{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T05:41:01Z","timestamp":1774935661744,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T00:00:00Z","timestamp":1662595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007109","name":"Laboratory of Mechatronics and Virtual Prototyping (LaMaViP) of Ferrara Technopole","doi-asserted-by":"publisher","award":["UNIFE FAR2020"],"award-info":[{"award-number":["UNIFE FAR2020"]}],"id":[{"id":"10.13039\/501100007109","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007109","name":"Laboratory of Mechatronics and Virtual Prototyping (LaMaViP) of Ferrara Technopole","doi-asserted-by":"publisher","award":["307249\/2021-2"],"award-info":[{"award-number":["307249\/2021-2"]}],"id":[{"id":"10.13039\/501100007109","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Raul Guenther Laboratory of Applied Robotics of the Federal University of Santa Catarina","award":["UNIFE FAR2020"],"award-info":[{"award-number":["UNIFE FAR2020"]}]},{"name":"Raul Guenther Laboratory of Applied Robotics of the Federal University of Santa Catarina","award":["307249\/2021-2"],"award-info":[{"award-number":["307249\/2021-2"]}]},{"name":"CNPq\u2013Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (National Council for Scientific and Technological Development)","award":["UNIFE FAR2020"],"award-info":[{"award-number":["UNIFE FAR2020"]}]},{"name":"CNPq\u2013Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (National Council for Scientific and Technological Development)","award":["307249\/2021-2"],"award-info":[{"award-number":["307249\/2021-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>The presence of collaborative robots in industrial environments requires that their control strategies include collision avoidance in the generation of trajectories. In general, collision avoidance is performed via additional displacements of the kinematic chain that make the robot move far from the objects that are occasionally inserted into its safety workspace. The variability of the coordinates of the collision points inside the safety volume leads to abrupt movements for the robot. This paper presents a general method for smoothing abrupt movements in robots with one degree of redundancy for collision-avoidance trajectories, employing a second-order digital filter designed with adjustable critical damping. The method is illustrated by applying it to a redundant robot with a spherical\u2013revolute\u2013spherical type (SRS-type) kinematic chain, which is a benchmark used to test the algorithms ideated for solving this problem. This paper also presents an alternative algorithm for the inverse kinematics of the SRS-type robot and the computational experiments that show the collision avoidance proposal\u2019s performance and its properties through graphical results.<\/jats:p>","DOI":"10.3390\/robotics11050093","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T09:51:09Z","timestamp":1662630669000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Collision Avoidance for Redundant 7-DOF Robots Using a Critically Damped Dynamic Approach"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1858-541X","authenticated-orcid":false,"given":"Henrique","family":"Simas","sequence":"first","affiliation":[{"name":"Raul Guenther Lab. of Applied Robotics, Department of Mechanical Engineering, Federal University of Santa Catarina, Florian\u00f3polis 88040-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3925-3016","authenticated-orcid":false,"given":"Raffaele","family":"Di Gregorio","sequence":"additional","affiliation":[{"name":"Lab. of Mechatronics and Virtual Prototyping (LaMaViP), Department of Engineering, University of Ferrara, Via Saragat,1, 44100 Ferrara, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mihelj, M., Bajd, T., Ude, A., Lenarcic, J., Stanovnik, A., Munih, M., Rejc, J., and \u0160lajpah, S. (2018). Robotics, Springer. [2nd ed.].","DOI":"10.1007\/978-3-319-72911-4"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Matheson, E., Minto, R., Zampieri, E.G.G., Faccio, M., and Rosati, G. (2019). Human\u2013Robot Collaboration in Manufacturing Applications: A Review. Robotics, 8.","DOI":"10.3390\/robotics8040100"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.robot.2019.03.003","article-title":"Cobot Programming for Collaborative Industrial Tasks: An Overview","volume":"116","author":"Marei","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.robot.2019.07.013","article-title":"On-Line Collision Avoidance for Collaborative Robot Manipulators by Adjusting off-Line Generated Paths: An Industrial Use Case","volume":"119","author":"Safeea","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.ifacol.2019.10.019","article-title":"Neural Network Model for Identifying Workspace, Forward and Inverse Kinematics of the 7-DOF YuMi 14000 ABB Collaborative Robot","volume":"52","author":"Alebooyeh","year":"2019","journal-title":"IFAC-PapersOnLine"},{"key":"ref_6","unstructured":"IFR (2018). A Positioning Paper: Demystifying Collaborative Industrial Robots, International Federation of Robotics."