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An effective dynamical evaluation and optimization mechanism for accurate motion primitives learning

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Abstract

Trajectory planning is an important stage in robot operation. Many imitation learning methods have been researched for learning operation skills from demonstrated trajectories. However, it is still a challenge to use the learned skill models to generate motion trajectories suitable for various changing conditions. In this paper, a closed-loop dynamical evaluation and optimization mechanism is proposed for imitation learning model to generate the optimal trajectories that can adapt to multiple conditions. This mechanism works by integrating the following parts: (1) imitation learning based on an improved dynamic motion primitive; (2) constructing the trajectory similarity evaluation function; (3) presenting an enhanced whale optimization algorithm(EWOA) by introducing the piecewise decay rate and inertia weight for avoiding getting stuck in local optima. The EWOA iteratively optimizes the key parameter of the skill learning model based on the cost function of the trajectory similarity evaluation for generating the trajectory with the highest similarity to the teaching trajectory. The effectiveness of the EWOA is validated using 10 functions by comparing with the other two methods. And the feasibility of the dynamical optimization mechanism is proved under different motion primitives and various generation conditions.

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Data Availability

Data sets proposed by other authors are not used in this paper.

References

  1. Ekrem Ö, Aksoy B (2023) Trajectory planning for a 6-axis robotic arm with particle swarm optimization algorithm. Eng Appl Artif Intell 122:106099

    Article  MATH  Google Scholar 

  2. Ma JW, Gao S, Yan HT, Lv Q, Hu GQ (2021) A new approach to time-optimal trajectory planning with torque and jerk limits for robot. Robot Auton Syst 140(3):103744

    Article  MATH  Google Scholar 

  3. Li J, Li Z, Li X, Feng Y, Xu B (2020) Skill learning strategy based on dynamic motion primitives for human-robot cooperative manipulation. IEEE Trans Cognit Dev Syst PP(99)

  4. Beliaev M, Shih A, Ermon S, Sadigh D, Pedarsani R (2022) Imitation learning by estimating expertise of demonstrators

  5. Yang C, Chen C, He W, Cui R, Li Z (2018) Robot learning system based on adaptive neural control and dynamic movement primitives. IEEE Trans Neural Netw Learn Syst 30(3):777–787

    Article  MathSciNet  MATH  Google Scholar 

  6. Ijspeert AJ, Nakanishi J, Hoffmann H, Pastor P, Schaal S (2013) Dynamical movement primitives: learning attractor models for motor behaviors. Neural Comput 25(2):328–373

    Article  MathSciNet  MATH  Google Scholar 

  7. Nazari Siahsar MA, Gholtashi S, Abolghasemi V, Chen Y (2017) Simultaneous denoising and interpolation of 2d seismic data using data-driven non-negative dictionary learning. Signal Process 141(dec):309–321

    Article  Google Scholar 

  8. Fiorini L, Mul MD, Fabbricotti I, Limosani R, Cavallo F (2019) Assistive robots to improve the independent living of older persons: results from a needs study. Disabil Rehabil Assist Technol

  9. Lee Y, Sun SH, Somasundaram S, Hu ES, Lim JJ (2018) Composing complex skills by learning transition policies. In: International conference on learning representations

  10. Colomé A, Torras C (2018) Dimensionality reduction in learning gaussian mixture models of movement primitives for contextualized action selection and adaptation. IEEE Robot Autom Lett 3(4):3922–3929

    Article  MATH  Google Scholar 

  11. Frank F, Paraschos A, Smagt P, Cseke B (2022) Constrained probabilistic movement primitives for robot trajectory adaptation. IEEE Trans Robot 38(4):2276–2294

    Article  Google Scholar 

  12. Liu A, Zhan S, Jin Z, Zhang W-A (2024) A variable impedance skill learning algorithm based on kernelized movement primitives. IEEE Trans Ind Electron 71(1):870–879

    Article  MATH  Google Scholar 

  13. Widmann D, Karayiannidis Y (2018) Human motion prediction in human-robot handovers based on dynamic movement primitives. IEEE

  14. Bian F, Ren D, Li R, Liang P, Wang K, Zhao L (2020) An extended dmp framework for robot learning and improving variable stiffness manipulation. Assembly Autom 40(1):85–94

    Article  MATH  Google Scholar 

  15. Lauretti C, Tamantini C, Zollo L (2024) A new dmp scaling method for robot learning by demonstration and application to the agricultural domain. IEEE Access PP:1–1

    Google Scholar 

  16. Todorov A (2016) An overview of the relief algorithm and advancements. Statistica L Approaches to Gene X Environment Interactions for Complex Phenotypes 10

  17. Garg H (2016) A hybrid pso-ga algorithm for constrained optimization problems. Appl Math Comput 274:292–305

    MathSciNet  MATH  Google Scholar 

  18. Wei C, Ji Z, Cai B (2020) Particle swarm optimization for cooperative multi-robot task allocation: a multi-objective approach. IEEE Robot Autom Lett 5(2):2530–2537

    Article  MATH  Google Scholar 

  19. Hamdia KM, Zhuang X, Rabczuk T (2020) An efficient optimization approach for designing machine learning models based on genetic algorithm. Neural Comput Appl 33(6):1923–1933

    Article  MATH  Google Scholar 

  20. Liu G, Bai Y, Zhu L, Wang Q, Zhang W (2024) A sequential excitation and simplified ant colony optimization based global extreme seeking control method for performance improvement. Swarm Evol Comput 86:101522

