This paper is concerned with the animation and control of vehicles with complex dynamics such as helicopters, boats, and cars. Motivated by recent developments in discrete geometric mechanics we develop a general framework for integrating the dynamics of holonomic and nonholonomic vehicles by preserving their state-space geometry and motion invariants. We demonstrate that the resulting integration schemes are superior to standard methods in numerical robustness and efficiency, and can be applied to many types of vehicles. In addition, we show how to use this framework in an optimal control setting to automatically compute accurate and realistic motions for arbitrary user-specified constraints.
Month: January 2009
Linear Time Super-Helices
Thin elastic rods such as cables, phone coils, tree branches, or hair, are common objects in the real world but computing their dynamics accurately remains challenging. The recent Super-Helix model, based on the discrete equations of Kirchhoff for a piecewise helical rod, is one of the most promising models for simulating non-stretchable rods that can bend and twist. However, this model suffers from a quadratic complexity in the number of discrete elements, which, in the context of interactive applications, makes it limited to a few number of degrees of freedom – or equivalently to a low number of variations in curvature along the mean curve. This paper proposes a new, recursive scheme for the dynamics of a Super-Helix, inspired by the popular algorithm of Featherstone for serial multibody chains. Similarly to Featherstone’s algorithm, we exploit the recursive kinematics of a Super-Helix to propagate elements inertias from the free end to the clamped end of the rod, while the dynamics is solved within a second pass traversing the rod in the reverse way. Besides the gain in linear complexity, which allows us to simulate a rod of complex shape much faster than the original approach, our algorithm makes it straightforward to simulate tree-like structures of Super-Helices, which turns out to be particularly useful for animating trees and plants realistically, under large displacements.
Continuum-based Strain Limiting
We present Continuum-based Strain Limiting (CSL) – a new method for limiting deformations in physically-based cloth simulations. Recent developments have led to methods which excel at simulating nearly inextensible materials, but the efficient simulation of general biphasic textiles and their anisotropic behavior remains challenging. Other approaches use softer materials and enforce limits on edge elongations, leading to discretization-dependent behavior. Moreover, they offer no explicit control over shearing and stretching unless specifically aligned meshes are used, which makes them less attractive for practical animation of anisotropic textiles. Based on a continuum deformation measure, our method allows accurate deformation control using individual thresholds for all types of strain. We impose deformation limits element-wise and cast the problem as a system of linear equations. We show how to further improve efficiency using an approximate formulation. CSL can be combined with any type of cloth simulator and, as a velocity filter, integrates seamlessly into standard collision handling frameworks.