{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T15:46:30Z","timestamp":1780674390479,"version":"3.54.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T00:00:00Z","timestamp":1774569600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":12,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2046582"],"award-info":[{"award-number":["2046582"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"DOI":"10.1007\/s10846-026-02368-y","type":"journal-article","created":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T08:54:45Z","timestamp":1774601685000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["BART\u00e9: Composite B\u00e9zier Curves for Racing Trajectory Estimation"],"prefix":"10.1007","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2510-2970","authenticated-orcid":false,"given":"Trent","family":"Weiss","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5921-0331","authenticated-orcid":false,"given":"Madhur","family":"Behl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,27]]},"reference":[{"key":"2368_CR1","unstructured":"O\u2019Kelly, M., Sukhil, V., Abbas, H., Harkins, J., Kao, C., Pant, Y.V., Mangharam, R., Agarwal, D., Behl, M., Burgio, P., Bertogna, M.: F1\/10: an open-source autonomous cyber-physical platform (2019). arXiv:1901.08567"},{"key":"2368_CR2","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1109\/OJITS.2022.3181510","volume":"3","author":"J Betz","year":"2022","unstructured":"Betz, J., Zheng, H., Liniger, A., Rosolia, U., Karle, P., Behl, M., Krovi, V., Mangharam, R.: Autonomous vehicles on the edge: A survey on autonomous vehicle racing. IEEE Open Journal of Intelligent Transportation Systems. 3, 458\u2013488 (2022). https:\/\/doi.org\/10.1109\/OJITS.2022.3181510","journal-title":"IEEE Open Journal of Intelligent Transportation Systems."},{"key":"2368_CR3","unstructured":"Indy Autonomous Challenge (2025). https:\/\/indyautonomouschallenge.com"},{"key":"2368_CR4","doi-asserted-by":"crossref","unstructured":"Ettinger, S., Cheng, S., Caine, B., Liu, C., Zhao, H., Pradhan, S., Chai, Y., Sapp, B., Qi, C.R., Zhou, Y., Yang, Z., Chouard, A., Sun, P., Ngiam, J., Vasudevan, V., McCauley, A., Shlens, J., Anguelov, D.: Large scale interactive motion forecasting for autonomous driving: The waymo open motion dataset. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV), pp. 9710\u20139719 (2021)","DOI":"10.1109\/ICCV48922.2021.00957"},{"key":"2368_CR5","doi-asserted-by":"crossref","unstructured":"Chen, K., Ge, R., Qiu, H., Ai-Rfou, R., Qi, C.R., Zhou, X., Yang, Z., Ettinger, S., Sun, P., Leng, Z., Mustafa, M., Bogun, I., Wang, W., Tan, M., Anguelov, D.: Womd-lidar: Raw sensor dataset benchmark for motion forecasting (2023). arXiv preprint arXiv:2304.03834","DOI":"10.1109\/ICRA57147.2024.10610651"},{"issue":"5","key":"2368_CR6","doi-asserted-by":"publisher","first-page":"3955","DOI":"10.1109\/TPAMI.2024.3352811","volume":"46","author":"S Shi","year":"2024","unstructured":"Shi, S., Jiang, L., Dai, D., Schiele, B.: Mtr++: Multi-agent motion prediction with symmetric scene modeling and guided intention querying. IEEE Trans. Pattern Anal. Mach. Intell. 46(5), 3955\u20133971 (2024). https:\/\/doi.org\/10.1109\/TPAMI.2024.3352811","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"2368_CR7","doi-asserted-by":"crossref","unstructured":"Karle, P., T\u00f6r\u00f6k, F., Geisslinger, M., Lienkamp, M.: MixNet: Structured Deep Neural Motion Prediction for Autonomous Racing (2022)","DOI":"10.1109\/ACCESS.2023.3303841"},{"issue":"4","key":"2368_CR8","doi-asserted-by":"publisher","first-page":"10414","DOI":"10.1109\/LRA.2022.3193496","volume":"7","author":"T Weiss","year":"2022","unstructured":"Weiss, T., Behl, M.: This is the way: Differential bayesian filtering for agile trajectory synthesis. IEEE Robotics and Automation Letters. 