Abstract Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone‐constrained linear response and a scalar non‐associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non‐associated coupling explicitly, and an inner solve for a strongly convex cone‐constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid‐body benchmarks with stick‐slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

Fit and sizing of clothing are fundamental problems in the field of garment design, manufacture, and retail. Here we propose new computational methods for adjusting the fit of clothing on realistic models of the human body by interactively modifying desired fit attributes . Clothing fit represents the relationship between the body and the garment, and can be quantified using physical fit attributes such as ease and pressure on the body. However, the relationship between pattern geometry and such fit attributes is notoriously complex and nonlinear, requiring deep pattern making expertise to adjust patterns to achieve fit goals. Such attributes can be computed by physically based simulations, using soft avatars. Here we propose a method to learn the relationship between the fit attributes and the space of 2D pattern edits. We demonstrate our method via interactive tools that directly edit fit attributes in 3D and instantaneously predict the corresponding pattern adjustments. The approach has been tested with a range of garment types, and validated by comparing with physical prototypes. Our method introduces an alternative way to directly express fit adjustment goals, making pattern adjustment more broadly accessible. As an additional benefit, the proposed approach allows pattern adjustments to be systematized, enabling better communication and audit of decisions.

Deep generative models such as Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and diffusion models have demonstrated their efficacy in generating 2D images and 3D meshes. However, interpreting and controlling the learned latent space is very difficult, severely limiting the utility of these methods. Worse, it has been shown that fully disentangling the latent space using only unsupervised methods is theoretically infeasible.

Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation of elastodynamics with friction. However, the resulting frictional behavior can be inaccurate and may not converge to analytic solutions. Here we evaluate the accuracy of lagged friction models in comparison with implicit frictional contact systems. We show that major inaccuracies near the stick-slip threshold in such systems are caused by lagging of friction forces rather than by smoothing the Coulomb friction curve. Furthermore, we demonstrate how systems involving implicit or lagged friction can be correctly used with higher-order time integration and highlight limitations in earlier attempts. We demonstrate how to exploit forward-mode automatic differentiation to simplify and, in some cases, improve the performance of the inexact Newton method. Finally, we show that other complex phenomena can also be simulated effectively while maintaining smoothness of the entire system. We extend our method to exhibit stick-slip frictional behavior and preserve volume on compressible and nearly-incompressible media using soft constraints.

Physics-based simulation methods for deformable objects suffer limitations due to the conflicting requirements that are placed on them. The work horse semi-implicit (SI) backward Euler method is very stable and inexpensive, but it is also a blunt instrument. It applies heavy damping, which depends on the timestep, to all solution modes and not just to high-frequency ones. As such, it makes simulations less lively, potentially missing important animation details. At the other end of the scale, exponential methods (exponential Rosenbrock Euler (ERE)) are known to deliver good approximations to all modes, but they get prohibitively expensive and less stable for very stiff material. In this article, we devise a hybrid, semi-implicit method called SIERE that allows the previous methods SI and ERE to each perform what they are good at. To do this, we employ at each timestep a partial spectral decomposition, which picks the lower, leading modes, applying ERE in the corresponding subspace. The rest is handled (i.e., effectively damped out) by SI. No solution of nonlinear algebraic equations is required throughout the algorithm. We show that the resulting method produces simulations that are visually as good as those of the exponential method at a computational price that does not increase with stiffness, while displaying stability and damping with respect to the high-frequency modes. Furthermore, the phenomenon of occasional divergence of SI is avoided.

Frictional contact between deformable elastic objects remains a difficult simulation problem in computer graphics. Traditionally, contact has been resolved using sophisticated collision detection schemes and methods that build on the assumption that contact happens between polygons. While polygonal surfaces are an efficient representation for solids, they lack some intrinsic properties that are important for contact resolution. Generally, polygonal surfaces are not equipped with an intrinsic inside and outside partitioning or a smooth distance field close to the surface. Here we propose a new method for resolving frictional contacts against deforming implicit surface representations that addresses these problems. We augment a moving least squares (MLS) implicit surface formulation with a local kernel for resolving contacts, and develop a simple parallel transport approximation to enable transfer of frictional impulses. Our variational formulation of dynamics and elasticity enables us to naturally include contact constraints, which are resolved as one Newton-Raphson solve with linear inequality constraints. We extend this formulation by forwarding friction impulses from one time step to the next, used as external forces in the elasticity solve. This maintains the decoupling of friction from elasticity thus allowing for different solvers to be used in each step. In addition, we develop a variation of staggered projections, that relies solely on a non-linear optimization without constraints and does not require a discretization of the friction cone. Our results compare favorably to a popular industrial elasticity solver (used for visual effects), as well as recent academic work in frictional contact, both of which rely on polygons for contact resolution. We present examples of coupling between rigid bodies, cloth and elastic solids.

The 2020 CHCCS Achievement Award from the Canadian Human-Computer Communications Society is presented to Prof. Dinesh Pai (UBC) for his numerous high-impact contributions to the field of computer graphics research. His diverse research addresses physics-based animation, multisensory displays including haptics and sound, and realistic digital human models. CHCCS invites a publication by the award winner to be included in the proceedings, and this year we continue the tradition of an interview format rather than a formal paper. This permits a casual discussion of the research areas, insights, and contributions of the award winner. What follows is an edited transcript of a conversation between Dinesh Pai and Doug James (Stanford CS Prof and former PhD student) that took place on 14 March, 2020, via Zoom.

