Abstract
Path planning and trajectory planning are crucial issues in the field of Robotics and, more generally, in the field of Automation. Indeed, the trend for robots and automatic machines is to operate at increasingly high speed, in order to achieve shorter production times. The high operating speed may hinder the accuracy and repeatability of the robot motion, since extreme performances are required from the actuators and the control system. Therefore, particular care should be put in generating a trajectory that could be executed at high speed, but at the same time harmless for the robot, in terms of avoiding excessive accelerations of the actuators and vibrations of the mechanical structure. Such a trajectory is defined as smooth. For such reasons, path planning and trajectory planning algorithms assume an increasing significance in robotics. Path planning algorithms generate a geometric path, from an initial to a final point, passing through pre-defined via-points, either in the joint space or in the operating space of the robot, while trajectory planning algorithms take a given geometric path and endow it with the time information. Trajectory planning algorithms are crucial in Robotics, because defining the times of passage at the via-points influences not only the kinematic properties of the motion, but also the dynamic ones. Namely, the inertial forces (and torques), to which the robot is subjected, depend on the accelerations along the trajectory, while the vibrations of its mechanical structure are basically determined by the values of the jerk (i.e. the derivative of the acceleration). Path planning algorithms are usually divided according to the methodologies used to generate the geometric path, namely:
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roadmap techniques
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cell decomposition algorithms
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artificial potential methods.
The algorithms for trajectory planning are usually named by the function that is optimized, namely:
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minimum time
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minimum energy
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minimum jerk.
Examples of hybrid algorithms, which optimize more than a single function, are also found in the scientific literature. In this chapter, the general problem of path planning and trajectory planning will be addressed, and an extended overview of the algorithms belonging to the categories mentioned above will be carried out, with references to the numerous contributions to this field.
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References
Amato NM, Wu Y (1996) A randomized roadmap method for path and manipulation planning. In: Proceedings of the 1996 IEEE international conference on robotics and automation, pp 113–120
Balkan T (1998) A dynamic programming approach to optimal control of robotic manipulators. Mech Res Commun 25(2):225–230
Bamdad M (2013) Time-energy optimal trajectory planning of cable-suspended manipulators. Cable-driven parallel robots. Springer, Berlin, pp 41–51
Barnett E, Gosselin C (2013) Time-optimal trajectory planning of cable-driven parallel mechanisms for fully-specified paths with g1 discontinuities. In: ASME 2013 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers
Barraquand J, Latombe JC (1991) Robot motion planning: a distributed representation approach. Int J Robot Res 10(6):628–649
Barre PJ, Bearee R, Borne P, Dumetz E (2005) Influence of a jerk controlled movement law on the vibratory behaviour of high-dynamics systems. J Intell Robot Syst 42(3):275–293
Bobrow JE, Dubowsky S, Gibson JS (1985) Time-optimal control of robotic manipulators along specified paths. Int J Robot Res 4(3):554–561
Bobrow JE, Martin BJ, Sohl G, Wang EC, Kim J (2001) Optimal robot motion for physical criteria. J Robot Syst 18(12):785–795
Boscariol P, Gasparetto A, Lanzutti A, Vidoni R, Zanotto V (2011) Experimental validation of minimum time-jerk algorithms for industrial robots. J Intell Robot Syst 64(2):197–219
Boscariol P, Gasparetto A (2013) Model-based trajectory planning for flexible link mechanisms with bounded jerk. Robot Comput Integr Manuf 29(4):90–99
Boscariol P, Gasparetto A, Vidoni R (2012) Jerk-continous trajectories for cyclic tasks. In: Proceedings of the ASME 2012 international design engineering technical conferences (IDETC), pp 1–10
Boscariol P, Gasparetto A, Vidoni R (2012) Planning continuous-jerk trajectories for industrial manipulators. In: Proceedings of the ESDA 2012 11th biennial conference on engineering system design and analysis, pp 1–10