7(4), 10414\u201310421 (2022). https:\/\/doi.org\/10.1109\/LRA.2022.3193496","journal-title":"IEEE Robotics and Automation Letters."},{"issue":"3","key":"2368_CR9","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1109\/TIV.2022.3167103","volume":"7","author":"Y Huang","year":"2022","unstructured":"Huang, Y., Du, J., Yang, Z., Zhou, Z., Zhang, L., Chen, H.: A survey on trajectory-prediction methods for autonomous driving. IEEE Transactions on Intelligent Vehicles. 7(3), 652\u2013674 (2022). https:\/\/doi.org\/10.1109\/TIV.2022.3167103","journal-title":"IEEE Transactions on Intelligent Vehicles."},{"key":"2368_CR10","doi-asserted-by":"publisher","unstructured":"Liu, J., Mao, X., Fang, Y., Zhu, D., Meng, M.Q.-H.: A survey on deep-learning approaches for vehicle trajectory prediction in autonomous driving. In: 2021 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 978\u2013985 (2021). https:\/\/doi.org\/10.1109\/ROBIO54168.2021.9739407","DOI":"10.1109\/ROBIO54168.2021.9739407"},{"key":"2368_CR11","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L.u., Polosukhin, I.: Attention is all you need. In: Guyon, I., Luxburg, U.V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., Garnett, R. (eds.) Advances in Neural Information Processing Systems, vol. 30 (2017)"},{"key":"2368_CR12","doi-asserted-by":"publisher","first-page":"30210","DOI":"10.1109\/ACCESS.2020.2971705","volume":"8","author":"S Zhang","year":"2020","unstructured":"Zhang, S., Zhi, Y., He, R., Li, J.: Research on traffic vehicle behavior prediction method based on game theory and hmm. IEEE Access. 8, 30210\u201330222 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.2971705","journal-title":"IEEE Access."},{"key":"2368_CR13","doi-asserted-by":"publisher","unstructured":"Berndt, H., Emmert, J., Dietmayer, K.: Continuous driver intention recognition with hidden markov models. In: 2008 11th International IEEE Conference on Intelligent Transportation Systems, pp. 1189\u20131194 (2008). https:\/\/doi.org\/10.1109\/ITSC.2008.4732630","DOI":"10.1109\/ITSC.2008.4732630"},{"key":"2368_CR14","doi-asserted-by":"publisher","unstructured":"Hou, H., Jin, L., Niu, Q., Sun, Y., Lu, M.: Driver intention recognition method using continuous hidden markov model. International Journal of Computational Intelligence Systems. May 2011, 386\u2013393 (2012). https:\/\/doi.org\/10.1080\/18756891.2011.9727797","DOI":"10.1080\/18756891.2011.9727797"},{"issue":"2","key":"2368_CR15","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TIV.2018.2804159","volume":"3","author":"N Deo","year":"2018","unstructured":"Deo, N., Rangesh, A., Trivedi, M.M.: How would surround vehicles move? a unified framework for maneuver classification and motion prediction. IEEE Transactions on Intelligent Vehicles. 3(2), 129\u2013140 (2018). https:\/\/doi.org\/10.1109\/TIV.2018.2804159","journal-title":"IEEE Transactions on Intelligent Vehicles."