladd, E. Plaku, L.E. Kavraki: Multiple query probabilistic roadmap planning using single query primitives, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2003)
5.37.
go back to reference M. Strandberg: Augmenting RRT-planners with local trees, IEEE Int. Conf. Robot. Autom. (2004) pp. 3258–3262 M. Strandberg: Augmenting RRT-planners with local trees, IEEE Int. Conf. Robot. Autom. (2004) pp. 3258–3262
5.38.
go back to reference J. J. Kuffner, S. M. LaValle: An efficient approach to path planning using balanced bidirectional RRT search, Techn. Rep. CMU-RI-TR-05-34 Robotics Institute, Carnegie Mellon University, Pittsburgh (2005) J. J. Kuffner, S. M. LaValle: An efficient approach to path planning using balanced bidirectional RRT search, Techn. Rep. CMU-RI-TR-05-34 Robotics Institute, Carnegie Mellon University, Pittsburgh (2005)
5.39.
go back to reference J. Bruce, M. Veloso: Real-time randomized path planning for robot navigation, IEEE/RSJ Int. Conf. Intell. Robot. Autom. (2002) J. Bruce, M. Veloso: Real-time randomized path planning for robot navigation, IEEE/RSJ Int. Conf. Intell. Robot. Autom. (2002)
5.40.
go back to reference E. Frazzoli, M.A. Dahleh, E. Feron: Real-time motion planning for agile autonomous vehicles, AIAA J. Guid. Contr. 25(1), 116–129 (2002)CrossRef E. Frazzoli, M.A. Dahleh, E. Feron: Real-time motion planning for agile autonomous vehicles, AIAA J. Guid. Contr. 25(1), 116–129 (2002)CrossRef
5.41.
go back to reference M. Kallmann, M. Mataric: Motion planning using dynamic roadmaps, IEEE Int. Conf. Robot. Autom. (2004) M. Kallmann, M. Mataric: Motion planning using dynamic roadmaps, IEEE Int. Conf. Robot. Autom. (2004)
5.42.
go back to reference A. Yershova, L. Jaillet, T. Simeon, S.M. LaValle: Dynamic-domain RRTs: efficient exploration by controlling the sampling domain, IEEE Int. Conf. Robot. Autom. (2005) A. Yershova, L. Jaillet, T. Simeon, S.M. LaValle: Dynamic-domain RRTs: efficient exploration by controlling the sampling domain, IEEE Int. Conf. Robot. Autom. (2005)
5.43.
go back to reference D. Hsu, J.C. Latombe, R. Motwani: Path planning in expansive configuration spaces, Int. J. Comput. Geom. Appl. 4, 495–512 (1999)CrossRefMathSciNet D. Hsu, J.C. Latombe, R. Motwani: Path planning in expansive configuration spaces, Int. J. Comput. Geom. Appl. 4, 495–512 (1999)CrossRefMathSciNet
5.44.
go back to reference D. Hsu, R. Kindel, J.C. Latombe, S. Rock: Randomized kinodynamic motion planning with moving obstacles. In: Algorithmic and Computational Robotics: New Directions, ed. by B.R. Donald, K.M. Lynch, D. Rus (A.K. Peters, Wellesley 2001) D. Hsu, R. Kindel, J.C. Latombe, S. Rock: Randomized kinodynamic motion planning with moving obstacles. In: Algorithmic and Computational Robotics: New Directions, ed. by B.R. Donald, K.M. Lynch, D. Rus (A.K. Peters, Wellesley 2001)
5.45.
go back to reference G. Sánchez, J.-C. Latombe: A single-query bi-directional probabilistic roadmap planner with lazy collision checking, ISRR Int. Symp. Robot. Res. (2001) G. Sánchez, J.-C. Latombe: A single-query bi-directional probabilistic roadmap planner with lazy collision checking, ISRR Int. Symp. Robot. Res. (2001)
5.46.
go back to reference S. Carpin, G. Pillonetto: Robot motion planning using adaptive random walks, IEEE Int. Conf. Robot. Autom. (2003) pp. 3809–3814 S. Carpin, G. Pillonetto: Robot motion planning using adaptive random walks, IEEE Int. Conf. Robot. Autom. (2003) pp. 3809–3814
5.47.
