ITR: Representations and Algorithms for Deformable Objects

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Deformable objects are ubiquitous in the physical world at all scales, from the molecular to the astrophysical. Many of life's basic functions, from protein folding and ligand binding at the micro level, to meiosis and mitosis at the cellular level, to the beating of a heart at the macro level, are best described as shape deformations in time. Flexible materials are finding increasing applications in engineering, across areas such as testing and manufacturing, and especially in biomedical applications, including prosthetic devices and minimally invasive imaging and surgical procedures. Special effects in the entertainment industry and haptics-based human-computer interfaces also require better models for flexible objects. Though deformation in nature can be based on a variety of underlying physical processes, we believe that there are a number of unifying principles common to understanding all deformations. Today, however, we lack a general computational theory of how to sense, represent, simulate, approximate, actuate, control, and render deformable objects.Research Goals and MethodsThe goal of this proposal is to undertake a foundational study of representations and algorithms for the computational modeling of deformable objects. Such modeling is challenging because deformations involve representations of shape and motion, and bring together continuous and discrete phenomena, as well as local and global constraints. Some of the specific challenges that have to be addressed are:1. the behavior of deformable objects is defined by both geometry and physics and characterized by complex high-dimensional energy landscapes that need to be compactly encoded and efficiently interrogated for actuation, control, and planning;2. physically accurate simulation of deformations is of-ten computationally expensive; we must find ways to approximate the full physics, while still guaranteeing the correctness, or at least appropriateness, of the solution that we compute in the parts of the system we care about;3. discrete events, such as collisions and self-collisions, alter the continuous evolution law of the system; these events must be efficiently predicted or detected, and processed;4. contact and self-contact must be modeled across rapid changes in the contact manifold, including its dimensionality (e.g., cloth draping over a rigid object);5. deformations are often associated with changes in the shape topology (e.g., the surgeon's scalpel cutting the patient's skin tissue); such topology modifications must be smoothly accommodated in our models.Towards this goal we have put together a team of PIs and consultants/advisors that combines expertise in scientific computing and physical simulation, geometric modeling and computation, motion planning and control, local and distributed sensing and actuation, model parameter estimation, as well as extensive experience in the computational modeling of specific deformable objects, from molecules to textiles, and in applications from medicine to entertainment