},{"key":"2368_CR16","doi-asserted-by":"publisher","unstructured":"Phan-Minh, T., Grigore, E., Boulton, F.A., Beijbom, O., Wolff, E.M.: Covernet: Multimodal behavior prediction using trajectory sets. In: 2020 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 14062\u201314071. IEEE Computer Society, Los Alamitos, CA, USA (2020). https:\/\/doi.org\/10.1109\/CVPR42600.2020.01408","DOI":"10.1109\/CVPR42600.2020.01408"},{"key":"2368_CR17","first-page":"2553","volume":"33","author":"Y Biktairov","year":"2020","unstructured":"Biktairov, Y., Stebelev, M., Rudenko, I., Shliazhko, O., Yangel, B.: Prank: motion prediction based on ranking. Adv. Neural. Inf. Process. Syst. 33, 2553\u20132563 (2020)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"7","key":"2368_CR18","doi-asserted-by":"publisher","first-page":"8370","DOI":"10.1007\/s10489-022-03961-y","volume":"53","author":"R Izquierdo","year":"2023","unstructured":"Izquierdo, R., Quintanar, \u00c1., Llorca, D.F., Daza, I.G., Hern\u00e1ndez, N., Parra, I., Sotelo, M.\u00c1.: Vehicle trajectory prediction on highways using bird eye view representations and deep learning. Appl. Intell. 53(7), 8370\u20138388 (2023)","journal-title":"Appl. Intell."},{"key":"2368_CR19","doi-asserted-by":"crossref","unstructured":"Qin, Y., Guan, Y.L., Yuen, C.: Spatiotemporal capsule neural network for vehicle trajectory prediction. IEEE Tran. Vehic. Technol. (2023)","DOI":"10.1109\/TVT.2023.3253695"},{"key":"2368_CR20","unstructured":"Sabour, S., Frosst, N., Hinton, G.E.: Dynamic routing between capsules. Advances in neural information processing systems, 30 (2017)"},{"key":"2368_CR21","doi-asserted-by":"crossref","unstructured":"Gao, J., Sun, C., Zhao, H., Shen, Y., Anguelov, D., Li, C., Schmid, C.: VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation (2020)","DOI":"10.1109\/CVPR42600.2020.01154"},{"key":"2368_CR22","doi-asserted-by":"crossref","unstructured":"Gu, J., Sun, C., Zhao, H.: Densetnt: End-to-end trajectory prediction from dense goal sets. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision, pp. 15303\u201315312 (2021)","DOI":"10.1109\/ICCV48922.2021.01502"},{"key":"2368_CR23","unstructured":"Ngiam, J., Vasudevan, V., Caine, B., Zhang, Z., Chiang, H.-T.L., Ling, J., Roelofs, R., Bewley, A., Liu, C., Venugopal, A., Weiss, D.J., Sapp, B., Chen, Z., Shlens, J.: Scene transformer: A unified architecture for predicting future trajectories of multiple agents. In: International Conference on Learning Representations (2022). https:\/\/openreview.net\/forum?id=Wm3EA5OlHsG"},{"key":"2368_CR24","doi-asserted-by":"crossref","unstructured":"Sun, Q., Huang, X., Gu, J., Williams, B.C., Zhao, H.: M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction (2022)","DOI":"10.1109\/CVPR52688.2022.00643"},{"key":"2368_CR25","doi-asserted-by":"publisher","unstructured":"Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural computation. 9, 1735\u201380 (1997). https:\/\/doi.org\/10.1162\/neco.1997.9.8.1735","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"2368_CR26","doi-asserted-by":"publisher","unstructured":"Zyner, A., Worrall, S., Ward, J., Nebot, E.: Long short term memory for driver intent prediction. In: 2017 IEEE Intelligent Vehicles Symposium (IV), pp. 1484\u20131489 (2017). https:\/\/doi.org\/10.1109\/IVS.2017.7995919","DOI":"10.1109\/IVS.2017.7995919"},{"issue":"3","key":"2368_CR27","doi-asserted-by":"publisher","first-page":"1759","DOI":"10.1109\/LRA.2018.2805314","volume":"3","author":"A Zyner","year":"2018","unstructured":"Zyner, A., Worrall, S., Nebot, E.: A recurrent neural network solution for predicting driver intention at unsignalized intersections. IEEE Robotics and Automation Letters. 3(3), 1759\u20131764 (2018). https:\/\/doi.org\/10.1109\/LRA.2018.2805314","journal-title":"IEEE Robotics and Automation Letters."