We propose a novel approach to proportional derivative (PD) control exploiting the fact that these equations can be solved analytically for a single degree of freedom. The analytic solution indicates what the PD controller would accomplish in isolation without interference from neighboring joints, gravity and external forces, outboard limbs, etc. Our approach to time integration includes an inverse dynamics formulation that automatically incorporates global feedback so that the per joint predictions are achieved. This effectively decouples stiffness from control so that we obtain the desired target regardless of the stiffness of the joint, which merely determines when we get there. We start with simple examples to illustrate our method, and then move on to more complex examples including PD control of line segment muscle actuators.

We present a new method for the efficient simulation of large bodies of water, especially effective when three-dimensional surface effects are important. Similar to a traditional two-dimensional height field approach, most of the water volume is represented by tall cells which are assumed to have linear pressure profiles. In order to avoid the limitations typically associated with a height field approach, we simulate the entire top surface of the water volume with a state of the art, fully three-dimensional Navier-Stokes free surface solver. Our philosophy is to use the best available method near the interface (in the three-dimensional region) and to coarsen the mesh away from the interface for efficiency. We coarsen with tall, thin cells (as opposed to octrees or AMR), because they maintain good resolution horizontally allowing for accurate representation of bottom topography.

We propose a novel technique for melting and burning solid materials, including the simulation of the resulting liquid and gas. The solid is simulated with traditional mesh-based techniques (triangles or tetrahedra) which enable robust handling of both deformable and rigid objects, collision and self-collision, rolling, friction, stacking, etc. The subsequently created liquid or gas is simulated with modern grid-based techniques, including vorticity confinement and the particle level set method. The main advantage of our method is that state-of-the-art techniques are used for both the solid and the fluid without compromising simulation quality when coupling them together or converting one into the other. For example, we avoid modeling solids as Eulerian grid-based fluids with high viscosity or viscoelasticity, which would preclude the handling of thin shells, self-collision, rolling, etc. Thus, our method allows one to achieve new effects while still using their favorite algorithms (and implementations) for simulating both solids and fluids, whereas other coupling algorithms require major algorithm and implementation overhauls and still fail to produce rich coupling effects (e.g., melting and burning solids).

We present a novel method for solid/fluid coupling that can treat infinitesimally thin solids modeled by a lower dimensional triangulated surface. Since classical solid/fluid coupling algorithms rasterize the solid body onto the fluid grid, an entirely new approach is required to treat thin objects that do not contain an interior region. Robust ray casting is used to augment a number of interpolation, finite difference and rendering techniques so that fluid does not leak through the triangulated surface. Moreover, we propose a technique for properly enforcing incompressibility so that fluid does not incorrectly compress (and appear to lose mass) near the triangulated surface. This allows for the robust interaction of cloth and shells with thin sheets of water. The proposed method works for both rigid body shells and for deformable manifolds such as cloth, and we present a two way coupling technique that allows the fluid's pressure to affect the solid. Examples illustrate that our method performs well, especially in the difficult case of water and cloth where it produces visually rich interactions between the particle level set method for treating the water/air interface and our newly proposed method for treating the solid/fluid interface. We have implemented the method on both uniform and adaptive octree grids.

We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this dual representation is shown to have many advantages. We propose a novel approach to time integration merging it with the collision and contact processing algorithms in a fashion that obviates the need for ad hoc threshold velocities. We show that this approach matches the theoretical solution for blocks sliding and stopping on inclined planes with friction. We also present a new shock propagation algorithm that allows for efficient use of the propagation (as opposed to the simultaneous) method for treating contact. These new techniques are demonstrated on a variety of problems ranging from simple test cases to stacking problems with as many as 1000 nonconvex rigid bodies with friction as shown in Figure 1.