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Automatic task scheduling optimization and collision-free path planning for multi-areas problem


Automatic task scheduling and collision-free path planning for multi-task optimization is a great challenge in various industrial applications. It is a typical coupling problem between task sequence optimization and collision-free path planning. When each task is considered as an area, the problem’s complexity and difficulty will be significantly increased. Task visited sequence, task region entry point optimization, and task switching collision-free path planning should be considered for trade-offs. This paper presents a novel automatic approach to solve task scheduling and collision-free path planning for the multi-areas problem. The proposed method decomposes the problem into two components: task sequence optimization problem and optimal collision-free path planning problem. Firstly, each task is simplified to a point based on the task equivalent center method, and then the task visited sequence is optimized based on Lin Kernighan Heuristic (LKH) algorithm and task equivalent center cost matrix. Secondly, a collision-free optimal tour obtained by performing the rubber-band algorithm (RBA) task entry point optimization and collision-free path planning. Finally, there are three major types of scenarios discussed in this paper: task planning in a complex environment, multi-task planning, and multi-mixed tasks planning in a complex environment, designed to demonstrate the proposed feasibility multi-task planning algorithm. The results show that the presented approach could find a feasible collision-free task visit tour in various complex multi-tasks planning.

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  1. 1.

    Abreu LR, Cunha JO, Prata BA, Framinan JM (2019) A genetic algorithm for scheduling open shops with sequence-dependent setup times. Comput Oper Res.

    Article  MATH  Google Scholar 

  2. 2.

    Alatartsev S, Belov A, Nykolaichuk M, Ortmeier F (2015a) Robot trajectory optimization for the relaxed end-effector path. In: International Conference on Informatics in Control

  3. 3.

    Alatartsev S, Mersheeva V, Augustine M, Ortmeier F (2013) On optimizing a sequence of robotic tasks. In: IEEE/RSJ international conference on intelligent robots and systems (IROS). IEEE, pp 217–223

  4. 4.

    Alatartsev S, Ortmeier F (2014) Improving the sequence of robotic tasks with freedom of execution. In: 2014 IEEE/RSJ international conference on intelligent robots and systems. IEEE, pp 4503–4510

  5. 5.

    Alatartsev S, Stellmacher S, Ortmeier F (2015) Robotic task sequencing problem: a survey. J Intell Rob Syst 80(2):279–298

    Article  Google Scholar 

  6. 6.

    Applegate DL, Bixby RE, Chvatal V, Cook WJ (2006) The traveling salesman problem: a computational study. Princeton University Press.

  7. 7.

    Bays MJ, Wettergren TA (2017) Service agent–transport agent task planning incorporating robust scheduling techniques. Robot Autonom Syst 89:15–26

    Article  Google Scholar 

  8. 8.

    Best G, Faigl J, Fitch R (2016) Multi-robot path planning for budgeted active perception with self-organising maps. In: IEEE/RSJ International conference on intelligent robots and systems (IROS). IEEE, pp 3164–3171

  9. 9.

    Best G, Faigl J, Fitch RJAR (2018) Online planning for multi-robot active perception with self-organising maps 42(4):715–738

    Google Scholar 

  10. 10.

    Eskandari L, Jafarian A, Rahimloo P, Baleanu D (2019) A modified and enhanced ant colony optimization algorithm for traveling salesman problem. In: Mathematical methods in engineering. Springer, pp 257–265.

  11. 11.

    Esposito JM, Wright JNJTIJORR (2019) Matrix completion as a post-processing technique for probabilistic roadmaps. IJRR 38:388–400

    Google Scholar 

  12. 12.

    Faigl J, Pěnička R, Best G (2016) Self-organizing map-based solution for the orienteering problem with neighborhoods. In: IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, pp 001315–001321

  13. 13.

    Faigl J, Vonásek V, Preucil L (2011) A multi-goal path planning for goal regions in the polygonal domain. In: ECMR, 2011. pp 171–176

  14. 14.

    Gammell JD, Srinivasa SS, Barfoot TD (2014) Informed RRT*: Optimal sampling-based path planning focused via direct sampling of an admissible ellipsoidal heuristic. In: 2014 IEEE/RSJ international conference on intelligent robots and systems, 2014. IEEE, pp. 2997–3004

  15. 15.

    Gao W, Tang Q, Yao J, Yang Y, Yu D (2018) Heuristic bidirectional fast marching tree for optimal motion planning. In: 2018 3rd Asia-Pacific conference on intelligent robot systems (ACIRS). IEEE, pp 71–77

  16. 16.

    Gentilini I, Margot F, Shimada K (2013) The travelling salesman problem with neighbourhoods: MINLP solution. Optimization Methods and Software 28(2):364–378

    MathSciNet  Article  Google Scholar 

  17. 17.

    Gombolay MC, Wilcox RJ, Shah JA (2018) Fast scheduling of robot teams performing tasks with temporospatial constraints. IEEE Trans Rob 34(1):220–239

    Article  Google Scholar 

  18. 18.

    Hart PE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science & Cybernetics 4(2):100–107

    Article  Google Scholar 

  19. 19.

    Helo P, Phuong D, Hao Y (2019) Cloud manufacturing–scheduling as a service for sheet metal manufacturing. Comput Oper Res 110:208–219

    MathSciNet  Article  Google Scholar 

  20. 20.

    Helsgaun KJE (2000) An effective implementation of the Lin-Kernighan traveling salesman heuristic. JoOR 126(1):106–130

    MathSciNet  MATH  Google Scholar 

  21. 21.