},{"key":"2368_CR28","doi-asserted-by":"publisher","unstructured":"Phillips, D.J., Wheeler, T.A., Kochenderfer, M.J.: Generalizable intention prediction of human drivers at intersections. In: 2017 IEEE Intelligent Vehicles Symposium (IV), pp. 1665\u20131670 (2017). https:\/\/doi.org\/10.1109\/IVS.2017.7995948","DOI":"10.1109\/IVS.2017.7995948"},{"key":"2368_CR29","doi-asserted-by":"publisher","unstructured":"Mercat, J., Gilles, T., El Zoghby, N., Sandou, G., Beauvois, D., Gil, G.P.: Multi-head attention for multi-modal joint vehicle motion forecasting. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 9638\u20139644 (2020). https:\/\/doi.org\/10.1109\/ICRA40945.2020.9197340","DOI":"10.1109\/ICRA40945.2020.9197340"},{"key":"2368_CR30","doi-asserted-by":"publisher","unstructured":"Deo, N., Trivedi, M.M.: Convolutional social pooling for vehicle trajectory prediction. In: 2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pp. 1549\u201315498 (2018). https:\/\/doi.org\/10.1109\/CVPRW.2018.00196","DOI":"10.1109\/CVPRW.2018.00196"},{"key":"2368_CR31","doi-asserted-by":"crossref","unstructured":"Chandra, R., Bhattacharya, U., Bera, A., Manocha, D.: Traphic: Trajectory prediction in dense and heterogeneous traffic using weighted interactions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 8483\u20138492 (2019)","DOI":"10.1109\/CVPR.2019.00868"},{"key":"2368_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11432-019-2761-y","volume":"63","author":"G Xie","year":"2020","unstructured":"Xie, G., Shangguan, A., Fei, R., Ji, W., Ma, W., Hei, X.: Motion trajectory prediction based on a cnn-lstm sequential model. SCIENCE CHINA Inf. Sci. 63, 1\u201321 (2020)","journal-title":"SCIENCE CHINA Inf. Sci."},{"issue":"1","key":"2368_CR33","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1109\/TIV.2020.2991952","volume":"6","author":"K Messaoud","year":"2021","unstructured":"Messaoud, K., Yahiaoui, I., Verroust-Blondet, A., Nashashibi, F.: Attention based vehicle trajectory prediction. IEEE Transactions on Intelligent Vehicles. 6(1), 175\u2013185 (2021). https:\/\/doi.org\/10.1109\/TIV.2020.2991952","journal-title":"IEEE Transactions on Intelligent Vehicles."},{"key":"2368_CR34","doi-asserted-by":"crossref","unstructured":"Kim, H., Kim, D., Kim, G., Cho, J., Huh, K.: Multi-head attention based probabilistic vehicle trajectory prediction. In: 2020 IEEE Intelligent Vehicles Symposium (IV), pp. 1720\u20131725 (2020). IEEE","DOI":"10.1109\/IV47402.2020.9304741"},{"key":"2368_CR35","doi-asserted-by":"publisher","unstructured":"Guo, H., Meng, Q., Cao, D., Chen, H., Liu, J., Shang, B.: Vehicle trajectory prediction method coupled with ego vehicle motion trend under dual attention mechanism. IEEE Transactions on Instrumentation and Measurement. 71, 1\u201316 (2022). https:\/\/doi.org\/10.1109\/TIM.2022.3163136","DOI":"10.1109\/TIM.2022.3163136"},{"key":"2368_CR36","first-page":"6531","volume":"35","author":"S Shi","year":"2022","unstructured":"Shi, S., Jiang, L., Dai, D., Schiele, B.: Motion transformer with global intention localization and local movement refinement. Adv. Neural. Inf. Process. Syst. 35, 6531\u20136543 (2022)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"7","key":"2368_CR37","doi-asserted-by":"publisher","first-page":"3871","DOI":"10.1109\/TIV.2023.3271624","volume":"8","author":"P Karle","year":"2023","unstructured":"Karle, P., Fent, F., Huch, S., Sauerbeck, F., Lienkamp, M.: Multi-modal sensor fusion and object tracking for autonomous racing. IEEE Transactions on Intelligent Vehicles. 8(7), 3871\u20133883 (2023). https:\/\/doi.org\/10.1109\/TIV.2023.3271624","journal-title":"IEEE Transactions on Intelligent Vehicles."