Abstract We present two practical methods for measurement of spectral skin reflectance suited for live subjects, and drive a spectral BSSRDF model with appropriate complexity to match skin appearance in photographs, including human faces. Our primary measurement method employs illuminating a subject with two complementary uniform spectral illumination conditions using a multispectral LED sphere to estimate spatially varying parameters of chromophore concentrations including melanin and hemoglobin concentration, melanin blend‐type fraction, and epidermal hemoglobin fraction. We demonstrate that our proposed complementary measurements enable higher‐quality estimate of chromophores than those obtained using standard broadband illumination, while being suitable for integration with multiview facial capture using regular color cameras. Besides novel optimal measurements under controlled illumination, we also demonstrate how to adapt practical skin patch measurements using a hand‐held dermatological skin measurement device, a Miravex Antera 3D camera, for skin appearance reconstruction and rendering. Furthermore, we introduce a novel approach for parameter estimation given the measurements using neural networks which is significantly faster than a lookup table search and avoids parameter quantization. We demonstrate high quality matches of skin appearance with photographs for a variety of skin types with our proposed practical measurement procedures, including photorealistic spectral reproduction and renderings of facial appearance.

Human motion capture using video-based or sensor-based methods gives animators the capability to directly translate complex human motions to create lifelike character animations. Advances in motion capture algorithms have improved their accuracy for estimating human generalized motion coordinates (joint angles and body positions). However, the traditional motion capture pipeline is not well suited to measure short duration, high acceleration impacts, such as running and jumping footstrikes. While high acceleration impacts have minimal influence on generalized coordinates, they play a big role in exciting soft tissue dynamics. Here we present a method for correcting motion capture trajectories using a sparse set of inertial measurement units (IMUs) collecting at high sampling rates to produce more accurate impact accelerations without sacrificing accuracy of the generalized coordinates representing gross motions. We demonstrate the efficacy of our method by correcting human motion captured experimentally using commercial motion capture systems with high rate IMUs sampling at 400Hz during basketball jump shots and running. With our method, we automatically corrected 185 jumping impacts and 1266 running impacts from 5 subjects. Post correction, we found an average increase of 84.6% and 91.1% in pelvis vertical acceleration and ankle dorsiflexion velocity respectively for basketball jump shots, and an average increase of 110% and 237% in pelvis vertical acceleration and ankle plantarflexion velocity respectively for running. In both activities, pelvis vertical position and ankle angle had small corrections on average below 2.0cm and 0.20rad respectively. Finally, when driving a human rig with soft tissue dynamics using corrected motions, we found a 143.4% and 11.2% increase in soft tissue oscillation amplitudes in basketball jump shots and running respectively. Our methodology can be generalized to correct impact accelerations for other body segments, and provide new tools to create realistic soft tissue animations during dynamic activities for more lifelike characters and better motion reconstruction for biomechanical analyses.

Motion in depth is commonly misperceived in Virtual Reality (VR), making it difficult to intercept moving objects, for example, in games. We investigate whether motion cues could be modified to improve these interactions in VR. We developed a time-to-contact estimation task, in which observers ($n=18$n=18) had to indicate by button press when a looming virtual object would collide with their head. We show that users consistently underestimate speed. We construct a user-specific model of motion-in-depth perception, and use this model to propose a novel method to modify monocular depth cues tailored to the specific user, correcting individual response errors in speed estimation. A user study was conducted in a simulated baseball environment and observers were asked to hit a looming baseball back in the direction of the pitcher. The study was conducted with and without intervention and demonstrates the effectiveness of the method in reducing interception errors following cue modifications. The intervention was particularly effective at fast ball speeds where performance is most limited by the user's sensorimotor constraints. The proposed approach is easy to implement and could improve the user experience of interacting with dynamic virtual environments.

Simulating how the human body deforms in contact with external objects, tight clothing, or other humans is of central importance to many fields. Despite great advances in numerical methods, the material properties required to accurately simulate the body of a real human have been sorely lacking. Here we show that mechanical properties of the human body can be directly measured using a novel hand-held device. We describe a complete pipeline for measurement, modeling, parameter estimation, and simulation using the finite element method. We introduce a phenomenological model (the sliding thick skin model) that is effective for both simulation and parameter estimation. Our data also provide new insights into how the human body actually behaves. The methods described here can be used to create personalized models of an individual human or of a population. Consequently, our methods have many potential applications in computer animation, product design, e-commerce, and medicine.

High quality simulations of the dynamics of soft flexible objects can be rather costly, because the assembly of internal forces through an often nonlinear stiffness at each time step is expensive. Many standard implicit integrators introduce significant, time-step dependent artificial damping. Here we propose and demonstrate the effectiveness of an exponential Rosenbrock-Euler (ERE) method which avoids discretization-dependent artificial damping. The method is relatively inexpensive and works well with the large time steps used in computer graphics. It retains correct qualitative behaviour even in challenging circumstances involving non-convex elastic energies. Our integrator is designed to handle and perform well even in the important cases where the symmetric stiffness matrix is not positive definite at all times. Thus we are able to address a wider range of practical situations than other related solvers. We show that our system performs efficiently for a wide range of soft materials.

We present a skin tracking and reconstruction method that uses a monocular camera and a depth sensor to recover skin sliding motions on the surface of a deforming object. Such depth cameras are widely available. Our key idea is to use a reduced coordinate framework that implicitly constrains skin to conform to the shape of the underlying object when it slides. The skin configuration in 3D can then be efficiently reconstructed by tracking two dimensional skin features in video. This representation is well suited for tracking subtle skin movements in the upper face and on the hand. The reconstructed skin motions have many uses, including synthesizing and retargeting animations, recognizing facial expressions, and for learning datadriven models of skin movement. In our face tracking examples, we recover subtle but important details of skin movement around the eyes. We validated the algorithm using a hand gesture sequence with known skin motion, recovering skin sliding motion with a low reconstruction error.