go back to reference A. Ladd, L.E. Kavraki: Fast exploration for robots with dynamics, Workshop Algorithm. Found. Robot. (Zeist, Amsterdam 2004) A. Ladd, L.E. Kavraki: Fast exploration for robots with dynamics, Workshop Algorithm. Found. Robot. (Zeist, Amsterdam 2004)
5.48.
go back to reference K.E. Bekris, L.E. Kavraki: Greedy but safe replanning under differential constraints, IEEE Int. Conf. Robot. Autom. (2007) K.E. Bekris, L.E. Kavraki: Greedy but safe replanning under differential constraints, IEEE Int. Conf. Robot. Autom. (2007)
5.49.
go back to reference C. OʼDunlaing, C.K. Yap: A retraction method for planning the motion of a disc, J. Algorithms 6, 104–111 (1982)CrossRefMathSciNet C. OʼDunlaing, C.K. Yap: A retraction method for planning the motion of a disc, J. Algorithms 6, 104–111 (1982)CrossRefMathSciNet
5.50.
go back to reference D. Leven, M. Sharir: Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams, Discrete Comput. Geom. 2, 9–31 (1987)CrossRefMATHMathSciNet D. Leven, M. Sharir: Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams, Discrete Comput. Geom. 2, 9–31 (1987)CrossRefMATHMathSciNet
5.51.
go back to reference M. Sharir: Algorithmic motion planning. In: Handbook of Discrete and Computational Geometry, 2nd edn., ed. by J. E. Goodman, J. OʼRourke (Chapman Hall/CRC Press, New York 2004) pp. 1037–1064 M. Sharir: Algorithmic motion planning. In: Handbook of Discrete and Computational Geometry, 2nd edn., ed. by J. E. Goodman, J. OʼRourke (Chapman Hall/CRC Press, New York 2004) pp. 1037–1064
5.52.
go back to reference N.J. Nilsson: A mobile automaton: An application of artificial intelligence techniques, 1st Int. Conf. Artif. Intell. (1969) pp. 509–520 N.J. Nilsson: A mobile automaton: An application of artificial intelligence techniques, 1st Int. Conf. Artif. Intell. (1969) pp. 509–520
5.53.
go back to reference J. OʼRourke: Visibility. In: Handbook of Discrete and Computational Geometry, 2nd edn., ed. by J. E. Goodman, J. OʼRourke (Chapman Hall/CRC Press, New York 2004) pp. 643–663 J. OʼRourke: Visibility. In: Handbook of Discrete and Computational Geometry, 2nd edn., ed. by J. E. Goodman, J. OʼRourke (Chapman Hall/CRC Press, New York 2004) pp. 643–663
5.54.
go back to reference B. Chazelle: Approximation and decomposition of shapes. In: Algorithmic and Geometric Aspects of Robotics, ed. by J.T. Schwartz, C.K. Yap (Lawrence Erlbaum, Hillsdale 1987) pp. 145–185 B. Chazelle: Approximation and decomposition of shapes. In: Algorithmic and Geometric Aspects of Robotics, ed. by J.T. Schwartz, C.K. Yap (Lawrence Erlbaum, Hillsdale 1987) pp. 145–185
5.55.
go back to reference M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf: Computational Geometry: Algorithms and Applications, 2nd edn. (Springer, Berlin 2000)MATH M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf: Computational Geometry: Algorithms and Applications, 2nd edn. (Springer, Berlin 2000)MATH
5.56.
go back to reference J.M. Keil: Polygon decomposition. In: Handbook on Computational Geometry, ed. by J.R. Sack, J. Urrutia (Elsevier, New York 2000) J.M. Keil: Polygon decomposition. In: Handbook on Computational Geometry, ed. by J.R. Sack, J. Urrutia (Elsevier, New York 2000)
5.57.
go back to reference J.T. Schwartz, M. Sharir: On the piano moversʼ problem: I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers, Commun. Pure Appl. Math. 36, 345–398 (1983)CrossRefMATHMathSciNet J.T. Schwartz, M. Sharir: On the piano moversʼ problem: I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers, Commun. Pure Appl. Math. 36, 345–398 (1983)CrossRefMATHMathSciNet
5.58.