},{"key":"2368_CR38","doi-asserted-by":"publisher","unstructured":"Sauerbeck, F., Huch, S., Fent, F., Karle, P., Kulmer, D., Betz, J.: Learn to see fast: Lessons learned from autonomous racing on how to develop perception systems. IEEE Access. 11, 44034\u201344050 (2023). https:\/\/doi.org\/10.1109\/ACCESS.2023.3272750","DOI":"10.1109\/ACCESS.2023.3272750"},{"key":"2368_CR39","doi-asserted-by":"publisher","unstructured":"Raji, A., Liniger, A., Giove, A., Toschi, A., Musiu, N., Morra, D., Verucchi, M., Caporale, D., Bertogna, M.: Motion planning and control for multi vehicle autonomous racing at high speeds. In: 2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC), pp. 2775\u20132782 (2022). https:\/\/doi.org\/10.1109\/ITSC55140.2022.9922239","DOI":"10.1109\/ITSC55140.2022.9922239"},{"key":"2368_CR40","unstructured":"Mortenson, M.E.: Mathematics for Computer Graphics Applications: An Introduction to the Mathematics and Geometry of CAD\/Cam, Geometric Modeling, Scientific Visualizati, 2nd edn. Industrial Press Inc, USA (1999)"},{"key":"2368_CR41","doi-asserted-by":"publisher","unstructured":"Farouki, R., Goodman, T.: On the optimal stability of the bernstein basis. Mathematics of Computation. 65, 1553\u20131566 (1996). https:\/\/doi.org\/10.1090\/S0025-5718-96-00759-4","DOI":"10.1090\/S0025-5718-96-00759-4"},{"key":"2368_CR42","unstructured":"Choi, J.-W., Elkaim, G.H.: B\u00e9zier curves for trajectory guidance. In: World Congress on Engineering and Computer Science, WCECS, pp. 22\u201324 (2008). Citeseer"},{"key":"2368_CR43","doi-asserted-by":"publisher","unstructured":"Weiss, T., Behl, M.: Deepracing: A framework for autonomous racing. In: 2020 Design, Automation & Test in Europe Conference & Exhibition (DATE), pp. 1163\u20131168 (2020). https:\/\/doi.org\/10.23919\/DATE48585.2020.9116486","DOI":"10.23919\/DATE48585.2020.9116486"},{"key":"2368_CR44","doi-asserted-by":"publisher","DOI":"10.1109\/iros55552.2023.10342053","author":"A Kulkarni","year":"2023","unstructured":"Kulkarni, A., Chrosniak, J., Ducote, E., Sauerbeck, F., Saba, A., Chirimar, U., Link, J., Behl, M., Cellina, M.: Racecar - the dataset for high-speed autonomous racing. (2023). https:\/\/doi.org\/10.1109\/iros55552.2023.10342053","journal-title":"Racecar - the dataset for high-speed autonomous racing."},{"key":"2368_CR45","unstructured":"Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization (2017). arXiv:1412.6980"},{"key":"2368_CR46","unstructured":"Shi, S., Jiang, L., Dai, D., Schiele, B.: Motion Transformer (MTR): A Strong Baseline for Multimodal Motion Prediction in Autonomous Driving. GitHub (2023)"}],"container-title":["Journal of Intelligent & Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-026-02368-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-026-02368-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-026-02368-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T11:05:28Z","timestamp":1775646328000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-026-02368-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,27]]},"references-count":46,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["2368"],"URL":"https:\/\/doi.org\/10.1007\/s10846-026-02368-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.36227\/techrxiv.174058869.96530302\/v1","asserted-by":"object"}]},"ISSN":["1573-0409"],"issn-type":[{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,27]]},"assertion":[{"value":"17 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"48"}}