{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:52:17Z","timestamp":1777715537790,"version":"3.51.4"},"reference-count":64,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2017,10,1]],"date-time":"2017-10-01T00:00:00Z","timestamp":1506816000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p>We propose a novel framework of haptic rendering and interactive simulation, which, by exploiting midpoint time integration, that is known for its superior energy-conserving property but has not yet been adopted for haptics and interactive simulation, can enforce discrete-time passivity of the simulation effectively in practice, while retaining real-time interactivity due to its being non-iterative. We derive this passive midpoint integration (PMI) simulation for mechanical systems both in maximal coordinates (i.e. in SE(3)) and in generalized coordinates (i.e. in[Formula: see text] ), with some potential actions as well to implement joint articulation, constraints, compliance, and so on. We also fully incorporate multi-point Coulomb frictional contact into them via the PMI-LCP (linear complementarity problem) formulation. The proposed PMI-based simulation framework is applied to some illustrative examples to demonstrate its advantages: (1) haptic rendering of a peg-in-hole task, where very light\/stiff articulated objects can be simulated with multi-point contact; (2) haptic interaction with a flexible beam, where marginally stable\/lossless behavior (i.e. vibration) can be stably emulated; and (3) under-actuated tendon-driven hand grasping, where mixed maximal-generalized coordinates are used with very light\/stiff fingers.<\/jats:p>","DOI":"10.1177\/0278364917731821","type":"journal-article","created":{"date-parts":[[2017,10,27]],"date-time":"2017-10-27T09:06:51Z","timestamp":1509095211000},"page":"1341-1362","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":20,"title":["Haptic rendering and interactive simulation using passive midpoint 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