{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T01:37:38Z","timestamp":1768009058172,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,4,7]],"date-time":"2020-04-07T00:00:00Z","timestamp":1586217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Locomotion over different terrain types, whether flat or uneven, is very important for a wide range of service operations in robotics. Potential applications range from surveillance, rescue, or hospital assistance. Wheeled-legged hexapod robots have been designed to solve these locomotion tasks. Given the wide range of feasible operations, one of the key operation planning issues is related to the robot balancing during motion tasks. Usually this problem is related with the pose of the robot\u2019s center of mass, which can be addressed using different mathematical techniques. This paper proposes a new practical technique for balancing wheeled-legged hexapod robots, where a Biodex Balance System model SD (for static &amp; dynamic) is used to obtain the effective position of the center of mass, thus it can be recalculated to its optimal position. Experimental tests are carried out to evaluate the effectiveness of this technique and modify and improve the position of hexapod robots\u2019 center of mass.<\/jats:p>","DOI":"10.3390\/robotics9020023","type":"journal-article","created":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T05:59:47Z","timestamp":1586325587000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Static Balancing of Wheeled-legged Hexapod Robots"],"prefix":"10.3390","volume":"9","author":[{"given":"Ernesto Christian","family":"Orozco-Magdaleno","sequence":"first","affiliation":[{"name":"CICATA Instituto Politecnico Nacional \u2013Unidad Queretaro, Quer\u00e9taro 76090, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5602-1519","authenticated-orcid":false,"given":"Daniele","family":"Cafolla","sequence":"additional","affiliation":[{"name":"IRCCS Neuromed, 86077 Pozzilli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3307-6947","authenticated-orcid":false,"given":"Eduardo","family":"Castillo-Castaneda","sequence":"additional","affiliation":[{"name":"CICATA Instituto Politecnico Nacional \u2013Unidad Queretaro, Quer\u00e9taro 76090, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0831-8358","authenticated-orcid":false,"given":"Giuseppe","family":"Carbone","sequence":"additional","affiliation":[{"name":"DIMEG, University of Calabria, 87036 Cosenza, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,7]]},"reference":[{"key":"ref_1","first-page":"121","article-title":"A Service Hexapod Robot as Hospital Guide","volume":"20","author":"Cafolla","year":"2019","journal-title":"Int. J. Mech. Control."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Schwarz, M., Rodehutskors, T., Schreiber, M., and Behnke, S. Hybrid driving-stepping locomotion with the wheeled-legged robot Momaro. Proceedings of the 2016 IEEE International Conference on Robotics and Automation (ICRA).","DOI":"10.1109\/ICRA.2016.7487776"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Carbone, G., and Gomez-Bravo, F. (2015). Motion and Operation Planning of Robotic Systems: Background and Practical Approaches, Springer.","DOI":"10.1007\/978-3-319-14705-5"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1109\/LRA.2019.2896721","article-title":"Trajectory Optimization for Wheeled-Legged Quadrupedal Robots Using Linearized ZMP Constraints","volume":"4","author":"Bjelonic","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_5","first-page":"149","article-title":"Operation Strategy for a Low-Cost Easy-Operation Cassino Hexapod","volume":"4","author":"Carbone","year":"2007","journal-title":"Appl. Bionics Biomech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1017\/S0263574714002069","article-title":"Design and numerical characterization of a new leg exoskeleton for motion assistance","volume":"33","author":"Copilusi","year":"2014","journal-title":"Robotica"},{"key":"ref_7","first-page":"117","article-title":"Design and Simulation of a Leg Exoskeleton Linkage for a Human Rehabilitation System","volume":"18","author":"Visa","year":"2014","journal-title":"The 11th IFToMM International Symposium on Science of Mechanisms and Machines. Mechanisms and Machine Science"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1109\/TRO.2017.2696022","article-title":"TurboQuad: A Novel Leg\u2013Wheel Transformable Robot With Smooth and Fast Behavioral Transitions","volume":"33","author":"Chen","year":"2017","journal-title":"IEEE Trans. Robot."