Boscariol P, Gasparetto A, Vidoni R (2013) Robust trajectory planning for flexible robots. In: Proceedings of the 2013 ECCOMAS multibody dynamics conference, pp 293–294
Boscariol P, Gasparetto A, Vidoni R, Romano A (2013) A model-based trajectory planning approach for flexible-link mechanisms. In: Proceedings of the ICM 2013—IEEE international conference on mechatronics, pp 1–6
Canny J, Donald B (1988) Simplified voronoi diagrams. Discret Comput Geom 3(1):219–236
Cao B, Dodds GI (1994) Time-optimal and smooth constrained path planning for robot manipulators. In: Proceedings of the 1994 IEEE international conference on robotics and automation, pp 1853–1858
Carbone G, Ceccarelli M, Oliveira PJ, Saramago SF, Carvalho JCM (2008) An optimum path planning for Cassino parallel manipulator by using inverse dynamics. Robotica 26(2):229–239
Caselli S, Reggiani M (2000) ERPP: an experience-based randomized path planner. In: Proceedings of the ICRA’00—IEEE international conference on robotics and automation, pp 1002–1008
Caselli S, Reggiani M, Rocchi R (2001) Heuristic methods for randomized path planning in potential fields. In: Proceedings of the 2001 IEEE international symposium on computational intelligence in robotics and automation, pp 426–431
Caselli S, Reggiani M, Sbravati R (2002) Parallel path planning with multiple evasion strategies. In: Proceedings of the ICRA’02—IEEE international conference on robotics and automation, pp 260–266
Chen CT, Liao TT (2011) A hybrid strategy for the time-and energy-efficient trajectory planning of parallel platform manipulators. Robot Comput-Integr Manuf 27(1):72–81
Chen CT, Pham HV (2012) Trajectory planning in parallel kinematic manipulators using a constrained multi-objective evolutionary algorithm. Nonlinear Dyn 67(2):1669–1681
Choset HM, Lynch KM, Hutchinson S, Kantor GA, Burgard W, Kavraki LE, Thrun S (2005) Principles of robot motion: theory, algorithms, and implementation. MIT Press, Cambridge
Clark CM, Rock S (2001) Randomized motion planning for groups of nonholonomic robots. In: Proceedings of the 6th international symposium on artificial intelligence, robotics and automation in space, pp 1–8
Connolly CI, Burns JB (1990) Path planning using Laplace’s equation. In: Proceedings of the 1985 IEEE international conference on robotics and automation, pp 2102–2106
Constantinescu D (1998) Smooth time optimal trajectory planning for industrial manipulators. Ph.D. Thesis, The University of British Columbia, 1998
Constantinescu D, Croft EA (2000) Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J Robot Syst 17(5):233–249
Croft EA, Benhabib B, Fenton RG (1995) Near time-optimal robot motion planning for on-line applications. J Robot Syst 12(8):553–567
Donald BR, Xavier PG (1990) Provably good approximation algorithms for optimal kinodynamic planning for Cartesian robots and open chain manipulators. In: Proceedings of the sixth annual symposium on computational geometry, pp 290–300
Dong J, Ferreira PM, Stori JA (2007) Feed-rate optimization with jerk constraints for generating minimum-time trajectories. Int J Mach Tools Manuf 47(12–13):1941–1955
Dongmei X, Daokui Q, Fang X (2006) Path constrained time-optimal robot control. In: Proceedings of the international conference on robotics and biomimetics, pp 1095–1100
Fiorini P, Shiller Z (1996) Time optimal trajectory planning in dynamic environments. In: Proceedings of the 1996 IEEE international conference on robotics and automation, pp 1553–1558
Fraichard T (1999) Trajectory planning in a dynamic workspace: a state-time space approach. Adv Robot 13(1):74–94
Fraichard T, Laugier C (1993) Dynamic trajectory planning, path-velocity decomposition and adjacent paths. In: Proceedings of the 1993 international joint conference on artificial intelligence, pp 1592–1597
Garrido S, Moreno L, Lima PU (2011) Robot formation motion planning using fast marching. Robot Auton Syst 59(9):675–683
Gasparetto A, Zanotto V (2007) A new method for smooth trajectory planning of robot manipulators. Mech Mach Theor 42(4):455–471
Gasparetto A, Zanotto V (2008) A technique for time-jerk optimal planning of robot trajectories. Robot Comput-Integr Manuf 24(3):415–426
Gasparetto A, Lanzutti A, Vidoni R, Zanotto V (2012) Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning. Robot Comput-Integr Manuf 28(2):164–181
Ge SS, Cui YJ (2000) New potential functions for mobile robot path planning. IEEE Trans Robot Autom 16(5):615–620
Guarino Lo Bianco C (2001a) A semi-infinite optimization approach to optimal spline trajectory planning of mechanical manipulators. In: Goberna MA, Lopez MA (eds) Semi-infinite programming: recent advances. Springer, pp 271–297