},{"key":"ref_7","unstructured":"(2016). Robots and Robotic Devices\u2014Collaborative Robots. Standard No. ISO\/TS 15066:2016."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"14588","DOI":"10.1016\/j.ifacol.2017.08.2108","article-title":"Task-Oriented Rigidity Optimization for 7 DOF Redundant Manipulators","volume":"50","author":"Busson","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10846-016-0449-6","article-title":"Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints","volume":"86","author":"Liu","year":"2017","journal-title":"J. Intell. Robot. Syst. Theory Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3269","DOI":"10.1007\/s00500-017-2975-y","article-title":"A Novel Artificial Bee Colony Algorithm for Inverse Kinematics Calculation of 7-DOF Serial Manipulators","volume":"23","author":"Zhang","year":"2019","journal-title":"Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, M.C., Tsai, H.H., and Hsiao, T. (2014, January 26\u201328). Kinematics-Based Studies on a 7-DOF Redundant Manipulator. Proceedings of the 2014 CACS International Automatic Control Conference (CACS 2014), Kaohsiung, Taiwan.","DOI":"10.1109\/CACS.2014.7097192"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s11012-017-0702-5","article-title":"Dimensional Synthesis of the Single-Loop Translational Parallel Manipulator PRRR-PRPU","volume":"53","author":"Simas","year":"2018","journal-title":"Meccanica"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1007\/978-3-030-20131-9_185","article-title":"Smooth Path Planning for Redundant Robots on Collision Avoidance","volume":"Volume 73","author":"Simas","year":"2019","journal-title":"Mechanisms and Machine Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1017\/S0263574709005426","article-title":"A New Method to Solve Robot Inverse Kinematics Using Assur Virtual Chains","volume":"27","author":"Simas","year":"2009","journal-title":"Robotica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3920","DOI":"10.3906\/elk-1608-143","article-title":"Inverse Kinematics of a 7-DOF Redundant Robot Manipulator Using the Active Set Approach under Joint Physical Limits","volume":"25","author":"Rouhani","year":"2017","journal-title":"Turk. J. Electr. Eng. Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1177\/0278364920918296","article-title":"Multimodal Trajectory Optimization for Motion Planning","volume":"39","author":"Osa","year":"2020","journal-title":"Int. J. Robot. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1080\/17415977.2019.1602124","article-title":"Calculation of the Inverse Kinematics Solution of the 7-DOF Redundant Robot Manipulator by the Firefly Algorithm and Statistical Analysis of the Results in Terms of Speed and Accuracy","volume":"28","author":"Dereli","year":"2020","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"172988141773724","DOI":"10.1177\/1729881417737241","article-title":"Real Time Optimum Trajectory Generation for Redundant\/Hyper-Redundant Serial Industrial Manipulators","volume":"14","author":"Ayten","year":"2017","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF00126069","article-title":"Kinematic Control of Redundant Robot Manipulators: A Tutorial","volume":"3","author":"Siciliano","year":"1990","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Quispe, A.H., and Stilman, M. (December, January 29). Deterministic Motion Planning for Redundant Robots along End-Effector Paths. Proceedings of the 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), Osaka, Japan.","DOI":"10.1109\/HUMANOIDS.2012.6651609"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/TRO.2011.2173852","article-title":"A General User-Oriented Framework for Holonomic Redundancy Resolution in Robotic Manipulators Using Task Augmentation","volume":"28","author":"Zanchettin","year":"2012","journal-title":"IEEE Trans. Robot."