We present a novel method to enrich standard rigid-body impact models with a spatially varying coefficient of restitution map, or Bounce Map. Even state-of-the art methods in computer graphics assume that for a single rigid body, post- and pre-impact dynamics are related with a single global, constant, namely the coefficient of restitution. We first demonstrate that this assumption is highly inaccurate, even for simple objects. We then present a technique to efficiently and automatically generate a function which maps locations on the object's surface along with impact normals, to a scalar coefficient of restitution value. Furthermore, we propose a method for two-body restitution analysis, and, based on numerical experiments, estimate a practical model for combining one-body Bounce Map values to approximate the two-body coefficient of restitution. We show that our method not only improves accuracy, but also enables visually richer rigid-body simulations.

The tendons of the hand and other biomechanical systems form a complex network of sheaths, pulleys, and branches. By modeling these anatomical structures, we obtain realistic simulations of coordination and dynamics that were previously not possible. First, we introduce Eulerian-on-Lagrangian discretization of tendon strands, with a new selective quasistatic formulation that eliminates unnecessary degrees of freedom in the longitudinal direction, while maintaining the dynamic behavior in transverse directions. This formulation also allows us to take larger time steps. Second, we introduce two control methods for biomechanical systems: first, a general-purpose learning-based approach requiring no previous system knowledge, and a second approach using data extracted from the simulator. We use various examples to compare the performance of these controllers.

We introduce a new framework for simulating the dynamics of musculoskeletal systems, with volumetric muscles in close contact and a novel data-driven muscle activation model. Muscles are simulated using an Eulerian-on-Lagrangian discretization that handles volume preservation, large deformation, and close contact between adjacent tissues. Volume preservation is crucial for accurately capturing the dynamics of muscles and other biological tissues. We show how to couple the dynamics of soft tissues with Lagrangian multi-body dynamics simulators, which are widely available. Our physiologically based muscle activation model utilizes knowledge of the active shapes of muscles, which can be easily obtained from medical imaging data or designed to meet artistic needs. We demonstrate results with models derived from MRI data and models designed for artistic effect.

We describe an Eulerian-on-Lagrangian solid simulator that reduces or eliminates many of the problems experienced by fully Eulerian methods but retains their advantages. Our method does not require the construction of an explicit object discretization and the fixed nature of the simulation mesh avoids tangling during large deformations. By introducing Lagrangian modes to the simulation we enable unbounded simulation domains and reduce the time-step restrictions which can plague Eulerian simulations. Our method features a new solver that can resolve contact between multiple objects while simultaneously distributing motion between the Lagrangian and Eulerian modes in a least-squares fashion. Our method successfully bridges the gap between Lagrangian and Eulerian simulation methodologies without having to abandon either one.

We present a novel approach for simulating thin hyperelastic skin. Real human skin is only a few millimeters thick. It can stretch and slide over underlying body structures such as muscles, bones, and tendons, revealing rich details of a moving character. Simulating such skin is challenging because it is in close contact with the body and shares its geometry. Despite major advances in simulating elastodynamics of cloth and soft bodies for computer graphics, such methods are difficult to use for simulating thin skin due to the need to deal with non-conforming meshes, collision detection, and contact response. We propose a novel Eulerian representation of skin that avoids all the difficulties of constraining the skin to lie on the body surface by working directly on the surface itself. Skin is modeled as a 2D hyperelastic membrane with arbitrary topology, which makes it easy to cover an entire character or object. Unlike most Eulerian simulations, we do not require a regular grid and can use triangular meshes to model body and skin geometry. The method is easy to implement, and can use low resolution meshes to animate high-resolution details stored in texture-like maps. Skin movement is driven by the animation of body shape prescribed by an artist or by another simulation, and so it can be easily added as a post-processing stage to an existing animation pipeline. We provide several examples simulating human and animal skin, and skin-tight clothes.

A method for image-based contact detection and modeling, with guaranteed precision on the intersection volume, is presented. Unlike previous image-based methods, our method optimizes a nonuniform ray sampling resolution and allows precise control of the volume error. By cumulatively projecting all mesh edges into a generalized 2D texture, we construct a novel data structure, the Error Bound Polynomial Image (EBPI), which allows efficient computation of the maximum volume error as a function of ray density. Based on a precision criterion, EBPI pixels are subdivided or clustered. The rays are then cast in the projection direction according to the non-uniform resolution. The EBPI data, combined with ray-surface intersection points and normals, is also used to detect transient edges at surface intersections. This allows us to model intersection volumes at arbitrary resolution, while avoiding the geometric computation of mesh intersections. Moreover, the ray casting acceleration data structures can be reused for the generation of high quality images.

We present a novel framework for animating human characters performing fast visually guided tasks, such as catching a ball. The main idea is to consider the coordinated dynamics of sensing and movement. Based on experimental evidence about such behaviors, we propose a generative model that constructs interception behavior online, using discrete submovements directed by uncertain visual estimates of target movement. An important aspect of this framework is that eye movements are included as well, and play a central role in coordinating movements of the head, hand, and body. We show that this framework efficiently generates plausible movements and generalizes well to novel scenarios.

We describe and test a non-linear control algorithm inspired by the behavior of motor neurons in humans and other animals during extremely fast saccadic eye movements. The algorithm is implemented on a robotic eye, which includes a stiff camera cable, similar to the optic nerve, which adds a complicated non-linear stiffness to the plant. For high speed movement, our "pulse-step" controller operates open-loop using an internal model of the eye plant learned from past measurements. We show that the controller approaches the performance seen in the human eye, producing fast movements with little overshoot. Interestingly, the controller reproduces the main sequence relationship observed in animal eye movements.

