Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
139 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A Dynamic Programming Framework for Optimal Planning of Redundant Robots Along Prescribed Paths With Kineto-Dynamic Constraints (2207.05622v2)

Published 12 Jul 2022 in cs.RO, cs.SY, eess.SY, and math.OC

Abstract: Offline optimal planning of trajectories for redundant robots along prescribed task space paths is usually broken down into two consecutive processes: first, the task space path is inverted to obtain a joint space path, then, the latter is parametrized with a time law. If the two processes are separated, they cannot optimize the same objective function, ultimately providing sub-optimal results. In this paper, a unified approach is presented where dynamic programming is the underlying optimization technique. Its flexibility allows accommodating arbitrary constraints and objective functions, thus providing a generic framework for optimal planning of real systems. To demonstrate its applicability to a real world scenario, the framework is instantiated for time-optimality on Franka Emika's Panda robot. The well-known issues associated with the execution of non-smooth trajectories on a real controller are partially addressed at planning level, through the enforcement of constraints, and partially through post-processing of the optimal solution. The experiments show that the proposed framework is able to effectively exploit kinematic redundancy to optimize the performance index defined at planning level and generate feasible trajectories that can be executed on real hardware with satisfactory results.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (59)
  1. P. Chiacchio, “Exploiting redundancy in minimum-time path following robot control,” in 1990 American Control Conference.   IEEE, May 1990, pp. 2313–2318.
  2. F. Basile and P. Chiacchio, “A contribution to minimum-time task-space path-following problem for redundant manipulators,” Robotica, vol. 21, no. 2, pp. 137–142, February 2003.
  3. K. Al Khudir and A. De Luca, “Faster motion on cartesian paths exploiting robot redundancy at the acceleration level,” IEEE Robotics and Automation Letters, vol. 3, no. 4, pp. 3553–3560, October 2018.
  4. J. E. Bobrow, S. Dubowsky, and J. S. Gibson, “Time-optimal control of robotic manipulators along specified paths,” The International Journal of Robotics Research, vol. 4, no. 3, pp. 3–17, September 1985.
  5. K. Shin and N. McKay, “Minimum-time control of robotic manipulators with geometric path constraints,” IEEE Transactions on Automatic Control, vol. 30, no. 6, pp. 531–541, June 1985.
  6. F. Pfeiffer and R. Johanni, “A concept for manipulator trajectory planning,” IEEE Journal on Robotics and Automation, vol. 3, no. 2, pp. 115–123, April 1987.
  7. J.-J. E. Slotine and H. S. Yang, “Improving the efficiency of time-optimal path-following algorithms,” IEEE Transactions on Robotics and Automation, vol. 5, no. 1, pp. 118–124, 1989.
  8. Y. Chen, S. Y.-P. Chien, and A. A. Desrochers, “General structure of time-optimal control of robotic manipulators moving along prescribed paths,” International Journal of Control, vol. 56, no. 4, pp. 767–782, October 1992.
  9. M. Galicki and I. Pajak, “Optimal motions of redundant manipulators with state equality constraints,” in Proceedings - IEEE International Symposium on Assembly and Task Planning (ISATP’99).   IEEE, July 1999, pp. 181–185.
  10. M. Galicki, “Time-optimal controls of kinematically redundant manipulators with geometric constraints,” IEEE Transactions on Robotics and Automation, vol. 16, no. 1, pp. 89–93, 2000.
  11. E. Ferrentino and P. Chiacchio, “Redundancy parametrization in globally-optimal inverse kinematics,” in Advances in Robot Kinematics 2018.   Springer International Publishing, June 2018, pp. 47–55.
  12. A. Reiter, K. Springer, H. Gattringer, and A. Müller, “An explicit approach for time-optimal trajectory planning for kinematically redundant serial robots,” PAMM, vol. 15, no. 1, pp. 67–68, oct 2015.
  13. S. Ma and M. Watanabe, “Time optimal path-tracking control of kinematically redundant manipulators,” JSME International Journal Series C, vol. 47, no. 2, pp. 582–590, 2004.
  14. A. Reiter, A. Müller, and H. Gattringer, “Inverse kinematics in minimum-time trajectory planning for kinematically redundant manipulators,” in IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society.   IEEE, October 2016, pp. 6873–6878.
  15. A. Reiter, H. Gattringer, and A. Müller, “Redundancy resolution in minimum-time path tracking of robotic manipulators,” in Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics.   SCITEPRESS - Science and Technology Publications, 2016, pp. 61–68.
  16. A. Reiter, H. Gattringer, and A. Müller, “On redundancy resolution in minimum-time trajectory planning of robotic manipulators along predefined end-effector paths,” in Informatics in Control, Automation and Robotics.   Springer International Publishing, nov 2017, pp. 190–206.
  17. A. Reiter, A. Müller, and H. Gattringer, “On higher order inverse kinematics methods in time-optimal trajectory planning for kinematically redundant manipulators,” IEEE Transactions on Industrial Informatics, vol. 14, no. 4, pp. 1681–1690, April 2018.
