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We present interactive simulations of passive systems such as deformable solids or fluids that are not only fast, but also directable: they follow given input trajectories while simultaneously reacting to user input and other unexpected disturbances. We achieve such directability using a real-time controller that runs in tandem with a real-time physically based simulation. To avoid stiff and over-controlled systems where the natural dynamics are overpowered, the injection of control forces has to be minimized. This search for gentle forces can be made tractable in real-time by linearizing the system dynamics around the input trajectory, and then using a time-varying linear quadratic regulator to build the controller. We show examples of controlled complex deformable solids and fluids, demonstrating that our approach generates a requested fixed outcome for reasonable user inputs, while simultaneously providing runtime motion variety.<\/jats:p>","DOI":"10.1145\/1409060.1409116","type":"journal-article","created":{"date-parts":[[2008,12,3]],"date-time":"2008-12-03T21:56:04Z","timestamp":1228341364000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":43,"title":["Real-time control of physically based simulations using gentle forces"],"prefix":"10.1145","volume":"27","author":[{"given":"Jernej","family":"Barbi\u010d","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jovan","family":"Popovi\u0107","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Barbi\u010d J. and James D. 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