{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:44:11Z","timestamp":1781534651903,"version":"3.54.5"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T00:00:00Z","timestamp":1777161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004489","name":"Mitacs","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004489","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/00cjrc276","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>This article presents an approach to extend the capabilities of vat photopolymerization (VPP) 3D printing using a robotic arm, with a focus on robust path planning. The robotic cell consists of a Mecademic Meca500 six-axis robot mounted on a Zaber X-LRQ300AP linear guide. The kinematic chain is inverted to reflect the logic of VPP: the world reference frame is fixed to the robot\u2019s tool (the build plate), while the tool frame is attached to the polymerization zone. A virtual degree of freedom for screen image rotation is introduced, bringing the system to eight degrees of freedom. Inverse kinematics are solved under constraints (pose tolerance, joint limits, collision avoidance, and continuity) and evaluated using multi-criteria metrics: manipulability, normalized joint-limit margin, and positional\/angular sensitivity. The algorithm follows a deterministic coarse-to-fine search procedure: discrete sweeping of global part orientations, initial sampling with Halton sequences, abd feasibility filtering on a sparsified trajectory, followed by refinement and multi-criteria ranking. The pipeline successfully discarded infeasible orientations and identified feasible printing trajectories for six of the seven benchmark parts, while the remaining case highlights a limitation that may be addressed in future improvements.<\/jats:p>","DOI":"10.3390\/robotics15050085","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T13:32:22Z","timestamp":1777469542000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Stage Parameter Search for Robot Path Planning in Bottom-Up Vat 3D Printing"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6854-2749","authenticated-orcid":false,"given":"Evan","family":"Rolland","sequence":"first","affiliation":[{"name":"Department of Systems Engineering, \u00c9cole de Technologie Sup\u00e9rieure, 1100 Notre-Dame Street West, Montreal, QC H3C 1K3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9663-2496","authenticated-orcid":false,"given":"Ilian A.","family":"Bonev","sequence":"additional","affiliation":[{"name":"Department of Systems Engineering, \u00c9cole de Technologie Sup\u00e9rieure, 1100 Notre-Dame Street West, Montreal, QC H3C 1K3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9047-2338","authenticated-orcid":false,"given":"Evan","family":"Jones","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengpeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7191-1528","authenticated-orcid":false,"given":"Nanzhu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Nissan Technical Center North America, 39001 Sunrise Dr., Farmington Hills, MI 48331, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2005672","DOI":"10.1002\/adma.202005672","article-title":"Conformal Geometry and Multimaterial Additive Manufacturing through Freeform Transformation of Building Layers","volume":"33","author":"Huang","year":"2021","journal-title":"Adv. Mater."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Makulavi\u010dius, M., Petkevi\u010dius, S., Ro\u017e\u0117n\u0117, J., Dzedzickis, A., and Bu\u010dinskas, V. (2023). Industrial Robots in Mechanical Machining: Perspectives and Limitations. Robotics, 12.","DOI":"10.3390\/robotics12060160"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Siciliano, B., Sciavicco, L., Villani, L., and Oriolo, G. (2009). Robotics, Springer. Advanced Textbooks in Control and Signal Processing.","DOI":"10.1007\/978-1-84628-642-1"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Latombe, J.C. (1991). Robot Motion Planning, Springer.","DOI":"10.1007\/978-1-4615-4022-9"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1016\/j.jmapro.2024.04.084","article-title":"A comparative review of multi-axis 3D printing","volume":"120","author":"Yao","year":"2024","journal-title":"J. Manuf. Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e2162929","DOI":"10.1080\/17452759.2022.2162929","article-title":"Teams of robots in additive manufacturing: A review","volume":"18","author":"Alhijaily","year":"2023","journal-title":"Virtual Phys. Prototyp."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"29754","DOI":"10.1038\/s41598-024-81174-8","article-title":"Real-time optimized inverse kinematics of redundant robots under inequality constraints","volume":"14","author":"Zhang","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4326","DOI":"10.1109\/TNNLS.2024.3363241","article-title":"Collective Neural Dynamics for Sparse Motion Planning of Redundant Manipulators Without Hessian Matrix Inversion","volume":"36","author":"Jin","year":"2025","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Huang, J., Zhang, B., Xiao, J., and Zhang, Q. (2022). An Approach to Improve the Resolution of DLP 3D Printing by Parallel Mechanism. Appl. Sci., 12.","DOI":"10.3390\/app122412905"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wu, C., Yi, R., Liu, Y.J., He, Y., and Wang, C.C. (2016, January 9\u201314). Delta DLP 3D printing with large size. Proceedings of the 2016 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Republic of Korea.","DOI":"10.1109\/IROS.2016.7759338"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1109\/70.508440","article-title":"Specification of force-controlled actions in the \u201ctask frame formalism\u201d\u2014A synthesis","volume":"12","author":"Bruyninckx","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_12","unstructured":"Pieper, D.L. (1968). The Kinematics of Manipulators Under Computer Control, Stanford University."