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1109\/TSMC.1983.6313123","article-title":"Review of Pseudoinverse Control for Use with Kinematically Redundant Manipulators","volume":"SMC-13","author":"Klein","year":"1983","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kalakrishnan, M., Chitta, S., Theodorou, E., Pastor, P., and Schaal, S. (2011, January 9\u201313). STOMP: Stochastic Trajectory Optimization for Motion Planning. Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980280"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.conengprac.2017.06.015","article-title":"FIR Filter-Based Online Jerk-Constrained Trajectory Generation","volume":"66","author":"Besset","year":"2017","journal-title":"Control Eng. Pract."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gerelli, O., and Guarino Lo Bianco, C. (2010, January 3\u20137). A Discrete-Time Filter for the on-Line Generation of Trajectories with Bounded Velocity, Acceleration, and Jerk. Proceedings of the 2010 IEEE International Conference on Robotics and Automation, Anchorage, AK, USA.","DOI":"10.1109\/ROBOT.2010.5509712"},{"key":"ref_26","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_27","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1177\/0278364918781734","article-title":"Simultaneous Self-Calibration and Navigation Using Trajectory Optimization","volume":"37","author":"Preiss","year":"2018","journal-title":"Int. J. Robot. Res."},{"key":"ref_28","unstructured":"Franklin, G.F., Powell, J.D., and Emami-Naeini, A. (2019). Feedback Control of Dynamic Systems, Pearson. [8th ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Colome, A., and Torras, C. (2012, January 7\u201312). Redundant Inverse Kinematics: Experimental Comparative Review and Two Enhancements. Proceedings of the 2012 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Vilamoura-Algarve, Portugal.","DOI":"10.1109\/IROS.2012.6385672"},{"key":"ref_30","unstructured":"Siciliano, B., Lorenzo, S., Villani, L., and Orilo, G. (2010). Robotics: Modelling, Planning and Control, Springer. [2nd ed.]."},{"key":"ref_31","unstructured":"Tsai, L.-W. (1999). Robot Analysis and Design: The Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, Inc.. [1st ed.]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s10462-019-09683-x","article-title":"A Meta-Heuristic Proposal for Inverse Kinematics Solution of 7-DOF Serial Robotic Manipulator: Quantum Behaved Particle Swarm Algorithm","volume":"53","author":"Dereli","year":"2020","journal-title":"Artif. Intell. Rev."},{"key":"ref_33","first-page":"1","article-title":"A Comparison of Automatic Nap-of-the-Earth Guidance Strategies for Helicopters","volume":"33","author":"Mooney","year":"2014","journal-title":"J. Field Robot."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhao, S., Zhu, Z., and Luo, J. (2019). Multitask-Based Trajectory Planning for Redundant Space Robotics Using Improved Genetic Algorithm. Appl. Sci., 9.","DOI":"10.3390\/app9112226"},{"key":"ref_35","unstructured":"Ogura, Y., Aikawa, H., Shimomura, K., Kondo, H., Morishima, A., Lim, H.O., and Takanishi, A. (2006, January 15\u201319). Development of a New Humanoid Robot WABIAN-2. Proceedings of the 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006, Orlando, FL, USA."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Starke, S., Hendrich, N., Krupke, D., and Zhang, J. (2017, January 24\u201328). Evolutionary Multi-Objective Inverse Kinematics on Highly Articulated and Humanoid Robots. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206620"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1002\/rob.21598","article-title":"Backward Ladder Climbing Locomotion of Humanoid Robot with Gain Overriding Method on Position Control","volume":"33","author":"Lim","year":"2016","journal-title":"J. Field Robot."