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bai, L., Hu, H., Chen, X., Sun, Y., Ma, C., and Zhong, Y. (2019). CPG-Based Gait Generation of the Curved-Leg Hexpod Robot with Smooth Gait Transition. Sensors, 19.","DOI":"10.3390\/s19173705"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2116","DOI":"10.1109\/LRA.2019.2899750","article-title":"Keep Rollin\u2019\u2014Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots","volume":"4","author":"Bjelonic","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"21","DOI":"10.5772\/5645","article-title":"A Low-Cost Easy-Operation Hexapod Walking Machine","volume":"5","author":"Carbone","year":"2008","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Giordano, P.R., Fuchs, M., Albu-Schaffer, A., and Hirzinger, G. (2009, January 12\u201317). On the kinematic modeling and control of a mobile platform equipped with steering wheels and movable legs. Proceedings of the 2009 IEEE International Conference on Robotics and Automation, Kobe, Japan.","DOI":"10.1109\/ROBOT.2009.5152625"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Tedeschi, F., and Carbone, G. (2017). Design of a Novel Leg-Wheel Hexapod Walking Robot. Robotics, 6.","DOI":"10.3390\/robotics6040040"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s10514-013-9358-8","article-title":"Implementation and stability analysis of prioritized whole-body compliant controllers on a wheeled humanoid robot in uneven terrains","volume":"35","author":"Sentis","year":"2013","journal-title":"Auton. Robot."},{"key":"ref_15","first-page":"229","article-title":"Optimum Path Planning of CaPaMan (Cassino Parallel Manipulator) by Using Inverse Dynamics","volume":"26","author":"Carbone","year":"2008","journal-title":"Robot. Int. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.mechmachtheory.2005.05.001","article-title":"Stiffness analysis of biped humanoid robot WABIAN-RIV","volume":"41","author":"Carbone","year":"2006","journal-title":"Mech. Mach. Theory"},{"key":"ref_17","first-page":"2391","article-title":"Experimental Validation of a Gait Planning for Obstacle Avoidance Using Mecanum Wheels","volume":"73","author":"Uhl","year":"2019","journal-title":"Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science"},{"key":"ref_18","first-page":"19","article-title":"Design and Operation of Cassino Hexapod II","volume":"15","author":"Tedeschi","year":"2014","journal-title":"Int. J. Mech. Control."},{"key":"ref_19","first-page":"205","article-title":"Experiences for a User-Friendly Operation of Cassino Hexapod III","volume":"67","author":"Aspragathos","year":"2018","journal-title":"Advances in Service and Industrial Robotics. RAAD 2018. Mechanisms and Machine Science"},{"key":"ref_20","first-page":"286","article-title":"Experiences on a Hybrid Locomotion Approach to Overcome Obstacles with Cassino Hexapod III","volume":"68","author":"Carbone","year":"2019","journal-title":"Advances in Italian Mechanism Science. IFToMM ITALY 2018. Mechanisms and Machine Science"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1729881418790692","article-title":"HeritageBot platform for service in Cultural Heritage frames","volume":"15","author":"Ceccarelli","year":"2018","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_22","unstructured":"Wen-Yu, Z., and Lei, Z. (2011, January 6\u20138). Research of a static balance method for a quadruped robot walking on a slope. Proceedings of the 2011 IEEE International Conference on Information and Automation, Shenzhen, China."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Magid, E., Tsubouchi, T., Koyanagi, E., and Yoshida, T. (2010, January 18\u201322). Static Balance for Rescue Robot Navigation: Loosing Balance on Purpose within Random Step Environment. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5649361"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1115\/1.2899226","article-title":"A Surface Integral Approach to the Motion Planning of Nonholonomic Systems","volume":"116","author":"Mukherjee","year":"1994","journal-title":"J. Dyn. Syst. Meas. Control."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1109\/9.277235","article-title":"Nonholonomic motion planning: Steering using sinusoids","volume":"38","author":"Murray","year":"1993","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1142\/S0219843604000083","article-title":"Zero-Moment Point \u2013 Thirty-Five Years of its Life","volume":"1","author":"Vukobratovic","year":"2004","journal-title":"Int. J. Hum. Robot."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6918","DOI":"10.3182\/20110828-6-IT-1002.02234","article-title":"Integrated Motion Planning for a Hexapod Robot Walking on Rough Terrain","volume":"44","author":"Belter","year":"2011","journal-title":"IFAC Proceedings Volumes"},{"key":"ref_28","unstructured":"Biodex (2020, March 31). Balance System SD Operation\/Service Manual. Available online: https:\/\/www.biodex.com\/sites\/default\/files\/950300man_08060.pdf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/s11370-008-0024-5","article-title":"Wheeled inverted pendulum type assistant robot: Design concept and mobile control","volume":"1","author":"Jeong","year":"2008","journal-title":"Intell. Serv. Robot."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1016\/j.procs.2018.07.114","article-title":"Person Identification in Smart Surveillance Robots using Sparse Interest Points","volume":"133","author":"Vinay","year":"2018","journal-title":"Procedia Comput. Sci."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/9\/2\/23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:16:20Z","timestamp":1760174180000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/9\/2\/23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,7]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["robotics9020023"],"URL":"https:\/\/doi.org\/10.3390\/robotics9020023","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,7]]}}}