go back to reference O. Khatib: Real-time obstacle avoidance for manipulators and mobile robots, Int. J. Robot. Res. 5(1), 90–98 (1986)CrossRefMathSciNet O. Khatib: Real-time obstacle avoidance for manipulators and mobile robots, Int. J. Robot. Res. 5(1), 90–98 (1986)CrossRefMathSciNet
5.59.
go back to reference J. Barraquand, J.-C. Latombe: Robot motion planning: A distributed representation approach, Int. J. Robot. Res. 10(6), 628–649 (1991)CrossRef J. Barraquand, J.-C. Latombe: Robot motion planning: A distributed representation approach, Int. J. Robot. Res. 10(6), 628–649 (1991)CrossRef
5.60.
go back to reference E. Rimon, D.E. Koditschek: Exact robot navigation using artificial potential fields, IEEE Trans. Robot. Autom. 8(5), 501–518 (1992)CrossRef E. Rimon, D.E. Koditschek: Exact robot navigation using artificial potential fields, IEEE Trans. Robot. Autom. 8(5), 501–518 (1992)CrossRef
5.61.
go back to reference J.P. Laumond: Trajectories for mobile robots with kinematic and environment constraints, Int. Conf. Intell. Auton. Syst. (1986) pp. 346–354 J.P. Laumond: Trajectories for mobile robots with kinematic and environment constraints, Int. Conf. Intell. Auton. Syst. (1986) pp. 346–354
5.62.
go back to reference J.P. Laumond, S. Sekhavat, F. Lamiraux: Guidelines in nonholonomic motion planning for mobile robots. In: Robot Motion Planning and Control, ed. by J.P. Laumond (Springer, Berlin 1998) pp. 1–53CrossRef J.P. Laumond, S. Sekhavat, F. Lamiraux: Guidelines in nonholonomic motion planning for mobile robots. In: Robot Motion Planning and Control, ed. by J.P. Laumond (Springer, Berlin 1998) pp. 1–53CrossRef
5.65.
go back to reference J. Canny, A. Rege, J. Reif: An exact algorithm for kinodynamic planning in the plane, Discrete Comput. Geom. 6, 461–484 (1991)CrossRefMATHMathSciNet J. Canny, A. Rege, J. Reif: An exact algorithm for kinodynamic planning in the plane, Discrete Comput. Geom. 6, 461–484 (1991)CrossRefMATHMathSciNet
5.66.
go back to reference J. Go, T. Vu, J.J. Kuffner: Autonomous behaviors for interactive vehicle animations, SIGGRAPH Symp. Comput. Animat. (2004) J. Go, T. Vu, J.J. Kuffner: Autonomous behaviors for interactive vehicle animations, SIGGRAPH Symp. Comput. Animat. (2004)
5.67.
go back to reference M. Pivtoraiko, A. Kelly: Generating near minimal spanning control sets for constrained motion planning in discrete state spaces, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2005) M. Pivtoraiko, A. Kelly: Generating near minimal spanning control sets for constrained motion planning in discrete state spaces, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2005)
5.68.
go back to reference J. Hollerbach: Dynamic scaling of manipulator trajectories, Tech. Rep. 700 (MIT A.I. Lab Memo, 1983) J. Hollerbach: Dynamic scaling of manipulator trajectories, Tech. Rep. 700 (MIT A.I. Lab Memo, 1983)
5.69.
go back to reference K.G. Shin, N.D. McKay: Minimum-time control of robot manipulators with geometric path constraints, IEEE Trans. Autom. Contr. 30(6), 531–541 (1985)CrossRefMATH K.G. Shin, N.D. McKay: Minimum-time control of robot manipulators with geometric path constraints, IEEE Trans. Autom. Contr. 30(6), 531–541 (1985)CrossRefMATH
5.70.
go back to reference K.G. Shin, N.D. McKay: A dynamic programming approach to trajectory planning of robotic manipulators, IEEE Trans. Autom. Contr. 31(6), 491–500 (1986)CrossRefMATH K.G. Shin, N.D. McKay: A dynamic programming approach to trajectory planning of robotic manipulators, IEEE Trans. Autom. Contr. 31(6), 491–500 (1986)CrossRefMATH
5.71.
go back to reference S. Sastry: Nonlinear Systems: Analysis, Stability, and Control (Springer, Berlin 1999)MATH S. Sastry: Nonlinear Systems: Analysis, Stability, and Control (Springer, Berlin 1999)MATH
5.72.
