{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T19:53:25Z","timestamp":1789588405098,"version":"build-2803163510"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T00:00:00Z","timestamp":1779408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"crossref","award":["124102100628-3"],"award-info":[{"award-number":["124102100628-3"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The design of active pneumatic upper limb exoskeletons is complicated by the challenge of reliably determining a kinematically safe workspace. Existing analytical kinematic methods are not sufficient to predict geometric collisions between elements of closed kinematic chains, which poses risks of mechanical damage and threats to user safety during exoskeleton operation. This paper proposes a hybrid algorithm for verifying the workspace of a pneumatic exoskeleton, combining analytical modelling in MATLAB R2020b based on the Product of Exponentials (PoE) method with high-performance static simulation in the Unity environment. At the initial stage, a discrete set comprising 758 million positions of the upper exoskeleton manipulator was generated. Subsequently, a multithreaded two-stage filtering process was implemented: analytical verification of rod stroke limits and angular constraints, followed by the detection of physical intersections of solid-state meshes using the PhysX engine. The results indicate that while the analytical model filters out 99.6% of invalid configurations. Yet, among the remaining positions\u2014formally correct from a mathematical standpoint\u2014up to 50% lead to critical geometric collisions or breaks in the kinematic chain. The computational efficiency of the proposed architecture enabled full static workspace verification in under 20 min. A reachable zone topology was established, revealing pronounced asymmetry and the presence of a \u201cmanoeuvrability core\u201d in the user\u2019s anterior hemisphere. The developed algorithm generates a verified set of kinematically safe exoskeleton states, providing a foundation for the kinematic safety layer of a hierarchical control system. These findings demonstrate the necessity of complementing analytical kinematics with physical collision detection when designing hybrid kinematic mechanisms, and the approach can be applied to verify collision-free movement trajectories in various robotic systems. The approach can be applied to verify collision-free movement trajectories in simulation, with physical validation deferred to future work.<\/jats:p>","DOI":"10.3390\/s26113308","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T16:06:08Z","timestamp":1779465968000},"page":"3308","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hybrid Analytical and Simulation-Based Approach for Workspace Verification of a Pneumatic Upper Limb Exoskeleton"],"prefix":"10.3390","volume":"26","author":[{"given":"Nikita","family":"Mayorov","sequence":"first","affiliation":[{"name":"Laboratory of VR Simulators, Tambov State Technical University, Tambov 392000, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniil","family":"Teselkin","sequence":"additional","affiliation":[{"name":"Laboratory of VR Simulators, Tambov State Technical University, Tambov 392000, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Dedov","sequence":"additional","affiliation":[{"name":"Laboratory of VR Simulators, Tambov State Technical University, Tambov 392000, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3450-5213","authenticated-orcid":false,"given":"Artem","family":"Obukhov","sequence":"additional","affiliation":[{"name":"Laboratory of VR Simulators, Tambov State Technical University, Tambov 392000, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, Y., Han, X., Xin, B., and Zhao, P. 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