{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T13:33:19Z","timestamp":1777987999917,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T00:00:00Z","timestamp":1692316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2014NextGenerationEU under the ECOSISTER Project\u2014Spoke 3"},{"name":"University of Modena and Reggio Emilia through the FARD-2022 Project"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>When humans and robots work together, ensuring safe cooperation must be a priority. This research aims to develop a novel real-time planning algorithm that can handle unpredictable human movements by both slowing down task execution and modifying the robot\u2019s path based on the proximity of the human operator. To achieve this, an efficient method for updating the robot\u2019s motion is developed using a two-fold control approach that combines B-splines and hidden Markov models. This allows the algorithm to adapt to a changing environment and avoid collisions. The proposed framework is thus validated using the Franka Emika Panda robot in a simple start\u2013goal task. Our algorithm successfully avoids collision with the moving hand of an operator monitored by a fixed camera.<\/jats:p>","DOI":"10.3390\/robotics12040118","type":"journal-article","created":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T10:14:38Z","timestamp":1692353678000},"page":"118","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Online Motion Planning for Safe Human\u2013Robot Cooperation Using B-Splines and Hidden Markov Models"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2230-8191","authenticated-orcid":false,"given":"Giovanni","family":"Braglia","sequence":"first","affiliation":[{"name":"Engineering Department Enzo Ferrari, University of Modena and Reggio Emilia, 41125 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5312-6537","authenticated-orcid":false,"given":"Matteo","family":"Tagliavini","sequence":"additional","affiliation":[{"name":"Ideativa, 41125 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9263-426X","authenticated-orcid":false,"given":"Fabio","family":"Pini","sequence":"additional","affiliation":[{"name":"Engineering Department Enzo Ferrari, University of Modena and Reggio Emilia, 41125 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2343-6929","authenticated-orcid":false,"given":"Luigi","family":"Biagiotti","sequence":"additional","affiliation":[{"name":"Engineering Department Enzo Ferrari, University of Modena and Reggio Emilia, 41125 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10514-015-9528-y","article-title":"Learning Potential Functions from Human Demonstrations with Encapsulated Dynamic and Compliant Behaviors","volume":"41","author":"Khatib","year":"2017","journal-title":"Auton. Robot."},{"key":"ref_2","doi-asserted-by":"publisher","first-page":"6783","DOI":"10.1007\/s00170-022-09781-1","article-title":"Enhancing fluency and productivity in human-robot collaboration through online scaling of dynamic safety zones","volume":"121","author":"Scalera","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s10846-022-01687-0","article-title":"Real-Time and Efficient Collision Avoidance Planning Approach for Safe Human-Robot Interaction","volume":"105","author":"Liu","year":"2022","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_4","doi-asserted-by":"publisher","first-page":"102223","DOI":"10.1016\/j.rcim.2021.102223","article-title":"Real-Time Motion Control of Robotic Manipulators for Safe Human-Robot Coexistence","volume":"73","author":"Merckaert","year":"2022","journal-title":"Robotics"},{"key":"ref_5","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.ifacol.2018.11.559","article-title":"Physical-Consistent Behavior Embodied in B-Spline Curves for Robot Path Planning","volume":"51","author":"Chiaravalli","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_6","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1109\/TRO.2019.2911800","article-title":"Adaptive Motion Planning for a Collaborative Robot Based on Prediction Uncertainty to Enhance Human Safety and Work Efficiency","volume":"35","author":"Kanazawa","year":"2019","journal-title":"IEEE Trans. Robot."},{"key":"ref_7","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1109\/TASE.2015.2412256","article-title":"Safety in Human-Robot Collaborative Manufacturing Environments: Metrics and Control","volume":"13","author":"Zanchettin","year":"2015","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_8","doi-asserted-by":"publisher","first-page":"1164","DOI":"10.1177\/0278364913488805","article-title":"Chomp: Covariant Hamiltonian Optimization for Motion Planning","volume":"32","author":"Zucker","year":"2013","journal-title":"Int. J. Robot. Res."