A new method to simulate deformable objects with heterogeneous material properties and complex geometries is presented. Given a volumetric map of the material properties and an arbitrary number of control nodes, a distribution of the nodes is computed automatically, as well as the associated shape functions. Reference frames attached to the nodes are used to apply skeleton subspace deformation across the volume of the objects. A continuum mechanics formulation is derived from the displacements and the material properties. We introduce novel material-aware shape functions in place of the traditional radial basis functions used in meshless frameworks. In contrast with previous approaches, these allow coarse deformation functions to efficiently resolve non-uniform stiffnesses. Complex models can thus be simulated at high frame rates using a small number of control nodes.

We present a new type of deformable model which combines the realism of physically-based continuum mechanics models and the usability of frame-based skinning methods. The degrees of freedom are coordinate frames. In contrast with traditional skinning, frame positions are not scripted but move in reaction to internal body forces. The displacement field is smoothly interpolated using dual quaternion blending. The deformation gradient and its derivatives are computed at each sample point of a deformed object and used in the equations of Lagrangian mechanics to achieve physical realism. This allows easy and very intuitive definition of the degrees of freedom of the deformable object. The meshless discretization allows on-the-fly insertion of frames to create local deformations where needed. We formulate the dynamics of these models in detail and describe some precomputations that can be used for speed. We show that our method is effective for behaviors ranging from simple unimodal deformations to complex realistic deformations comparable with Finite Element simulations. To encourage its use, the software will be freely available in the simulation platform SOFA.

Simulating viscoelastic solids undergoing large, nonlinear deformations in close contact is challenging. In addition to inter-object contact, methods relying on Lagrangian discretizations must handle degenerate cases by explicitly remeshing or resampling the object. Eulerian methods, which discretize space itself, provide an interesting alternative due to the fixed nature of the discretization. In this paper we present a new Eulerian method for viscoelastic materials that features a collision detection and resolution scheme which does not require explicit surface tracking to achieve accurate collision response. Time-stepping with contact is performed by the efficient solution of large sparse quadratic programs; this avoids constraint sticking and other difficulties. Simulation and collision processing can share the same uniform grid, making the algorithm easy to parallelize. We demonstrate an implementation of all the steps of the algorithm on the GPU. The method is effective for simulation of complicated contact scenarios involving multiple highly deformable objects, and can directly simulate volumetric models obtained from medical imaging techniques such as CT and MRI.

A significant challenge in applications of computer animation is the simulation of ropes, cables, and other highly constrained strandlike physical curves. Such scenarios occur frequently, for instance, when a strand wraps around rigid bodies or passes through narrow sheaths. Purely Lagrangian methods designed for less constrained applications such as hair simulation suffer from difficulties in these important cases. To overcome this, we introduce a new framework that combines Lagrangian and Eulerian approaches. The two key contributions are the reduced node , whose degrees of freedom precisely match the constraint, and the Eulerian node , which allows constraint handling that is independent of the initial discretization of the strand. The resulting system generates robust, efficient, and accurate simulations of massively constrained systems of rigid bodies and strands.

Abstract Creating and animating subject‐specific anatomical models is traditionally a difficult process involving medical image segmentation, geometric corrections and the manual definition of kinematic parameters. In this paper, we introduce a novel template morphing algorithm that facilitates three‐dimensional modelling and parameterization of skeletons. Target data can be either medical images or surfaces of the whole skeleton. We incorporate prior knowledge about bone shape, the feasible skeleton pose and the morphological variability in the population. This allows for noise reduction, bone separation and the transfer, from the template, of anatomical and kinematical information not present in the input data. Our approach treats both local and global deformations in successive regularization steps: smooth elastic deformations are represented by an as‐rigid‐as‐possible displacement field between the reference and current configuration of the template, whereas global and discontinuous displacements are estimated through a projection onto a statistical shape model and a new joint pose optimization scheme with joint limits.

We present a new discrete velocity-level formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduce a simple fixed-point property of this coupled system. This allows us to construct a novel algorithm for accurate frictional contact resolution based on a simple staggered sequence of projections. The algorithm accelerates performance using warm starts to leverage the potentially high temporal coherence between contact states and provides users with direct control over frictional accuracy. Applying this algorithm to rigid and deformable systems, we obtain robust and accurate simulations of frictional contact behavior not previously possible, at rates suitable for interactive haptic simulations, as well as large-scale animations. By construction, the proposed algorithm guarantees exact, velocity-level contact constraint enforcement and obtains long-term stable and robust integration. Examples are given to illustrate the performance, plausibility and accuracy of the obtained solutions.

We describe an automatic technique for generating the motion of tendons and muscles under the skin of a traditionally animated character. This is achieved by integrating the traditional animation pipeline with a novel biomechanical simulator capable of dynamic simulation with complex routing constraints on muscles and tendons. We also describe an algorithm for computing the activation levels of muscles required to track the input animation. We demonstrate the results with several animations of the human hand.

Polarization has been used in numerous prior studies for separating diffuse and specular reflectance components, but in this work we show that it also can be used to separate surface reflectance contributions from individual light sources. Our approach is called polarization multiplexing and it has a significant impact in appearance modeling where the image as a function of illumination direction is needed. Multiple unknown light sources can illuminate the scene simultaneously, and the individual contributions to the overall surface reflectance are estimated. Polarization multiplexing relies on the relationship between the light source direction and the intensity modulation. Inverting this transformation enables the individual intensity contributions to be estimated. In addition to polarization multiplexing, we show that phase histograms from the intensity modulations can be used to estimate scene properties including the number of light sources.