    Article  MATH  Google Scholar 

  21. Ginesi M, Sansonetto N, Fiorini P (2021) Overcoming some drawbacks of dynamic movement primitives. Robot Auton Syst 144:103844

    Article  Google Scholar 

  22. Xie F (2021) Euclidean representation of low-rank matrices and its statistical applications. arXiv:2103.04220

  23. Laperre B, Amaya J, Lapenta G (2020) Dynamic time warping as a new evaluation for dst forecast with machine learning. Front Astron Space Sci 7:39

    Article  Google Scholar 

  24. Han L, Kang P, Chen Y, Xu W, Li B (2019) Trajectory optimization and force control with modified dynamic movement primitives under curved surface constraints*

  25. Xia P, Zhang L, Li F (2015) Learning similarity with cosine similarity ensemble. Inf Sci 307:39–52

    Article  MathSciNet  MATH  Google Scholar 

  26. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  MATH  Google Scholar 

  27. Yang W, Xia K, Fan S, Wang L, Li T, Zhang J, Feng Y (2022) A multi-strategy whale optimization algorithm and its application. Eng Appl Artif Intell 108:104558

    Article  MATH  Google Scholar 

  28. Huang Y, Rozo L, Silvério J, Caldwell DG (2019) Kernelized movement primitives. Int J Robot Res 38(7):833–852

    Article  Google Scholar 

  29. Hua J, Zeng L, Li G, Ju Z (2021) Learning for a robot: deep reinforcement learning, imitation learning, transfer learning. Sensors 21(4):1278

    Article  MATH  Google Scholar 

  30. Edmonds M, Gao F, Xie X, Liu H, Qi S, Zhu Y, Rothrock B, Zhu S-C (2017) Feeling the force: integrating force and pose for fluent discovery through imitation learning to open medicine bottles. In: 2017 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp. 3530–3537. IEEE

  31. Chen Y, Fu Y, Zhang B, Fu W, Shen C (2022) Path planning of the fruit tree pruning manipulator based on improved rrt-connect algorithm. Int J Agri Biol Eng 15(2):177–188

    MATH  Google Scholar 

  32. Chi M, Yao Y, Liu Y, Zhong M (2019) Learning, generalization, and obstacle avoidance with dynamic movement primitives and dynamic potential fields. Appl Sci 9(8):1535

    Article  MATH  Google Scholar 

  33. Chang C, Haninger K, Shi Y, Yuan C, Chen Z, Zhang J (2022) Impedance adaptation by reinforcement learning with contact dynamic movement primitives 1185–1191. IEEE

  34. Vollmer A-L, Hemion NJ (2018) A user study on robot skill learning without a cost function: optimization of dynamic movement primitives via naive user feedback. Front Robot AI 5:77

    Article  MATH  Google Scholar 

  35. Dou S, Xiao J, Zhao W, Yuan H, Liu H (2022) A robot skill learning framework based on compliant movement primitives. J Intell Robot Syst 104(3):53

    Article  MATH  Google Scholar 

  36. Wahrburg A, Guida S, Enayati N, Zanchettin AM, Rocco P (2020) Extending dynamic movement primitives towards high-performance robot motion. In: 2020 IEEE 16th international workshop on advanced motion control (AMC), pp 52–58. IEEE

  37. Kim H, Kim BK (2021) Energy-optimal transport trajectory planning and online trajectory modification for holonomic robots. Asian J Control 23(5):2185–2200

    Article  MATH  Google Scholar 

  38. Lauretti C, Cordella F, Zollo L (2019) A hybrid joint/cartesian dmp-based approach for obstacle avoidance of anthropomorphic assistive robots. Int J Soc Robot 11(5):783–796

    Article  Google Scholar 

  39. Zhou X (2021) Operational safe control for reinforcement-learning-based robot autonomy. In: 2021 40th chinese control conference (CCC), pp 4091–4095. IEEE

  40. Lu Z, Wang N, Yang C (2021) A constrained dmps framework for robot skills learning and generalization from human demonstrations. IEEE/ASME Trans Mechatron 26(6):3265–3275

    Article  MATH  Google Scholar 

  41. Kroemer O, Niekum S, Konidaris G (2021) A review of robot learning for manipulation: challenges, representations, and algorithms. J Mach Learn Res 22(30):1–82

    MathSciNet  MATH  Google Scholar 

  42. Li J, Li Z, Li X, Feng Y, Hu Y, Xu B (2020) Skill learning strategy based on dynamic motion primitives for human-robot cooperative manipulation. IEEE Trans Cognit Dev Syst 13(1):105–117

    Article  MATH  Google Scholar 

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Acknowledgements

The research leading to these results received funding from Scientific Research Project of Beijing Educational Committee (KM202110005023), National Science Foundation of China (62273012, 62373016,62373012) and Beijing Natural Science Foundation (4212033).

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Chunfang Liu was responsible for the overall planning and revision of the paper, Changfeng Li was responsible for the program writing and experimental data collation and analysis, Xiaoli Li was responsible for the thought guidance of the paper, Guoyu Zuo was responsible for the revision of the paper and Pan Yu was responsible for the revision of the document format of the paper.

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Correspondence to Chunfang Liu.

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Liu, C., Li, C., Li, X. et al. An effective dynamical evaluation and optimization mechanism for accurate motion primitives learning. Appl Intell 55, 209 (2025). https://doi.org/10.1007/s10489-024-06147-w

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