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.mechmachtheory.2017.10.025","article-title":"Position-Based Kinematics for 7-DoF Serial Manipulators with Global Configuration Control, Joint Limit and Singularity Avoidance","volume":"121","author":"Faria","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wang, Y., and Artemiadis, P. (2013). Closed-Form Inverse Kinematic Solution for Anthropomorphic Motion in Redundant Robot Arms. Adv. Robot. Autom., 2.","DOI":"10.4172\/2168-9695.1000110"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1017\/S0263574718000899","article-title":"Position Analysis, Singularity Loci and Workspace of a Novel 2PRPU Schoenflies-Motion Generator","volume":"37","author":"Simas","year":"2019","journal-title":"Robotica"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Simas, H., and Di Gregorio, R. (2017). Kinetostatics and Optimal Design of a 2PRPU Shoenflies-Motion Generator. Mechanisms and Machine Science, Springer Cham.","DOI":"10.1007\/978-3-319-67567-1_13"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1080\/0951192X.2016.1268269","article-title":"Active Collision Avoidance for Human\u2013Robot Collaboration Driven by Vision Sensors","volume":"30","author":"Mohammed","year":"2017","journal-title":"Int. J. Comput. Integr. Manuf."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"S\u00fcli, E., and Mayers, D.F. (2003). An Introduction to Numerical Analysis, Cambridge University Press.","DOI":"10.1017\/CBO9780511801181"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Luo, R.C., Ko, M.C., Chung, Y.T., and Chatila, R. (2014, January 8\u201311). Repulsive Reaction Vector Generator for Whole-Arm Collision Avoidance of 7-DoF Redundant Robot Manipulator. Proceedings of the 2014 IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Besacon, France.","DOI":"10.1109\/AIM.2014.6878217"},{"key":"ref_45","unstructured":"(2022, July 09). KUKA Sensitive Robotics: LBR iiwa. Catalog published by KUKA Roboter GmbH: Augsburg, Germany. Available online: https:\/\/pdf.directindustry.com\/pdf\/kuka-ag\/kuka-sensitive-robotics-lbr-iiwa\/17587-724449.html."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Huber, G., and Wollherr, D. (2019). Efficient Closed-Form Task Space Manipulability for a 7-DOF Serial Robot. Robotics, 8.","DOI":"10.3390\/robotics8040098"},{"key":"ref_47","unstructured":"Larson, R., and Edwards, B.H. (2009). Multivariable Calculus, Cengage Learning. [9th ed.]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1007\/978-3-319-67567-1_15","article-title":"Maximum Isotropic Force Capability Maps in Planar Cooperative Systems: A Practical Case Study","volume":"Volume 54","author":"Simoni","year":"2018","journal-title":"Mechanisms and Machine Science"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Oh, J., Bae, H., and Oh, J.H. (2017, January 10\u201312). Analytic Inverse Kinematics Considering the Joint Constraints and Self-Collision for Redundant 7DOF Manipulator. Proceedings of the 2017 First IEEE International Conference on Robotic Computing (IRC), Taichung, Taiwan.","DOI":"10.1109\/IRC.2017.46"},{"key":"ref_50","unstructured":"(2022, July 09). Video that presents the complete simulation experiment. Available online: https:\/\/youtu.be\/BfRjA8dgnq8."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s40430-018-1090-z","article-title":"Wrench Distribution of a Cooperative Robotic System Using a Modified Scaling Factor Method","volume":"40","author":"Frantz","year":"2018","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s11370-015-0180-3","article-title":"Practical Analytical Inverse Kinematic Approach for 7-DOF Space Manipulators with Joint and Attitude Limits","volume":"8","author":"Zhou","year":"2015","journal-title":"Intell. Serv. Robot."},{"key":"ref_53","unstructured":"Scimmi, L.S., Melchiorre, M., Mauro, S., and Pastorelli, S. (2018, January 29\u201331). Multiple Collision Avoidance between Human Limbs and Robot Links Algorithm in Collaborative Tasks. Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics, Porto, Portugal."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Karimi, G., and Jahanian, O. (2012). Genetic Algorithm Application in Swing Phase Optimization of AK Prosthesis with Passive Dynamics and Biomechanics Considerations. Genetic. Algorithms Application, Intechopen.","DOI":"10.5772\/38211"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Xu, Z., Gan, Y., and Dai, X. (2019, January 3\u20135). Obstacle Avoidance of 7-DOF Redundant Manipulators. Proceedings of the 2019 Chinese Control And Decision Conference (CCDC), Nanchang, China.","DOI":"10.1109\/CCDC.2019.8832418"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/11\/5\/93\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:27:39Z","timestamp":1760142459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/11\/5\/93"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,8]]},"references-count":55,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["robotics11050093"],"URL":"https:\/\/doi.org\/10.3390\/robotics11050093","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,8]]}}}