We describe an architecture for coping with latency and asynchrony of multisensory events in interactive virtual environments. We propose to decompose multisensory interactions into a series of discrete, perceptually significant events, and structure the application architecture within this event-based context. We analyze the sources of latency, and develop a framework for event prediction and scheduling. Our framework decouples synchronization from latency, and uses prediction to reduce latency when possible. We evaluate the performance of the architecture using vision-based motion sensing and multisensory rendering using haptics, sounds, and graphics. The architecture makes it easy to achieve good performance using commodity off-the-shelf hardware.

Simulating sounds produced by realistic vibrating objects is challenging because sound radiation involves complex diffraction and interreflection effects that are very perceptible and important. These wave phenomena are well understood, but have been largely ignored in computer graphics due to the high cost and complexity of computing them at audio rates.We describe a new algorithm for real-time synthesis of realistic sound radiation from rigid objects. We start by precomputing the linear vibration modes of an object, and then relate each mode to its sound pressure field, or acoustic transfer function, using standard methods from numerical acoustics. Each transfer function is then approximated to a specified accuracy using low-order multi-pole sources placed near the object. We provide a low-memory, multilevel, randomized algorithm for optimized source placement that is suitable for complex geometries. At runtime, we can simulate new interaction sounds by quickly summing contributions from each mode's equivalent multipole sources. We can efficiently simulate global effects such as interreflection and changes in sound due to listener location. The simulation costs can be dynamically traded-off for sound quality. We present several examples of sound generation from physically based animations.

Modifying motion capture to satisfy the constraints of new animation is difficult when contact is involved, and a critical problem for animation of hands. The compliance with which a character makes contact also reveals important aspects of the movement's purpose. We present a new technique called interaction capture , for capturing these contact phenomena. We capture contact forces at the same time as motion, at a high rate, and use both to estimate a nominal reference trajectory and joint compliance. Unlike traditional methods, our method estimates joint compliance without the need for motorized perturbation devices. New interactions can then be synthesized by physically based simulation. We describe a novel position-based linear complementarity problem formulation that includes friction, breaking contact, and the compliant coupling between contacts at different fingers. The technique is validated using data from previous work and our own perturbation-based estimates.

Our goal is to incorporate polarization in appearance-based modeling in an efficient and meaningful way. Polarization has been used in numerous prior studies for separating diffuse and specular reflectance components, but in this work we show that it also can be used to separate surface reflectance contributions from individual light sources. Our approach is called polarization multiplexing and it has significant impact in appearance modeling and bidirectional imaging where the image as a function of illumination direction is needed. Multiple unknown light sources can illuminate the scene simultaneously, and the individual contributions to the overall surface reflectance can be estimated. To develop the method of polarization multiplexing, we use a relationship between light source direction and intensity modulation. Inverting this transformation enables the individual intensity contributions to be estimated. In addition to polarization multiplexing, we show that phase histograms from the intensity modulations can be used to estimate scene properties including the number of light sources.

We describe an efficient algorithm for the simulation of large sets of non-convex rigid bodies. The algorithm finds a simultaneous solution for a multi-body system that is linear in the total number of contacts detected in each iteration. We employ a novel contact model that uses mass, location, and velocity information from all contacts, at the moment of maximum compression, to constrain rigid body velocities. We also develop a new friction model in the configuration space of rigid bodies. These models are used to compute the feasible velocity and the frictional response of each body. Implementation is simple and leads to a fast rigid body simulator that computes steps on the order of seconds for simulations involving over one thousand non-convex objects in high contact configurations.

We introduce the Bounded Deformation Tree, or BD-Tree, which can perform collision detection with reduced deformable models at costs comparable to collision detection with rigid objects. Reduced deformable models represent complex deformations as linear superpositions of arbitrary displacement fields, and are used in a variety of applications of interactive computer graphics. The BD-Tree is a bounding sphere hierarchy for output-sensitive collision detection with such models. Its bounding spheres can be updated after deformation in any order, and at a cost independent of the geometric complexity of the model; in fact the cost can be as low as one multiplication and addition per tested sphere, and at most linear in the number of reduced deformation coordinates. We show that the BD-Tree is also extremely simple to implement, and performs well in practice for a variety of real-time and complex off-line deformable simulation examples.

We present a method to estimate a positive semidefinite matrix by linear least squares, and we apply this method to the estimation of local compliance matrices during deformable object modeling. Estimation of physical quantities from measurements has to consider noise due to measurement and modeling inaccuracy. Enforcing constraints during estimation can guarantee physically plausible results even under difficult measurement conditions.

Rigid body dynamics with contact constraints can be solved locally using linear complementarity techniques. However, these techniques do not impose the original constraints and need stabilization. In this paper we show how constraint stabilization can also be done in a complementarity framework. Our technique effectively eliminates the drift problem for both equality and inequality constraints and requires no parameter tweaking. We describe results from an implemented system, and compare the new technique to the well known Baumgarte stabilization.

Motion capture is widely used for character animation. One of the major challenges of this technique is how to modify the captured motion in plausible ways. Previous work has focused on transformations based on kinematics and dynamics, but has not explicitly taken into account the emerging knowledge of how humans control their movement. In this paper, we show how this can be done using a simple human neuromuscular control model. Our model of muscle forces includes a feedforward term, and low-gain passive feedback. The feedforward component is calculated from motion capture data using inverse dynamics. The feedback component generates reaction forces to unexpected external disturbances. The perturbed animation is then resynthesized using forward dynamics. This allows us to create animation where the character reacts to unexpected external forces in a natural way (e.g., when the character is hit by a flying object), and still retain the quality of the captured motions. This technique is useful for applications such as interactive sports video games.