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1115\/1.2919218","article-title":"Inverse Kinematics of the General 6R Manipulator and Related Linkages","volume":"115","author":"Raghavan","year":"1993","journal-title":"J. Mech. Des."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1090\/qam\/10666","article-title":"A method for the solution of certain non-linear problems in least squares","volume":"2","author":"Levenberg","year":"1944","journal-title":"Q. Appl. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An Algorithm for Least-Squares Estimation of Nonlinear Parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1109\/TSMC.1977.4309644","article-title":"Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms","volume":"7","year":"1977","journal-title":"IEEE Trans. Syst. Man. Cybern."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1109\/TSMC.1986.289285","article-title":"Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods","volume":"16","author":"Wampler","year":"1986","journal-title":"IEEE Trans. Syst. Man. Cybern."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Schulman, J., Ho, J., Lee, A., Awwal, I., Bradlow, H., and Abbeel, P. (2013). Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization. Proceedings of the Robotics: Science and Systems IX, Robotics: Science and Systems Foundation.","DOI":"10.15607\/RSS.2013.IX.031"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Beeson, P., and Ames, B. (2015, January 3\u20135). TRAC-IK: An open-source library for improved solving of generic inverse kinematics. Proceedings of the 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), Seoul, Republic of Korea.","DOI":"10.1109\/HUMANOIDS.2015.7363472"},{"key":"ref_20","first-page":"813","article-title":"Verteilungsfunktionen I","volume":"38","year":"1935","journal-title":"Proc. K. Akad. Van. Wet."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/BF01386213","article-title":"On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals","volume":"2","author":"Halton","year":"1960","journal-title":"Numer. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1016\/S0895-7177(00)00178-3","article-title":"Randomized Halton sequences","volume":"32","author":"Wang","year":"2000","journal-title":"Math. Comput. Model."},{"key":"ref_23","first-page":"720","article-title":"Improving printing orientation for Fused Deposition Modeling printers by analyzing connected components","volume":"22","author":"Benes","year":"2018","journal-title":"Addit. Manuf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498500400201","article-title":"Manipulability of Robotic Mechanisms","volume":"4","author":"Yoshikawa","year":"1985","journal-title":"Int. J. Robot. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1109\/TRO.2006.878978","article-title":"Error propagation on the Euclidean group with applications to manipulator kinematics","volume":"22","author":"Wang","year":"2006","journal-title":"IEEE Trans. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Miettinen, K. (1998). Nonlinear Multiobjective Optimization, Springer. International Series in Operations Research & Management Science.","DOI":"10.1007\/978-1-4615-5563-6"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Beschi, M., Mutti, S., Nicola, G., Faroni, M., Magnoni, P., Villagrossi, E., and Pedrocchi, N. (2019). Optimal Robot Motion Planning of Redundant Robots in Machining and Additive Manufacturing Applications. Electronics, 8.","DOI":"10.3390\/electronics8121437"},{"key":"ref_29","unstructured":"Mvolo Evina Alegue, E. (2024). Solutions d\u2019Optimisation Pour la Fabrication Additive Robotis\u00e9e Multi-Proc\u00e9d\u00e9s DED de Pi\u00e8ces de Grandes Dimensions M\u00e9talliques. [Ph.D. Thesis, Universit\u00e9 Clermont Auvergne]."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Rybczak, M., Popowniak, N., and Lazarowska, A. (2024). A Survey of Machine Learning Approaches for Mobile Robot Control. Robotics, 13.","DOI":"10.3390\/robotics13010012"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1177\/0278364913495721","article-title":"Reinforcement learning in robotics: A survey","volume":"32","author":"Kober","year":"2013","journal-title":"Int. J. Robot. Res."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Qureshi, A.H., Simeonov, A., Bency, M.J., and Yip, M.C. (2019, January 20\u201324). Motion Planning Networks. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8793889"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Janson, L., Ichter, B., and Pavone, M. (2016). Deterministic Sampling-Based Motion Planning: Optimality, Complexity, and Performance. arXiv.","DOI":"10.1007\/978-3-319-60916-4_29"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103059","DOI":"10.1016\/j.rcim.2025.103059","article-title":"Novel calibration method for robotic bottom-up vat polymerization additive manufacturing systems","volume":"97","author":"Rolland","year":"2025","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_35","unstructured":"Bonev, I., Sun, C., Zhang, P., Krim, Y., Jones, E., and Zhao, N. (2025). Calibration Tool for Three-Dimensional Printing System. (Application US20250249641A1), U.S. Patent."},{"key":"ref_36","unstructured":"do Carmo, M.P. (1976). Differential Geometry of Curves and Surfaces, Prentice-Hall."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1109\/TRO.2009.2037252","article-title":"Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices","volume":"26","author":"Cardou","year":"2010","journal-title":"IEEE Trans. Robot."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/15\/5\/85\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T07:22:28Z","timestamp":1779693748000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/15\/5\/85"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,26]]},"references-count":37,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["robotics15050085"],"URL":"https:\/\/doi.org\/10.3390\/robotics15050085","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,26]]}}}