go back to reference D.J. Balkcom, M.T. Mason: Time optimal trajectories for bounded velocity differential drive vehicles, Int. J. Robot. Res. 21(3), 199–217 (2002)CrossRef D.J. Balkcom, M.T. Mason: Time optimal trajectories for bounded velocity differential drive vehicles, Int. J. Robot. Res. 21(3), 199–217 (2002)CrossRef
5.73.
go back to reference P. Souères, J.-D. Boissonnat: Optimal trajectories for nonholonomic mobile robots. In: Robot Motion Planning and Control, ed. by J.P. Laumond (Springer, Berlin 1998) pp. 93–169CrossRef P. Souères, J.-D. Boissonnat: Optimal trajectories for nonholonomic mobile robots. In: Robot Motion Planning and Control, ed. by J.P. Laumond (Springer, Berlin 1998) pp. 93–169CrossRef
5.74.
go back to reference P. Svestka, M.H. Overmars: Coordinated motion planning for multiple car-like robots using probabilistic roadmaps, IEEE Int. Conf. Robot. Autom. (1995) pp. 1631–1636 P. Svestka, M.H. Overmars: Coordinated motion planning for multiple car-like robots using probabilistic roadmaps, IEEE Int. Conf. Robot. Autom. (1995) pp. 1631–1636
5.75.
go back to reference S. Sekhavat, P. Svestka, J.-P. Laumond, M.H. Overmars: Multilevel path planning for nonholonomic robots using semiholonomic subsystems, Int. J. Robot. Res. 17, 840–857 (1998)CrossRef S. Sekhavat, P. Svestka, J.-P. Laumond, M.H. Overmars: Multilevel path planning for nonholonomic robots using semiholonomic subsystems, Int. J. Robot. Res. 17, 840–857 (1998)CrossRef
5.76.
go back to reference P. Ferbach: A method of progressive constraints for nonholonomic motion planning, IEEE Int. Conf. Robot. Autom. (1996) pp. 2949–2955 P. Ferbach: A method of progressive constraints for nonholonomic motion planning, IEEE Int. Conf. Robot. Autom. (1996) pp. 2949–2955
5.77.
go back to reference S. Pancanti, L. Pallottino, D. Salvadorini, A. Bicchi: Motion planning through symbols and lattices, IEEE Int. Conf. Robot. Autom. (2004) pp. 3914–3919 S. Pancanti, L. Pallottino, D. Salvadorini, A. Bicchi: Motion planning through symbols and lattices, IEEE Int. Conf. Robot. Autom. (2004) pp. 3914–3919
5.78.
go back to reference J. Barraquand, J.-C. Latombe: Nonholonomic multibody mobile robots: controllability and motion planning in the presence of obstacles, Algorithmica 10, 121–155 (1993)CrossRefMATHMathSciNet J. Barraquand, J.-C. Latombe: Nonholonomic multibody mobile robots: controllability and motion planning in the presence of obstacles, Algorithmica 10, 121–155 (1993)CrossRefMATHMathSciNet
5.79.
go back to reference S.M. LaValle, J.J. Kuffner: Randomized kinodynamic planning, IEEE Int. Conf. Robot. Autom. (1999) pp. 473–479 S.M. LaValle, J.J. Kuffner: Randomized kinodynamic planning, IEEE Int. Conf. Robot. Autom. (1999) pp. 473–479
5.80.
go back to reference A. M. Ladd, L. E. Kavraki: Motion planning in the presence of drift underactuation and discrete system changes. In: Robotics: Science and Systems I ed. by (MIT Press, Boston 2005) pp. 233–241 A. M. Ladd, L. E. Kavraki: Motion planning in the presence of drift underactuation and discrete system changes. In: Robotics: Science and Systems I ed. by (MIT Press, Boston 2005) pp. 233–241
5.81.