We present a framework for low-latency interactive simulation of linear elastostatic models, and other systems arising from linear elliptic partial differential equations, which makes it feasible to interactively simulate large-scale physical models. The deformation of the models is described using precomputed Green's functions (GFs), and runtime boundary value problems (BVPs) are solved using existing Capacitance Matrix Algorithms (CMAs). Multiresolution techniques are introduced to control the amount of information input and output from the solver thus making it practical to simulate and store very large models. A key component is the efficient compressed representation of the precomputed GFs using second-generation wavelets on surfaces. This aids in reducing the large memory requirement of storing the dense GF matrix, and the fast inverse wavelet transform allows for fast summation methods to be used at run-time for response synthesis. Resulting GF compression factors are directly related to interactive simulation speedup, and examples are provided with hundredfold improvements at modest error levels. We also introduce a multiresolution constraint satisfaction technique formulated as a hierarchical CMA, so named because of its use of hierarchical GFs describing the response due to hierarchical basis constraints. This direct solution approach is suitable for hard real-time simulation since it provides a mechanism for gracefully degrading to coarser resolution constraint approximations. The GFs' multiresolution displacement fields also allow for run-time adaptive multiresolution rendering.

Dynamics simulation of smooth surfaced rigid bodies in contact is a critical problem in physically based animation and interactive virtual environments. We describe a technique that uses reduced coordinates to evolve a single continuous contact between smooth piecewise parametric surfaces. The incorporation of friction into our algorithm is straightforward. The dynamics equations, although slightly more complex due to the reduced coordinate formulation, can be integrated easily using explicit integrators without the need for constraint stabilization. Reduced coordinates confine integration errors to the constraint manifold, thereby permitting a wide choice of step sizes with visually acceptable results. We demonstrate these results using Loop Subdivision surfaces with parametric evaluation.

We introduce precomputed multizone elastokinematic models for interactive simulation of multibody kinematic systems which include elastostatic deformations. This enables an efficient form of domain decomposition, suitable for interactive simulation of stiff flexible structures for real time applications such as interactive assembly. One advantage of multizone models is that each zone can have small strains, and hence be modeled with linear elasticity, while the entire multizone/multibody system admits large nonlinear relative strains. This permits fast capacitance matrix algorithms and precomputed Green's functions to be used for efficient real time simulation. Examples are given for a human finger modeled as a kinematic chain with a compliant elastic covering.

We describe techniques for automatically acquiring observations of a deforming object and for estimating a model of the deformation from these observations. A robotic system was developed for measuring deformation, and has been previously reported (Pai et al., 2000, 2001). The present paper describes new techniques for the estimation of deformable models based on discrete Green's functions, from measurements acquired using stereo vision and a robot arm's position and force sensors. This kind of robotic measurement presents new challenges for measurement and estimation, that we address here. Our techniques for robotic acquisition of deformable, object models have potential applications in robotics, haptic interfaces, simulation, computer graphics and virtual reality.

This paper presents a new technique for the extraction of surfaces from 3D ultrasound data. Surface extraction from ultrasound data is challenging for a number of reasons including noise and artifacts in the images and nonuniform data sampling. A method is proposed to fit an approximating radial basis function to the group of data samples. An explicit surface is then obtained by iso-surfacing the function. In most previous 3D ultrasound research, a pre-processing step is taken to interpolate the data into a regular voxel array and a corresponding loss of resolution. We are the first to represent the set of semi-structured ultrasound pixel data as a single function. From this we are able to extract surfaces without first reconstructing the irregularly spaced pixels into a regular 3D voxel array.

Strandsare thin elastic solids that are visually well approximated as smooth curves, and yet possess essential physical behaviors characteristic of solid objects such as twisting. Common examples in computer graphics include: sutures, catheters, and tendons in surgical simulation; hairs, ropes, and vegetation in animation. Physical models based on spring meshes or 3D finite elements for such thin solids are either inaccurate or inefficient for interactive simulation. In this paper we show that models based on the Cosserat theory of elastic rods are very well suited for interactive simulation of these objects. The physical model reduces to a system of spatial ordinary differential equations that can be solved efficiently for typical boundary conditions. The model handles the important geometric non-linearity due to large changes in shape. We introduce Cosserat-type physical models, describe efficient numerical methods for interactive simulation of these models, and implementation results.

In this paper we describe how to simulate geometrically complex, interactive, physically-based, volumetric, dynamic deformation models with negligible main CPU costs. This is achieved using a Dy namic R esponse T exture, or DyRT, that can be mapped onto any conventional animation as an optional rendering stage using commodity graphics hardware. The DyRT simulation process employs precomputed modal vibration models excited by rigid body motions. We present several examples, with an emphasis on bone-based character animation for interactive applications.

This paper discusses the robotic acquisition and characterization of surface friction and roughness for real-world objects. Our motivation is the construction of detailed "reality-based" models for existing objects that can be used in haptic displays and other applications involving simulation. A key challenge addressed in this paper is the acquisition of these surface properties on real objects with nontrivial shape, and registration of these properties with respect to geometric models of the shape. We show how Coulomb friction may be effectively estimated in the presence of variations in surface normal. We also show how to estimate a stochastic process model of surface roughness. Finally, we demonstrate the robotic mapping of surface friction over an entire object, using the UBC Active Measurement Facility (ACME).

