Figure 1 : Real-time control ensures fixed simulation outcome regardless of runtime user forces: First: the rest configuration of the "T"-shape structure and the two target balls. Second: reference motion from an external simulator; the two ends of the "T" impact the two balls. Third: user-perturbed real-time simulation, without control. The two ends miss the target. Forth: controlled user-perturbed real-time simulation, with gentle control forces, tracks the reference motion and successfully

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... pacts the target. The perturbation force load (green arrow; applied 1/5 through the simulation, only in the third and fourth motion) pushes the "T" in the opposite direction of motion. Abstract Recent advances have brought real-time physically based simulation within reach, but simulations are still difficult to control in real time. 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 overcontrolled 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.