52.4 Summary, References

We have presented an overview of trajectory planning and optimization methods, with a special emphasis on those relevant to industrial robotic manipulators. It appears from this overview that very efficient methods exist for planning high-quality trajectories when the environment (consisting of the robot, the obstacles, etc.) is well defined and static. A typical work flow, may integrate some of these methods as sketched in Fig. 5. The main current challenge of trajectory planning in classical factory automation lies mainly in the development of robust software, as well as practical integration into the work place.
The next major step in factory automation is to integrate the robot more tightly with human operators. For this, new methods must be developed, taking into account environments that are by nature time changing, and sometimes in an unpredictable way, because of the close, possibly physical interaction with human operators. In this context, other types of constraints and optimization objectives must also be considered, such as safety or compliance.


Fig. 5 Typical work flow as practiced in a company specialized in motion planning for industrial robots

References

Bobrow J (1988) Optimal robot plant planning using the minimum-time criterion. IEEE J Robot Autom 4(4):443–450

Bobrow J, Dubowsky S, Gibson J (1985) Time-optimal control of robotic manipulators along specified paths. Int J Robot Res 4(3):3–17

Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271

Donald B, Xavier P, Canny J, Reif J (1993) Kinodynamic motion planning. J Assoc Comput Mach 40(5):1048–1066

Geering HP, Guzzella L, Hepner SA, Onder CH (1985) Time-optimal motions of robots in assembly tasks. In: Proceedings of the 24th IEEE conference on decision and control, vol 24. IEEE, Fort Lauderdale, pp 982–989

Geraerts R, Overmars M (2007) Creating high-quality paths for motion planning. Int J Robot Res 26(8):845–863

Hart PE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 4(2):100–107

Hauser K (2013) Fast interpolation and time-optimization on implicit contact submanifolds. In: Proceedings of the robotics: science and systems, Berlin, 2013

Hauser K, Ng-Thow-Hing V (2010) Fast smoothing of manipulator trajectories using optimal bounded-acceleration shortcuts. In: Proceedings of the IEEE international conference on robotics and automation, 2010. Anchorage, pp 2493–2498

Hsu D, Kindel R, Latombe J-C, Rock S (2002) Randomized kinodynamic motion planning with moving obstacles. Int J Robot Res 21(3):233–255

Hwang YK, Ahuja N (1992) Gross motion planning – a survey. ACM Comput Surv (CSUR) 24 (3):219–291

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

Kavraki L, Svestka P, Latombe J, Overmars M (1996) Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans Robot Autom 12(4):566–580

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

Kuffner J, LaValle S (2000) RRT-connect: an efficient approach to single-query path planning. In: Proceedings of the IEEE international conference on robotics and automation, San Francisco, 2000

Kuffner J, Kagami S, Nishiwaki K, Inaba M, Inoue H (2002) Dynamically-stable motion planning for humanoid robots. Auton Robot 12(1):105–118

Kunz T, Stilman M (2012) Time-optimal trajectory generation for path following with bounded acceleration and velocity. Robot Sci Syst 8:09–13

Lavalle SM (1998) Rapidly-exploring random trees: a new tool for path planning. Technical report 98–11, Iowa State University

LaValle S (2006) Planning algorithms. Cambridge University Press, Cambridge 

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

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

Lozano-Perez T (1983) Spatial planning: a configuration space approach. IEEE Trans Comput 100 (2):108–120

Meier E-B, Ryson AE (1990) Efficient algorithm for time-optimal control of a two-link manipulator. J Guid Control Dyn 13(5):859–866

Pfeiffer F, Johanni R (1987) A concept for manipulator trajectory planning. IEEE Trans Robot Autom 3(2):115–123

Pham Q-C (2012) Planning manipulator trajectories under dynamics constraints using minimum time shortcuts. In: Proceedings of the second IFToMM ASIAN conference on mechanism and machine science, Tokyo, 2012

Pham Q-C (2013) Characterizing and addressing dynamic singularities in the time-optimal path parameterization algorithm. In: Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Tokyo, 2013

Pham Q-C, Caron S, Nakamura Y (2013) Kinodynamic planning in the configuration space via velocity interval propagation. In: Proceedings of the robotics: science and system, Berlin, 2013

Shiller Z, Dubowsky S (1989) Robot path planning with obstacles, actuator, gripper, and payload constraints. Int J Robot Res 8(6):3–18

Shiller Z, Dubowsky S (1991) On computing the global time-optimal motions of robotic manipulators in the presence of obstacles. IEEE Trans Robot Autom 7(6):785–797

Shiller Z, Gwo Y (1991) Dynamic motion planning of autonomous vehicles. IEEE Trans Robot Autom 7(2):241–249

Shiller Z, Lu H (1992) Computation of path constrained time optimal motions with dynamic singularities. J Dyn Syst Meas Control 114:34

Shin K, McKay N (1985) Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans Autom Control 30(6):531–541

Slotine J, Yang H (1989) Improving the efficiency of time-optimal path-following algorithms. IEEE Trans Robot Autom 5(1):118–124

Verscheure D, Demeulenaere B, Swevers J, De Schutter J, Diehl M (2009) Time-optimal path tracking for robots: a convex optimization approach. IEEE Trans Autom Control 54 (10):2318–2327

Yang H, Slotine J (1994) Fast algorithms for near-minimum-time control of robot manipulators. Int J Robot Res 13(6):521–532