5.82.
go back to reference D. Cox, J. Little, D. OʼShea: Ideals, Varieties, and Algorithms (Springer, Berlin 1992)MATH D. Cox, J. Little, D. OʼShea: Ideals, Varieties, and Algorithms (Springer, Berlin 1992)MATH
5.83.
go back to reference R.J. Milgram, J.C. Trinkle: The geometry of configuration spaces for closed chains in two and three dimensions, Homol. Homot. Appl. 6(1), 237–267 (2004)MATHMathSciNet R.J. Milgram, J.C. Trinkle: The geometry of configuration spaces for closed chains in two and three dimensions, Homol. Homot. Appl. 6(1), 237–267 (2004)MATHMathSciNet
5.84.
go back to reference J. Yakey, S.M. LaValle, L.E. Kavraki: Randomized path planning for linkages with closed kinematic chains, IEEE Trans. Robot. Autom. 17(6), 951–958 (2001)CrossRef J. Yakey, S.M. LaValle, L.E. Kavraki: Randomized path planning for linkages with closed kinematic chains, IEEE Trans. Robot. Autom. 17(6), 951–958 (2001)CrossRef
5.85.
go back to reference L. Han, N.M. Amato: A kinematics-based probabilistic roadmap method for closed chain systems. In: Algorithmic and Computational Robotics: New Directions, ed. by B.R. Donald, K.M. Lynch, D. Rus (A.K. Peters, Wellesley 2001) pp. 233–246 L. Han, N.M. Amato: A kinematics-based probabilistic roadmap method for closed chain systems. In: Algorithmic and Computational Robotics: New Directions, ed. by B.R. Donald, K.M. Lynch, D. Rus (A.K. Peters, Wellesley 2001) pp. 233–246
5.86.
go back to reference J. Cortés: Motion Planning Algorithms for General Closed-Chain Mechanisms. Ph.D. Thesis (Institut National Polytechnique do Toulouse, Toulouse 2003) J. Cortés: Motion Planning Algorithms for General Closed-Chain Mechanisms. Ph.D. Thesis (Institut National Polytechnique do Toulouse, Toulouse 2003)
5.87.
go back to reference R. Alami, J.-P. Laumond, T. Siméon: Two manipulation planning algorithms. In: Algorithms for Robotic Motion and Manipulation, ed. by J.P. Laumond, M. Overmars (A.K. Peters, Wellesley 1997) R. Alami, J.-P. Laumond, T. Siméon: Two manipulation planning algorithms. In: Algorithms for Robotic Motion and Manipulation, ed. by J.P. Laumond, M. Overmars (A.K. Peters, Wellesley 1997)
5.88.
go back to reference L.E. Kavraki, M. Kolountzakis: Partitioning a planar assembly into two connected parts is NP-complete, Inform. Process. Lett. 55(3), 159–165 (1995)CrossRefMATHMathSciNet L.E. Kavraki, M. Kolountzakis: Partitioning a planar assembly into two connected parts is NP-complete, Inform. Process. Lett. 55(3), 159–165 (1995)CrossRefMATHMathSciNet
5.89.
go back to reference M.T. Mason: Mechanics of Robotic Manipulation (MIT Press, Cambridge 2001) M.T. Mason: Mechanics of Robotic Manipulation (MIT Press, Cambridge 2001)
5.91.
go back to reference J.H. Reif, M. Sharir: Motion planning in the presence of moving obstacles, J. ACM 41, 764–790 (1994)CrossRefMATH J.H. Reif, M. Sharir: Motion planning in the presence of moving obstacles, J. ACM 41, 764–790 (1994)CrossRefMATH
5.93.
go back to reference J. van den Berg, M. Overmars: Prioritized motion planning for multiple robots, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2005) pp. 2217–2222 J. van den Berg, M. Overmars: Prioritized motion planning for multiple robots, IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2005) pp. 2217–2222
5.94.
go back to reference T. Siméon, S. Leroy, J.-P. Laumond: Path coordination for multiple mobile robots: A resolution complete algorithm, IEEE Trans. Robot. Autom. 18(1), 42–49 (2002)CrossRef T. Siméon, S. Leroy, J.-P. Laumond: Path coordination for multiple mobile robots: A resolution complete algorithm, IEEE Trans. Robot. Autom. 18(1), 42–49 (2002)CrossRef
5.95.
go back to reference R. Ghrist, J.M. OʼKane, S.M. LaValle: Pareto optimal coordination on roadmaps, Workshop Algorithm. Found. Robot. (2004) pp. 185–200 R. Ghrist, J.M. OʼKane, S.M. LaValle: Pareto optimal coordination on roadmaps, Workshop Algorithm. Found. Robot. (2004) pp. 185–200
5.96.