Guarino Lo Bianco C, Piazzi A (2001b) A hybrid algorithm for infinitely constrained optimization. Int J Syst Sci 32(1):91–102
Guldner J, Utkin VI (1995) Sliding mode control for gradient tracking and robot navigation using artificial potential fields. IEEE Trans Robot Autom 11(2):247–254
Gupta K, Del Pobil AP (1998) Practical motion planning in robotics: current approaches and future directions. Wiley
Hansen C, Oltjen J, Meike D, Ortmaier T (2012) Enhanced approach for energy-efficient trajectory generation of industrial robots. In: Proceedings of the 2012 IEEE international conference on automation science and engineering (CASE 2012), pp 1–7
Hsu D, Kindel R, Latombe JC, Rock S (2002) Randomized kinodynamic motion planning with moving obstacles. Int J Robot Res 21(3):233–255
Huang P, Xu Y, Liang B (2006) Global minimum-jerk trajectory planning of space manipulator. Int J Control, Autom Syst 4(4):405–413
Ismail M, Samir L, Romdhane L (2013) Dynamic in path planning of a cable driven robot. Design and modeling of mechanical systems. Springer, Berlin, pp 11–18
Jing XJ (2008) Edited by. Motion planning, InTech
Kazemi M, Gupta K, Mehrandezh M (2010) Path-planning for visual servoing: a review and issues. Visual servoing via advanced numerical methods. Springer, London, pp 189–207
Khatib O (1985) Real-time obstacle avoidance for manipulators and mobile robots. In: Proceedings of the 1985 IEEE international conference on robotics and automation, pp 500–505
Kim JO, Khosla PK (1992) Real-time obstacle avoidance using harmonic potential functions. IEEE Trans Robot Autom 8(3):338–349
Kim J, Kim SR, Kim SJ, Kim DH (2010) A practical approach for minimum-time trajectory planning for industrial robots. Ind Robot: Int J 37(1):51–61
Koditschek DE (1992) Exact robot navigation using artificial potential functions. IEEE Trans Robot Autom 8(5):501–518
Kumar V, Zefran M, Ostrowski JP (1999) Motion planning and control of robots. In: Nof Shimon Y (ed) Handbook of industrial robotics, 2nd edn, vol 2. Wiley
Kunchev V, Jain L, Ivancevic V, Finn A (2006) Path planning and obstacle avoidance for autonomous mobile robots: a review. Knowledge-based intelligent information and engineering systems. Springer, Berlin, pp 537–544
Kyriakopoulos KJ, Saridis GN (1988) Minimum jerk path generation. In: Proceedings of the 1988 IEEE international conference on robotics and automation, pp 364–369
Latombe JC (1991) Robot motion planning. Kluwer
LaValle SM (2006) Planning algorithms. Cambridge University Press
Lin CS, Chang PR, Luh JYS (1983) Formulation and optimization of cubic polynomial joint trajectories for industrial robots. IEEE Trans Autom Control 28(12):1066–1073
Liu H, Lai X, Wu W (2013) Time-optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints. Robot Comput-Integr Manuf 29(2):309–317
Lombai F, Szederkenyi G (2008) Trajectory tracking control of a 6-degree-of-freedom robot arm using nonlinear optimization. In: Proceedings of the 10th IEEE international workshop on advanced motion control, pp 655–660
Lombai F, Szederkenyi G (2009) Throwing motion generation using nonlinear optimization on a 6-degree-of-freedom robot manipulator. In: Proceedings of the 2009 IEEE international conference on mechatronics, pp 1–6
Lozano-Pérez T, Wesley MA (1979) An algorithm for planning collision-free paths among polyhedral obstacles. Commun ACM 22(10):560–570
Lozano-Perez T (1983) Spatial planning: a configuration space approach. IEEE Trans Comput 100(2):108–120
Martin BJ, Bobrow JE (1999) Minimum effort motions for open chain manipulators with task-dependent end-effector constraints. Int J Robot Res 18(2):213–224
Nissoux C, Simon T, Latombe JC (1999) Visibility based probabilistic roadmaps. In: Proceedings of the 1999 IEEE international conference on intelligent robots and systems, pp 1316–1321
Pardo-Castellote G, Cannon RH (1996) Proximate time-optimal algorithm for on-line path parameterization and modification. In: Proceedings of the 1996 IEEE international conference on robotics and automation, pp 1539–1546
Pellicciari M, Berselli G, Leali F, Vergnano A (2013) A method for reducing the energy consumption of pick-and-place industrial robots. Mechatronics 23(3):326–334
Petrinec K, Kovacic Z (2007) Trajectory planning algorithm based on the continuity of jerk. In: Proceedings of the 2007 Mediterranean conference on control and automation, pp 1–5
Piazzi A, Visioli A (2000) Global minimum-jerk trajectory planning of robot manipulators. IEEE Trans Ind Electron 47(1):140–149