},{"key":"ref_9","doi-asserted-by":"publisher","first-page":"10041","DOI":"10.1109\/LRA.2022.3191170","article-title":"Collaborative Navigation and Manipulation of a Cable-Towed Load by Multiple Quadrupedal Robots","volume":"7","author":"Yang","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_10","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1177\/0278364918790369","article-title":"Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference","volume":"37","author":"Mukadam","year":"2018","journal-title":"Int. J. Robot. Res."},{"key":"ref_11","unstructured":"Toussaint, M., and Goerick, C. (2010). From Motor Learning to Interaction Learning in Robots, Springer."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Fisac, J.F., Bajcsy, A., Herbert, S.L., Fridovich-Keil, D., Wang, S., Tomlin, C.J., and Dragan, A.D. (2018). Probabilistically Safe Robot Planning with Confidence-Based Human Predictions. arXiv.","DOI":"10.15607\/RSS.2018.XIV.069"},{"key":"ref_13","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1109\/TSMCB.2006.886952","article-title":"On Learning, Representing, and Generalizing a Task in a Humanoid Robot","volume":"37","author":"Calinon","year":"2007","journal-title":"IEEE Trans. Syst. Man Cybern. Part Cybern."},{"key":"ref_14","unstructured":"Kavraki, L.E., and LaValle, S.M. (2016). Springer Handbook of Robotics, Springer."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jankowski, J., Bruderm\u00fcller, L., Hawes, N., and Calinon, S. (2022). VP-STO: Via-Point-Based Stochastic Trajectory Optimization for Reactive Robot Behavior. arXiv.","DOI":"10.1109\/ICRA48891.2023.10160214"},{"key":"ref_16","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.rcim.2017.05.013","article-title":"Dynamic Obstacle Avoidance for Manipulators Using Distance Calculation and Discrete Detection","volume":"49","author":"Han","year":"2018","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_17","unstructured":"Khatib, O. (1985, January 25\u201328). Real-time Obstacle Avoidance for Manipulators and Mobile Robots. Proceedings of the 1985 IEEE International Conference on Robotics and Automation, St. Louis, MO, USA."},{"key":"ref_18","unstructured":"Quinlan, S., and Khatib, O. (1993, January 2\u20136). Elastic Bands: Connecting Path Planning and Control. Proceedings of the [1993] Proceedings IEEE International Conference on Robotics and Automation, Atlanta, GA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Flacco, F., Kr\u00f6ger, T., Luca, A.D., and Khatib, O. (2012, January 14\u201318). A Depth Space Approach to Human-Robot Collision Avoidance. Proceedings of the 2012 IEEE International Conference on Robotics and Automation, St. Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6225245"},{"key":"ref_20","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s11370-023-00465-7","article-title":"A collision-free path planning method for industrial robot manipulators considering safe human-robot interaction","volume":"16","author":"Secil","year":"2023","journal-title":"Intell. Serv. Robot."},{"key":"ref_21","unstructured":"(2016). Robots and Robotic Devices\u2014Collaborative Robots. Standard No. ISO\/TS 15066."},{"key":"ref_22","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.procir.2018.01.026","article-title":"Human Robot Collaboration\u2014Using Kinect v2 for ISO\/TS 15066 Speed and Separation Monitoring","volume":"76","author":"Rosenstrauch","year":"2018","journal-title":"Procedia CIRP"},{"key":"ref_23","doi-asserted-by":"publisher","first-page":"4378","DOI":"10.1109\/LRA.2023.3280752","article-title":"Maximising Coefficiency of Human-Robot Handovers through Reinforcement Learning","volume":"8","author":"Lagomarsino","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Siciliano, B., and Khatib, O. (2008). Springer Handbook of Robotics, Springer.","DOI":"10.1007\/978-3-540-30301-5"},{"key":"ref_25","unstructured":"Biagiotti, L., and Melchiorri, C. (2008). Trajectory Planning for Automatic Machines and Robots, Springer Science & Business Media."},{"key":"ref_26","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1162\/089976699300016890","article-title":"Modeling and Prediction of Human Behavior","volume":"11","author":"Pentland","year":"1999","journal-title":"Neural Comput."},{"key":"ref_27","unstructured":"Hovland, G.E., Sikka, P., and McCarragher, B.J. (1996, January 22\u201328). Skill Acquisition from Human Demonstration Using a Hidden Markov Model. Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA."},{"key":"ref_28","doi-asserted-by":"publisher","first-page":"103711","DOI":"10.1016\/j.robot.2020.103711","article-title":"Human-Robot Collaboration in Sensorless Assembly Task Learning Enhanced by Uncertainties Adaptation via Bayesian Optimization","volume":"136","author":"Roveda","year":"2021","journal-title":"Robot. Auton. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Biagiotti, L., and Melchiorri, C. (2013, January 3\u20137). Online Trajectory Planning and Filtering for Robotic Applications via B-Spline Smoothing Filters. Proceedings of the 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan.","DOI":"10.1109\/IROS.2013.6697177"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Sayols, N., Sozzi, A., Piccinelli, N., Hernansanz, A., Casals, A., Bonf\u00e8, M., and Muradore, R. (August, January 31). Global\/Local Motion Planning Based on Dynamic Trajectory Reconfiguration and Dynamical Systems for Autonomous Surgical Robots. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.","DOI":"10.1109\/ICRA40945.2020.9197525"},{"key":"ref_31","unstructured":"Jurafsky, D., and Martin, J. (2008). Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition, Prentice Hall PTR. Available online: https:\/\/dl.acm.org\/doi\/10.5555\/555733."},{"key":"ref_32","doi-asserted-by":"publisher","first-page":"1706","DOI":"10.1162\/neco.2008.10-06-351","article-title":"Online Learning with Hidden Markov Models","volume":"20","author":"Mongillo","year":"2008","journal-title":"Neural Comput."},{"key":"ref_33","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1109\/TITS.2009.2020208","article-title":"Incremental Learning of Statistical Motion Patterns with Growing Hidden Markov Models","volume":"10","author":"Vasquez","year":"2009","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Walter, M., Psarrou, A., Psarrou, R., and Gong, S. (1999, January 13\u201316). Learning Prior and Observation Augmented Density Models for Behaviour Recognition. Proceedings of the BMVC 1999\u2014British Machine Vision Conference 1999, Nottingham, UK.","DOI":"10.5244\/C.13.3"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Meuter, M., Iurgel, U., Park, S.-B., and Kummert, A. (2008, January 4\u20136). The Unscented Kalman Filter for Pedestrian Tracking from a Moving Host. Proceedings of the 2008 IEEE Intelligent Vehicles Symposium, Eindhoven, The Netherlands.","DOI":"10.1109\/IVS.2008.4621191"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wiest, J., H\u00f6ffken, M., Kre\u00dfel, U., and Dietmayer, K. (2012, January 3\u20137). Probabilistic Trajectory Prediction with Gaussian Mixture Models. Proceedings of the 2012 IEEE Intelligent Vehicles Symposium, Madrid, Spain.","DOI":"10.1109\/IVS.2012.6232277"},{"key":"ref_37","doi-asserted-by":"publisher","first-page":"4147","DOI":"10.1109\/LRA.2019.2931248","article-title":"Dynamic Identification of the Franka Emika Panda Robot with Retrieval of Feasible Parameters Using Penalty-Based Optimization","volume":"4","author":"Gaz","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_38","unstructured":"Quigley, M., Gerkey, B., and Smart, W.D. (2015). Programming Robots with ROS: A Practical Introduction to the Robot Operating System, O\u2019Reilly Media, Inc."},{"key":"ref_39","doi-asserted-by":"publisher","first-page":"2280","DOI":"10.1016\/j.patcog.2014.01.005","article-title":"Automatic Generation and Detection of Highly Reliable Fiducial Markers Under Occlusion","volume":"47","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_40","unstructured":"Kohler, M. (1997). Using the Kalman Filter to Track Human Interactive Motion: Modelling and Initialization of the Kalman Filter for Translational Motion, Citeseer."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Julier, S.J., and Uhlmann, J.K. (1997, January 21\u201324). New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of the Signal Processing, Sensor Fusion, and Target Recognition VI, Orlando, FL, USA.","DOI":"10.1117\/12.280797"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/4\/118\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:36:26Z","timestamp":1760128586000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/4\/118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,18]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["robotics12040118"],"URL":"https:\/\/doi.org\/10.3390\/robotics12040118","relation":{"has-preprint":[{"id-type":"doi","id":"10.36227\/techrxiv.22354438","asserted-by":"object"},{"id-type":"doi","id":"10.36227\/techrxiv.22354438.v1","asserted-by":"object"}],"is-supplemented-by":[{"id-type":"doi","id":"10.36227\/techrxiv.22354438","asserted-by":"object"}]},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,18]]}}}