We describe algorithms for real-time synthesis of realistic sound effects for interactive simulations (e.g., games) and animation. These sound effects are produced automatically, from 3D models using dynamic simulation and user interaction. We develop algorithms that are efficient, physically-based, and can be controlled by users in natural ways. We develop effective techniques for producing high quality continuous contact sounds from dynamic simulations running at video rates which are slow relative to audio synthesis. We accomplish this using modal models driven by contact forces modeled at audio rates, which are much higher than the graphics frame rate. The contact forces can be computed from simulations or can be custom designed. We demonstrate the effectiveness with complex realistic simulations.

We describe a system for constructing computer models of several aspects of physical interaction behavior, by scanning the response of real objects. The behaviors we can successfully scan and model include deformation response, contact textures for interaction with force-feedback, and contact sounds. The system we describe uses a highly automated robotic facility that can scan behavior models of whole objects. We provide a comprehensive view of the modeling process, including selection of model structure, measurement, estimation, and rendering at interactive rates. The results are demonstrated with two examples: a soft stuffed toy which has significant deformation behavior, and a hard clay pot which has significant contact textures and sounds. The results described here make it possible to quickly construct physical interaction models of objects for applications in games, animation, and e-commerce.

We present techniques for constructing approximate stochastic models of complicated dynamical systems for applications in interactive computer graphics. The models are designed to produce realistic interaction at low cost. We describe two kinds of stochastic models: continuous state (ARX) models and discrete state (Markov chains) models. System identi cation techniques are used for learning the input-output dynamics automatically, from either measurements of a real system or from an accurate simulation. The synthesis of behavior in this manner is several orders of magnitude faster than physical simulation.We demonstrate the techniques with two examples: (1) the dynamics of candle ame in the wind, modeled using data from a real candle and (2) the motion of a falling leaf, modeled using data from a complex simulation. We have implemented an interactive Java program which demonstrates real-time interaction with a realistically behaving simulation of a cartoon candle ame. The user makes the ame animation icker by blowing into a microphone.

We describe a framework for derivation of several forward dynamics algorithms used in robotics. The framework is based on formulating an augmented system and performing block matrix elimination on this system. Several popular algorithms such as the O(N) articulated body method, and the composite rigid body method can be easily derived. We also derive an algorithm for simulation of contact between smooth bodies of arbitrary shape, in contact coordinates. Finally, we discuss some potential numerical difficulties that could arise and their solution.

We describe a system for robotic measurement of contact sounds. This system is well suited for acquiring impulse-response sound models. A brief explanation of the sound models is included. We also describe experimental results to illustrate the process of acquiring sound models using our system, and a brief analysis of the results. The initial results are promising and could lead to applications in reality-based modeling and object recognition.

We have implemented a computer interface that renders synchronized auditory and haptic stimuli with very low (0.5ms) latency.The audio and haptic interface (AHI) includes a Pantograph haptic device that reads position input from a user and renders force output based on this input.We synthesize audio by convolving the force profile generated by user interaction with the impulse response of the virtual surface.Auditory and haptic modes are tightly coupled because we produce both stimuli from the same force profile.We have conducted a user study with the AHI to verify that the 0.5ms system latency lies below the perceptual threshold for detecting separation between auditory and haptic contact events.We discuss future applications of the AHI for further perceptual studies and for synthesizing continuous contact interactions in virtual environments.

The method of programmed constraints has recently been proposed as an executable specification language for robot programming. The mathematical structures behind such problems are viability problems for control systems described by ordinary differential equations (ODE) subject to user-defined inequality constraints. This paper describes a method for the numerical solution of such problems, improving and extending some of our previous results. The algorithm presented is composed of three parts: delay-free discretization, local control, and local planning. Delay-free discretizations are consistent discretizations of control systems described by ODEs with discontinuous inputs. The local control is based on the minimization of an artificial, logarithmic barrier potential function. Local planning is a computationally inexpensive way to increase the robustness of the solution procedure, making it a refinement to a strategy based on viability alone. Simulations of a mobile robot are used to demonstrate the proposed strategy. Some complementarity is shown between the programmed-constraints approach to robot programming and optimal control. Moreover, we demonstrate the relative efficiency of our algorithm compared to optimal control: Typically, our method is able to find a solution on the order of 100 times faster than an optimal-control solver.

This paper describes a mobile manipulator that uses its wheels for manipulation as well as locomotion. This robot, named the mobipulator, looks like a small car with four independently powered wheels, none of them steered. It is designed to manipulate paper and other objects on the surface of a desk. The wheels are used for locomotion or for manipulation, switching functions dynamically as the task demands. So far we have preliminary demonstrations of a variety of motions, and performance data for the task of moving a sheet of paper in a square while maintaining constant orientation.

We introduce a method of planning fault tolerant trajectories based on the least constraint (LC) framework. Fault tolerance is achieved in two ways: exploiting properties of LC itself, and using a performance measure which assess the fault tolerant potential of a given configuration. LC encourages designs which are based solely on salient constraints of the task, allowing the inherent redundancy of the robot to be used to maintain a safe configuration. We compute the effects of faults on the topology of the configuration space and construct optimal recovery motions for a set of faults. We describe an efficient algorithm for computing the optimal recovery motions for a large number of faults over the entire configuration space simultaneously. A performance measure, called longevity, quantifies the ability of the recovery motions to complete the task. From the performance measure fault tolerant paths are constructed. We look at the simple task of positioning the end effector of a Puma 560 at a given point in the workspace.

In this article, we discuss the application, of a Green's function approach to contact maps. We apply the contact map algorithm to the case of an elastic bar impacting on a massive foundation. It is demonstrated that the energy lost to elastic waves is an important factor in post-contact states.

