Abstract
Trajectory optimization has recently been addressed to compute energy-efficient routes for ornithopter navigation, but its online application remains a challenge. To overcome the high computation time of traditional approaches, this paper proposes algorithms that recursively generate trajectories based on the output of neural networks and random forest. To this end, we create a large data set composed by energy-efficient trajectories obtained by running a competitive planner. To the best of our knowledge our proposed data set is the first one with a high number of pseudo-optimal paths for ornithopter trajectory optimization. We compare the performance of three methods to compute low-cost trajectories: two classification approaches to learn maneuvers and an alternative regression method that predicts new states. The algorithms are tested in several scenarios, including the landing case. The effectiveness and efficiency of the proposed algorithms are demonstrated through simulation, which show that the machine learning techniques can be used to compute the flight path of the ornithopter in real time, even under uncertainties such as wrong sensor readings or re-positioning of the target. Random Forest obtains the higher performance with more than 99% and 97% of accuracy in a landing and a mid-range scenario, respectively.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ba, J.L., Kiros, J.R., Hinton, G.E.: Layer normalization. arXiv:http://arxiv.org/abs/1607.06450 (2016)
Breiman, L.: Random forests. Machine Learning 45(1), 5–32 (2001)
Chai, R., Savvaris, A., Tsourdos, A., Chai, S.: Overview of trajectory optimization techniques. In: Design of Trajectory Optimization Approach for Space Maneuver Vehicle Skip Entry Problems. Springer, pp. 7–25 (2020)
Coutinho, W.P., Battarra, M., Fliege, J.: The unmanned aerial vehicle routing and trajectory optimisation problem, a taxonomic review. Comput. Indust. Eng. 120, 116–128 (2018)
DeLaurier, J.D.: An ornithopter wing design. Canadian aeronautics and space journal 40(1), 10–18 (1994)
Han, T., Jiang, D., Zhao, Q., Wang, L., Yin, K.: Comparison of random forest, artificial neural networks and support vector machine for intelligent diagnosis of rotating machinery. Trans. Inst. Meas. Control. 40(8), 2681–2693 (2018)
Hausknecht, M., Stone, P.: Deep recurrent q-learning for partially observable Mdps. In: 2015 Aaai Fall Symposium Series (2015)
He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778 (2016)
Hinton, G.E., Srivastava, N., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.R.: Improving neural networks by preventing co-adaptation of feature detectors. arXiv:http://arxiv.org/abs/1207.0580 (2012)
Horn, J.F., Schmidt, E.M., Geiger, B.R., DeAngelo, M.P.: Neural network-based trajectory optimization for unmanned aerial vehicles. J. Guidance Control Dynam. 35(2), 548–562 (2012)
Ilin, R., Kozma, R., Werbos, P.J.: Beyond feedforward models trained by backpropagation: a practical training tool for a more efficient universal approximator. IEEE Trans. Neural Netw. 19(6), 929–937 (2008)
Kalakrishnan, M., Chitta, S., Theodorou, E., Pastor, P., Schaal, S.: Stomp: Stochastic trajectory optimization for motion planning. In: 2011 IEEE International Conference on Robotics and Automation. IEEE, pp. 4569–4574 (2011)
Kelly, M.: An introduction to trajectory optimization: How to do your own direct collocation. SIAM Rev. 59(4), 849–904 (2017)
Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv:http://arxiv.org/abs/1412.6980 (2014)
Kosari, A., Maghsoudi, H., Lavaei, A., Ahmadi, R.: Optimal online trajectory generation for a flying robot for terrain following purposes using neural network. Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering 229(6), 1124–1141 (2015)
Lu, Y., Yi, S., Liu, Y., Ji, Y.: A novel path planning method for biomimetic robot based on deep learning. Assembly Automation (2016)
Mirzaei, M., Kosari, A., Maghsoudi, H.: Optimal path planning for two Uavs in a pursuit-evasion game. In: 2021 IEEE International Conference on Automation/XXIV Congress of the Chilean Association of Automatic Control (ICA-ACCA). IEEE, pp. 1–7 (2021)
Mordatch, I., Todorov, E.: Combining the benefits of function approximation and trajectory optimization. In: Robotics: Science and Systems, vol. 4 (2014)
Mordatch, I., Todorov, E., Popović, Z.: Discovery of complex behaviors through contact-invariant optimization. ACM Transactions on Graphics (TOG) 31(4), 1–8 (2012)
Nguyen, T.A., Phan, H.V., Au, T.K.L., Park, H.C.: Experimental study on thrust and power of flapping-wing system based on rack-pinion mechanism. Bioinspiration & Biomimetics 11(4), 046001 (2016). https://doi.org/10.1088/1748-3190/11/4/046001