Piazzi A, Visioli A (1997b) A cutting-plane algorithm for minimum-time trajectory planning of industrial robots. In: Proceedings of the 36th Conference on decision and control, pp 1216–1218
Piazzi A, Visioli A (1997a) A global optimization approach to trajectory planning for industrial robots, In: Proceedings of the 1997 IEEE-RSJ international conference on intelligent robots and systems, pp 1553–1559
Piazzi A, Visioli A (1997c) An interval algorithm for minimum-jerk trajectory planning of robot manipulators. In: Proceedings of the 36th Conference on decision and control, pp 1924–1927
Rubio F, Valero F, Sunyer J, Cuadrado J (2012) Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints. Ind Robot Int J 39(1):92–100
Saramago SFP, Steffen V Jr (1998) Optimization of the trajectory planning of robot manipulators tacking into account the dynamics of the system. Mech Mach Theory 33(7):883–894
Saramago SFP, Steffen V Jr (2000) Optimal trajectory planning of robot manipulators in the presence of moving obstacles. Mech Mach Theory 35(8):1079–1094
Saravan R, Ramabalan R, Balamurugan C (2009) Evolutionary multi-criteria trajectory modeling of industrial robots in the presence of obstacles. Eng Appl Artif Intell 22(2):329–342
Sciavicco L, Siciliano B, Villani L, Oriolo G (2009) Robotics. Modelling, planning and control. Springer, London
Shiller Z (1996) Time-energy optimal control of articulated systems with geometric path constraints. J Dyn Syst Meas Control 118:139–143
Shin KG, McKay ND (1985) Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans Autom Control 30(6):531–541
Shin KG, McKay ND (1986) A Dynamic programming approach to trajectory planning of robotic manipulators. IEEE Trans Autom Control 31(6):491–500
Simon D (1993) The application of neural networks to optimal robot trajectory planning. Robot Auton Syst 11(1):23–34
Simon D, Isik C (1993) A trigonometric trajectory generator for robotic arms. Int J Control 57(3):505–517
Takahashi O, Schilling RJ (1989) Motion planning in a plane using generalized Voronoi diagrams. IEEE Trans Robot Autom 5(2):143–150
Tangpattanakul P, Meesomboon A, Artrit P (2010) Optimal trajectory of robot manipulator using harmony search algorithms. Recent advances in harmony search algorithm. Springer, Berlin, pp 23–36
Tangpattanakul P, Artrit P (2009) Minimum-time trajectory of robot manipulator using harmony search algorithm. In: Proceedings of the IEEE 6th international conference on ECTI-CON 2009, pp 354–357
Trevisani A (2010) Underconstrained planar cable-direct-driven robots: a trajectory planning method ensuring positive and bounded cable tensions. Mechatronics 20(1):113–127
Trevisani A (2013) Experimental validation of a trajectory planning approach avoiding cable slackness and excessive tension in underconstrained translational planar cable-driven robots. Cable-driven parallel robots. Springer, Berlin, pp 23–29
Van Dijk NJM, Van de Wouw N, Nijmeijer H, Pancras WCM (2007) Path-constrained motion planning for robotics based on kinematic constraints. In: Proceedings of the ASME 2007 international design engineering technical conference and computers and information in engineering conference, pp 1–10
Verscheure D, Demeulenaere B, Swevers J, De Schutter J, Diehl M (2008) Time-energy optimal path tracking for robots: a numerically efficient optimization approach. In: Proceedings of the 10th international workshop on advanced motion control, pp 727–732
Volpe RA (1990) Real and artificial forces in the control of manipulators: theory and experiments. The Robotics Institute, Carnegie Mellon University, Pittsburgh, 1990
Volpe RA, Khosla PK (1990) Manipulator control with superquadric artificial potential functions: theory and experiments. IEEE Trans Syst, Man, Cybern 20(6):1423–1436
Wang CH, Horng JG (1990) Constrained minimum-time path planning for robot manipulators via virtual knots of the cubic B-spline functions. IEEE Trans Autom Control 35(5):573–577
Williams RL, Gallina P (2002) Planar cable-direct-driven robots: design for wrench exertion. J Intell Robot Syst 35(2):203–219
Xu H, Zhuang J, Wang S, Zhu Z (2009) Global time-energy optimal planning of robot trajectories. In: Proceedings of the international conference on mechatronics and automation, pp 4034–4039
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Gasparetto, A., Boscariol, P., Lanzutti, A., Vidoni, R. (2015). Path Planning and Trajectory Planning Algorithms: A General Overview. In: Carbone, G., Gomez-Bravo, F. (eds) Motion and Operation Planning of Robotic Systems. Mechanisms and Machine Science, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-14705-5_1
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