  18. X. Wang, Y. Gan, and X. Dai, “Time-optimal and smooth trajectory planning based on continuous pseudo-acceleration,” in 2023 International Conference on Advanced Robotics and Mechatronics (ICARM).   IEEE, jul 2023.
  19. U. Wolinski and M. Wojtyra, “A novel QP-based kinematic redundancy resolution method with joint constraints satisfaction,” IEEE Access, vol. 10, pp. 41 023–41 037, 2022.
  20. Y. Zhang and Y. Jia, “Motion planning of redundant dual-arm robots with multicriterion optimization,” IEEE Systems Journal, vol. 17, no. 3, pp. 4189–4199, sep 2023.
  21. T. Marauli, H. Gattringer, and A. Müller, “Time-optimal path following for non-redundant serial manipulators using an adaptive path-discretization,” Robotica, vol. 41, no. 6, pp. 1856–1871, mar 2023.
  22. J. Ogbemhe, K. Mpofu, and N. Tlale, “Optimal trajectory scheme for robotic welding along complex joints using a hybrid multi-objective genetic algorithm,” IEEE Access, vol. 7, pp. 158 753–158 769, 2019.
  23. Z. Wang, Y. Li, K. Shuai, W. Zhu, B. Chen, and K. Chen, “Multi-objective trajectory planning method based on the improved elitist non-dominated sorting genetic algorithm,” Chinese Journal of Mechanical Engineering, vol. 35, no. 1, feb 2022.
  24. X. Zhang and G. Shi, “Multi-objective optimal trajectory planning for manipulators in the presence of obstacles,” Robotica, vol. 40, no. 4, pp. 888–906, jul 2021.
  25. Z. Wang, Y. Li, P. Sun, Y. Luo, B. Chen, and W. Zhu, “A multi-objective approach for the trajectory planning of a 7-DOF serial-parallel hybrid humanoid arm,” Mechanism and Machine Theory, vol. 165, p. 104423, nov 2021.
  26. M. Schappler, “Pose optimization of task-redundant robots in second-order rest-to-rest motion with cascaded dynamic programming and nullspace projection,” in Informatics in Control, Automation and Robotics.   Springer International Publishing, 2023, pp. 106–131.
  27. G. Singh and V. K. Banga, “Combinations of novel hybrid optimization algorithms-based trajectory planning analysis for an industrial robotic manipulators,” Journal of Field Robotics, vol. 39, no. 5, pp. 650–674, mar 2022.
  28. J. Ma, Z. Cheng, X. Zhang, Z. Lin, F. L. Lewis, and T. H. Lee, “Local learning enabled iterative linear quadratic regulator for constrained trajectory planning,” IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 9, pp. 5354–5365, sep 2023.
  29. G. Chen, M. Ma, S. Guo, B. Hou, and J. Wang, “An easy-implemented optimization method of trajectory planning based on polynomial interpolation,” in 2021 40th Chinese Control Conference (CCC).   IEEE, jul 2021.
  30. H. Wu, J. Yang, S. Huang, X. Ning, and Z. Zhang, “Multi-objective adaptive trajectory optimization for industrial robot based on acceleration continuity constraint,” Robotics and Computer-Integrated Manufacturing, vol. 84, p. 102597, dec 2023.
  31. L. Zlajpah and A. Muller, “A task space decomposition algorithm for the inverse kinematics of functionally redundant manipulators,” in 2021 20th International Conference on Advanced Robotics (ICAR).   IEEE, dec 2021.
  32. A. P. Pashkevich, A. B. Dolgui, and O. A. Chumakov, “Multiobjective optimization of robot motion for laser cutting applications,” International Journal of Computer Integrated Manufacturing, vol. 17, no. 2, pp. 171–183, March 2004.
  33. A. Dolgui and A. Pashkevich, “Manipulator motion planning for high-speed robotic laser cutting,” International Journal of Production Research, vol. 47, no. 20, pp. 5691–5715, July 2009.
  34. A. Guigue, M. Ahmadi, R. Langlois, and M. J. D. Hayes, “Pareto optimality and multiobjective trajectory planning for a 7-dof redundant manipulator,” IEEE Transactions on Robotics, vol. 26, no. 6, pp. 1094–1099, December 2010.
  35. J. Gao, A. Pashkevich, and S. Caro, “Optimization of the robot and positioner motion in a redundant fiber placement workcell,” Mechanism and Machine Theory, vol. 114, pp. 170–189, August 2017.
  36. E. Ferrentino and P. Chiacchio, “On the optimal resolution of inverse kinematics for redundant manipulators using a topological analysis,” Journal of Mechanisms and Robotics, vol. 12, no. 3, June 2020.
  37. K. Shin and N. McKay, “A dynamic programming approach to trajectory planning of robotic manipulators,” IEEE Transactions on Automatic Control, vol. 31, no. 6, pp. 491–500, June 1986.