de Oliveira, G.G., Ruiz, L.F.C., Guasselli, L.A., Haetinger, C.: Random forest and artificial neural networks in landslide susceptibility modeling: a case study of the fão river basin, southern brazil. Nat. Hazards 99(2), 1049–1073 (2019)
Otte, M., Correll, N.: C-forest: Parallel shortest path planning with superlinear speedup. IEEE Trans. Robot. 29(3), 798–806 (2013)
Park, J.H., Yoon, K.J.: Designing a biomimetic ornithopter capable of sustained and controlled flight. Journal of Bionic Engineering 5(1), 39–47 (2008)
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al: Pytorch: an imperative style, high-performance deep learning library. Advances in Neural Information Processing Systems 32, 8026–8037 (2019)
Pérez-Cutiño, M., Rodríguez, F., Pascual, L., Díaz-Báñez, J.: Neural Networks Algorithms for Ornithopter Trajectory Optimization. In: 2021 International Conference on Unmanned Aircraft Systems (ICUAS). IEEE, pp. 1665–1670 (2021)
Quinlan, J.R.: Induction of decision trees. Machine Learning 1(1), 81–106 (1986)
Rodríguez, F., Díaz-Báñez, J.M., Sanchez-Laulhe, E., Capitán, J., Ollero, A.: Kinodynamic planning for an energy-efficient autonomous ornithopter. Computers & Industrial Engineering 163, 107814 (2022)
Salloom, T., Kaynak, O., He, W.: A novel deep neural network architecture for real-time water demand forecasting. J. Hydrol. 599, 126353 (2021)
Salloom, T., Kaynak, O., Yu, X., He, W.: Proportional integral derivative booster for neural networks-based time-series prediction: Case of water demand prediction. Eng. Appl. Artif. Intel. 108, 104570 (2022)
Salloom, T., Yu, X., He, W., Kaynak, O.: Adaptive neural network control of underwater robotic manipulators tuned by a genetic algorithm. J. Intell. Robot. Syst. 97(3), 657–672 (2020)
Suarez, A., Perez, M., Heredia, G., Ollero, A.: Small-Scale Compliant Dual Arm with Tail for Winged Aerial Robots. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, pp. 208–214 (2019)
Woo, M.H., Lee, S.H., Cha, H.M.: A study on the optimal route design considering time of mobile robot using recurrent neural network and reinforcement learning. J. Mech. Sci. Technol. 32(10), 4933–4939 (2018)
Wu, H., Yan, W., Xu, Z., Li, S., Cheng, T., Zhou, X.: Multimodal prediction-based robot abnormal movement identification under variable time-length experiences. Journal of Intelligent & Robotic Systems 104(1), 1–15 (2022)
Yijing, Z., Zheng, Z., Xiaoyi, Z., Yang, L.: Q Learning Algorithm Based Uav Path Learning and Obstacle Avoidence Approach. In: 2017 36Th Chinese Control Conference (CCC). IEEE, pp. 3397–3402 (2017)
Yu, X., He, W., Li, H., Sun, J.: Adaptive Fuzzy Full-State and Output-Feedback Control for Uncertain Robots with Output Constraint. IEEE Transactions on Systems Man, and Cybernetics Systems (2020)
Zekić-Sušac, M., Has, A., Knežević, M.: Predicting energy cost of public buildings by artificial neural networks, cart, and random forest. Neurocomputing 439, 223–233 (2021)
Zhang, B., Liu, W., Mao, Z., Liu, J., Shen, L.: Cooperative and geometric learning algorithm (cgla) for path planning of uavs with limited information. Automatica 50(3), 809–820 (2014)
Zhang, B., Mao, Z., Liu, W., Liu, J.: Geometric reinforcement learning for path planning of uavs. Journal of Intelligent & Robotic Systems 77(2), 391–409 (2015)
Acknowledgements
This work is partially supported by the Spanish Ministry of Economy and Competitiveness (MTM2016-76272-R AEI/FEDER,UE), the Spanish Ministry of Science and Innovation CIN/AEI/10.13039/501100011033/ (PID2020-114154RB-I00) and European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement #734922.
Funding
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by M.A. Pérez-Cutiño, F. Rodríguez and L.D. Pascual. The first draft of the manuscript was written by J.M. Díaz-Bañez and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Conceptualization and supervision was mainly performed by J.M. Díaz-Bañez.
Corresponding author
Ethics declarations
Ethics approval
All of the authors confirm that there is no potential acts of misconduct in this work, and approve of the journal upholding the integrity of the scientific record.
Consent for Publication
The authors consent to publish.
Conflict of Interests
The authors have no conflicts of interest to declare that are relevant to the content of this article.
Additional information
Code or data availability
The Ornithopter Trajectory Optimization (OTO) data set and evaluation code can be found at https://github.com/mpcutino/OTO_dataset.
Consent to participate
The authors consent to participate.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Pérez-Cutiño, M.A., Rodríguez, F., Pascual, L.D. et al. Ornithopter Trajectory Optimization with Neural Networks and Random Forest. J Intell Robot Syst 105, 17 (2022). https://doi.org/10.1007/s10846-022-01612-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-022-01612-5