go back to reference S.M. LaValle, S.A. Hutchinson: Optimal motion planning for multiple robots having independent goals, IEEE Trans. Robot. Autom. 14(6), 912–925 (1998)CrossRef S.M. LaValle, S.A. Hutchinson: Optimal motion planning for multiple robots having independent goals, IEEE Trans. Robot. Autom. 14(6), 912–925 (1998)CrossRef
5.97.
go back to reference W.M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd edn. (Academic, New York 2003) W.M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd edn. (Academic, New York 2003)
5.98.
go back to reference A. Hatcher: Algebraic Topology (Cambridge Univ Press, Cambridge 2002)MATH A. Hatcher: Algebraic Topology (Cambridge Univ Press, Cambridge 2002)MATH
5.99.
go back to reference G.S. Chirikjian, A.B. Kyatkin: Engineering Applications of Noncommutative Harmonic Analysis (CRC, Boca Raton 2001)MATH G.S. Chirikjian, A.B. Kyatkin: Engineering Applications of Noncommutative Harmonic Analysis (CRC, Boca Raton 2001)MATH
5.100.
go back to reference J. Arvo: Fast random rotation matrices. In: Graphics Gems III, ed. by D. Kirk (Academic, New York 1992) pp. 117–120 J. Arvo: Fast random rotation matrices. In: Graphics Gems III, ed. by D. Kirk (Academic, New York 1992) pp. 117–120
5.101.
go back to reference H. Niederreiter: Random Number Generation and Quasi-Monte-Carlo Methods (Society for Industrial and Applied Mathematics, Philadelphia 1992)MATH H. Niederreiter: Random Number Generation and Quasi-Monte-Carlo Methods (Society for Industrial and Applied Mathematics, Philadelphia 1992)MATH
5.102.
go back to reference S. Basu, R. Pollack, M.-F. Roy: Algorithms in Real Algebraic Geometry (Springer, Berlin 2003)MATH S. Basu, R. Pollack, M.-F. Roy: Algorithms in Real Algebraic Geometry (Springer, Berlin 2003)MATH
5.103.
go back to reference B. Mishra: Computational real algebraic geometry. In: Handbook of Discrete and Computational Geometry, ed. by J.E. Goodman, J. OʼRourke (CRC, New York 1997) pp. 537–556 B. Mishra: Computational real algebraic geometry. In: Handbook of Discrete and Computational Geometry, ed. by J.E. Goodman, J. OʼRourke (CRC, New York 1997) pp. 537–556
5.104.
go back to reference J.T. Schwartz, M. Sharir: On the piano moversʼ problem: II. General techniques for computing topological properties of algebraic manifolds, Commun. Pure Appl. Math. 36, 345–398 (1983)CrossRefMATHMathSciNet J.T. Schwartz, M. Sharir: On the piano moversʼ problem: II. General techniques for computing topological properties of algebraic manifolds, Commun. Pure Appl. Math. 36, 345–398 (1983)CrossRefMATHMathSciNet
5.105.
go back to reference B.R. Donald: A search algorithm for motion planning with six degrees of freedom, Artif. Intell. J. 31, 295–353 (1987)CrossRefMATH B.R. Donald: A search algorithm for motion planning with six degrees of freedom, Artif. Intell. J. 31, 295–353 (1987)CrossRefMATH
5.107.
go back to reference G.E. Collins: Quantifier elimination by cylindrical algebraic decomposition–twenty years of progress. In: Quantifier Elimination and Cylindrical Algebraic Decomposition, ed. by B.F. Caviness, J.R. Johnson (Springer, Berlin 1998) pp. 8–23 G.E. Collins: Quantifier elimination by cylindrical algebraic decomposition–twenty years of progress. In: Quantifier Elimination and Cylindrical Algebraic Decomposition, ed. by B.F. Caviness, J.R. Johnson (Springer, Berlin 1998) pp. 8–23
Metadata
Title
Motion Planning
Authors
Lydia E. Kavraki, Prof
Steven M. LaValle, Prof
Copyright Year
2008
DOI
https://doi.org/10.1007/978-3-540-30301-5_6