  38. S. Singh and M. C. Leu, “Optimal trajectory generation for robotic manipulators using dynamic programming,” Journal of Dynamic Systems, Measurement, and Control, vol. 109, no. 2, pp. 88–96, 1987.
  39. D. Kaserer, H. Gattringer, and A. Müller, “Nearly optimal path following with jerk and torque rate limits using dynamic programming,” IEEE Transactions on Robotics, vol. 35, no. 2, pp. 521–528, April 2019.
  40. ——, “Time optimal motion planning and admittance control for cooperative grasping,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 2216–2223, April 2020.
  41. V. Petrone, E. Ferrentino, and P. Chiacchio, “Time-optimal trajectory planning with interaction with the environment,” IEEE Robotics and Automation Letters, vol. 7, no. 4, pp. 10 399–10 405, oct 2022.
  42. J. A. Pámanes, P. Wenger, and J. L. Zapata, “Motion planning of redundant manipulators for specified trajectory tasks,” in Advances in Robot Kinematics.   Springer Netherlands, 2002, pp. 203–212.
  43. P. Wenger, P. Chedmail, and F. Reynier, “A global analysis of following trajectories by redundant manipulators in the presence of obstacles,” in [1993] Proceedings IEEE International Conference on Robotics and Automation.   IEEE Comput. Soc. Press, 1993.
  44. H. Pham and Q.-C. Pham, “On the structure of the time-optimal path parameterization problem with third-order constraints,” in 2017 IEEE International Conference on Robotics and Automation (ICRA).   IEEE, May 2017.
  45. A. Guigue, M. Ahmadi, M. J. D. Hayes, and R. G. Langlois, “A discrete dynamic programming approximation to the multiobjective deterministic finite horizon optimal control problem,” SIAM Journal on Control and Optimization, vol. 48, no. 4, pp. 2581–2599, January 2009.
  46. C. Gaz, M. Cognetti, A. Oliva, P. Robuffo Giordano, and A. De Luca, “Dynamic identification of the Franka Emika Panda robot with retrieval of feasible parameters using penalty-based optimization,” IEEE Robotics and Automation Letters, vol. 4, no. 4, pp. 4147–4154, October 2019.
  47. R. Diankov, “Automated construction of robotic manipulation programs,” Ph.D. dissertation, The Robotics Institute, Carnegie Mellon University, 2010.
  48. F. Storiale, E. Ferrentino, and P. Chiacchio, “Two-stage time-optimal planning of robots along pre-scribed paths with integral optimization of redundancy,” in 9th International Conference on Control, Decision and Information Technologies (CoDIT), 2023.
  49. J. Kim and E. A. Croft, “Online near time-optimal trajectory planning for industrial robots,” Robotics and Computer-Integrated Manufacturing, vol. 58, pp. 158–171, August 2019.
  50. H. Arai, K. Tanie, and S. Tachi, “Path tracking control of a manipulator considering torque saturation,” IEEE Transactions on Industrial Electronics, vol. 41, no. 1, pp. 25–31, 1994.
  51. O. Dahl and L. Nielsen, “Torque-limited path following by online trajectory time scaling,” IEEE Transactions on Robotics and Automation, vol. 6, no. 5, pp. 554–561, October 1990.
  52. Z. Shiller and H. Chang, “Trajectory preshaping for high-speed articulated systems,” Journal of Dynamic Systems, Measurement, and Control, vol. 117, no. 3, pp. 304–310, sep 1995.
  53. Z. Shiller, H. Chang, and V. Wong, “The practical implementation of time-optimal control for robotic manipulators,” Robotics and Computer-Integrated Manufacturing, vol. 12, no. 1, pp. 29–39, mar 1996.
  54. J. Kieffer, A. Cahill, and M. James, “Robust and accurate time-optimal path-tracking control for robot manipulators,” IEEE Transactions on Robotics and Automation, vol. 13, no. 6, pp. 880–890, 1997.
  55. O. Dahl, “Path-constrained robot control with limited torques-experimental evaluation,” IEEE Transactions on Robotics and Automation, vol. 10, no. 5, pp. 658–669, 1994.
  56. J. Moreno-Valenzuela, “Tracking control of on-line time-scaled trajectories for robot manipulators under constrained torques,” in Proceedings - 2006 IEEE International Conference on Robotics and Automation (ICRA).   IEEE, 2006, pp. 19–24.
  57. K. S. Eom, I. H. Suh, and W. K. Chung, “Disturbance observer based path tracking control of robot manipulator considering torque saturation,” Mechatronics, vol. 11, no. 3, pp. 325–343, apr 2001.
  58. W. Niu and M. Tomizuka, “A new approach of coordinated motion control subjected to actuator saturation,” Journal of Dynamic Systems, Measurement, and Control, vol. 123, no. 3, pp. 496–504, jul 1999.
  59. H. Tam, “Minimum time closed-loop tracking of a specified path by robot,” in 29th IEEE Conference on Decision and Control.   IEEE, December 1990, pp. 3132–3137.
Citations (6)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now