    Hong X, Yuan L, Kaifu Z, Jianfeng Y, Zhenxing L, Jianbin S (2010) Multi-objective optimization method for automatic drilling and riveting sequence planning. Chin J Aeronaut 23(6):734–742

    Article  Google Scholar 

  22. 22.

    Janson L, Schmerling E, Clark A, Pavone M (2015) Fast marching tree: a fast marching sampling-based method for optimal motion planning in many dimensions. Int J Robot Res 34(7):883–921

    Article  Google Scholar 

  23. 23.

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

    Article  Google Scholar 

  24. 24.

    Kavraki L, Svestka P, Overmars MH (1994) Probabilistic roadmaps for path planning in high-dimensional configuration spaces, vol 1994. Unknown Publisher.

  25. 25.

    Kolakowska E, Smith SF, Kristiansen M (2014) Constraint optimization model of a scheduling problem for a robotic arm in automatic systems. Robot Auton Syst 62(2):267–280

    Article  Google Scholar 

  26. 26.

    Kothari, R., Ghosh, D. J. C., & Research, O (2013) Insertion based Lin-Kernighan heuristic for single row facility layout 40(1):129–136

    Google Scholar 

  27. 27.

    Kurtser P, Edan Y (2020) Planning the sequence of tasks for harvesting robots. Robot Autonom Syst 103591

  28. 28.

    Li J, Deng G, Luo C, Lin Q, Zhong M (2016) A Hybrid Path Planning Method in Unmanned Air/Ground Vehicle (UAV/UGV) Cooperative Systems. IEEE Trans Vehic Technol 99:1

    Google Scholar 

  29. 29.

    Liu Y, Bucknall R (2018) Efficient multi-task allocation and path planning for unmanned surface vehicle in support of ocean operations. Neurocomputing 275:S092523121731617X

    Google Scholar 

  30. 30.

    Liu Y, Xu X, Zhang L, Wang L, Zhong RY (2017) Workload-based multi-task scheduling in cloud manufacturing. Robotics and Computer-Integrated Manufacturing 45:3–20

    Article  Google Scholar 

  31. 31.

    Lopes TC, Sikora CGS, Molina RG, Schibelbain D, Rodrigues LC, Magatão L (2017) Balancing a robotic spot welding manufacturing line: an industrial case study. Eur J Oper Res 263(3):1033–1048

    Article  Google Scholar 

  32. 32.

    Mohammed MA, Ghani MKA, Hamed RI, Mostafa SA, Ahmad MS, Ibrahim DA (2017) Solving vehicle routing problem by using improved genetic algorithm for optimal solution. J Comput Sci 21:255–262

    Article  Google Scholar 

  33. 33.

    Nasir J, Islam F, Malik U, Ayaz Y, Hasan O, Khan M, et al (2013) RRT*-SMART: A rapid convergence implementation of RRT. 10(7):299.

  34. 34.

    Song G, Miller S, Amato NM (2001) Customizing PRM roadmaps at query time. In: Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation, 2001, vol 25. IEEE, pp 1500–150

  35. 35.

    Suárez-Ruiz F, Lembono TS, Pham Q-C (2018) Robotsp–a fast solution to the robotic task sequencing problem. In: IEEE international conference on robotics and automation (ICRA). IEEE, pp 1611–1616

  36. 36.

    Tong G, Jiang N, Biyue L, Xi Z, Ya W, Wenbo D (2020) UAV navigation in high dynamic environments: A deep reinforcement learning approach. Chin. J Aeronaut

  37. 37.

    Váňa P, Sláma J, Faigl J (2018) The Dubins traveling salesman problem with neighborhoods in the three-dimensional space. In: IEEE international conference on robotics and automation (ICRA). IEEE, pp 374–379

  38. 38.

    Vitolo F, Franciosa P, Ceglarek D, Patalano S, De Martino MA (2019) Generalised multi-attribute task sequencing approach for robotics optical inspection systems. In 2019 II workshop on metrology for industry 4.0 and IoT (MetroInd4. 0&IoT), 2019. IEEE, pp 117–122

  39. 39.

    Wang H, Zhang N, Créput JC (2017) A massively parallel neural network approach to large-scale Euclidean traveling salesman problems. Neurocomputing 240:137–151

    Article  Google Scholar 

  40. 40.

    Wong C, Yang E, Yan X-T, Gu D (2018) Optimal path planning based on a multi-tree T-RRT* approach for robotic task planning in continuous cost spaces. In: 12th France–Japan and 10th Europe-Asia congress on mechatronics. IEEE, pp 242–247

  41. 41.

    Ye B, Tang Q, Yao J, Gao W (2017) Collision-free path planning and delivery sequence optimization in noncoplanar radiation therapy. IEEE Trans Cybern 49(1):42–55

    Article  Google Scholar 

  42. 42.

    Zacharia PT, Aspragathos N (2005) Optimal robot task scheduling based on genetic algorithms. Robot Comput-Integr Manuf 21(1):67–79

    Article  Google Scholar 

  43. 43.

    Zacharia PT, Xidias EK, Aspragathos NA (2013) Task scheduling and motion planning for an industrial manipulator. Robot Comput-Integr Manuf 29(6):449–462

    Article  Google Scholar 

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Correspondence to Wenxiang Gao.

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Gao, W., Liu, C., Zhan, Y. et al. Automatic task scheduling optimization and collision-free path planning for multi-areas problem. Intel Serv Robotics 14, 583–596 (2021).

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  • Task scheduling
  • Collision-free
  • Path planning
  • Multi-areas
  • Optimization