Article ArtDefo: accurate real time deformable objects Share on Authors: Doug L. James Institute of Applied Mathematics, University of British Columbia Institute of Applied Mathematics, University of British ColumbiaView Profile , Dinesh K. Pai Institute of Applied Mathematics and Dept. of Computer Science, 2366 Main Mall, UBC, Vancouver, Canada and University of British Columbia Institute of Applied Mathematics and Dept. of Computer Science, 2366 Main Mall, UBC, Vancouver, Canada and University of British ColumbiaView Profile Authors Info & Claims SIGGRAPH '99: Proceedings of the 26th annual conference on Computer graphics and interactive techniquesJuly 1999 Pages 65–72https://doi.org/10.1145/311535.311542Online:01 July 1999Publication History 303citation1,655DownloadsMetricsTotal Citations303Total Downloads1,655Last 12 Months56Last 6 weeks8 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We present an integrated system in which an operator uses a simulated environment to program part-mating and contact tasks. Generation of models within this virtual environment is facilitated using a fast, occlusion tolerant, 3D grey-scale vision system which can recognize and accurately locate objects within the work site. A major goal of this work is to make robotic programming easy and intuitive for untrained users working with standard desktop hardware. Simulation offers the ease-of-use benefits of "programming by demonstration", coupled with the ability to create a programmer-friendly virtual environment. Within a simulated environment, it is also straightforward to track and interpret an operator's actions. The simulator models objects as polyhedra and implements full 3D contact dynamics. When a manipulation task is completed, local planning techniques are used to turn the virtual environment's motion sequence history into a set of robot motion commands capable of realizing the prescribed task.

We describe the generation and use of "contact response maps" for real time dynamic simulation. Contact response maps are geometry and material dependent maps on physical objects which describe the surface tractions associated with local deformations during contact. We develop a technique for precomputing contact response maps for elastic bodies using the boundary element method to solve the corresponding plane strain problem. Such maps can then be used in a real time simulation environment to accurately resolve collision dynamics.

We describe a new approach to the problem of motion planning for mobile robots on natural rough terrain. Our approach computes a multiresolution representation of the terrain using wavelets, and hierarchically plans the path through sections which are well approximated on coarser levels and relatively smooth. Unlike most methods, the hierarchical approximation errors are used explicitly in a cost function to distinguish preferred terrain sections. The error is computed using the corresponding wavelet coefficients. We also propose a new nonscalar path cost measure based on the sorted terrain costs along the path. This measure can be incorporated into standard global path search algorithms and yields paths which avoid high cost terrain areas when possible. Additional constraints for specific robots can be integrated into this approach for efficient hierarchical motion planning on rough terrain. We present the algorithms and experimental results for real terrain data.

We describe an implemented model-based telerobotic system designed to investigate assembly and other tasks involving contact and manipulation of known objects. Key features of our system include ease of maintaining a world model at the operator site and a task-centric operator interface. Our system incorporates gray-scale model-based vision to assist in building and maintaining the local model. The local model is used to provide a task-centric operator interface, emphasizing the natural and direct manipulation of objects, with the robot's presence indicated in a more abstract fashion. The operator interface is designed to work with widely available and inexpensive desktop computers with low DOF input devices (such as a mouse). We also describe experimental results to date, which include performing assembly-like tasks over the Internet.

We present a geometric theory of the performance of robot manipulators, applicable to systems with constraints, which may be nonholonomic. The performance is quantified by a geometrical object, the induced metric tensor, from which scalars may be constructed by invariant tensor operations to give performance measures. The measures thus defined depend on the metric structure of configuration and workspace, which should be chosen appropriately for the problem at hand. The generality of this approach allows us to specify a system of joint connected rigid bodies with a large class of metrics. We describe how the induced metric can be computed for such a system of joint connected rigid bodies and describe a MATLAB program that allows the automatic computation of the performance measures for such systems. We illustrate these ideas with some computations of measures for the SARCOS dextrous arm, and the Platonic Beast, a multilegged walking machine.

We describe the architecture of a system for programming the high degree-of-freedom Platonic Beast legged robot with constraints. This includes software for distributed control of the robot using the least constraint approach, and hardware for supporting this programming model with distributed computing and communication. We have implemented this system, and we describe results to date.

All objects have a surface roughness which manifests itself as small forces when objects slide under load against each other. Simulating this roughness haptically enriches the interaction between a user and a virtual world, just as creating graphical textures enhances the depiction of a scene. As with graphical textures, a major design constraint for haptic textures is the generation of a sufficiently "realistic" texture given hard constraints on computational costs. The authors present a simple, fast algorithm to synthesize haptic textures from statistical properties of surfaces. The synthesized texture can be overlaid on other contact models, such as hard contact with Coulomb friction. The algorithm requires minimal hardware support, and can be implemented on a variety of force-feedback mechanisms. It has been successfully implemented on a two-degree-of-freedom haptic interface (the Pantograph).

The authors identify an important phenomenon they call "formulation stiffness" in the numerical simulation of tree-structured multibody systems such as robot manipulators. The numerical simulation problem is usually treated as two separate problems: (i) the forward dynamics problem for computing system accelerations, and (ii) the numerical integration problem far advancing the state in time. The authors show that the interaction of these two problems leads to new conclusions about the overall efficiency of multibody simulation algorithms; in particular the fastest forward dynamics methods are not necessarily best when considered in conjunction with the popular adaptive stepsize integration methods. Specifically, the authors show that the articulated-body method is better suited to deal with certain types of numerical problems than the composite rigid body method. The authors present examples of simulations and discuss the practical implications of these results.

Recently, new robot programming approaches have proposed the use of programmed constraints as an executable specification language for the desired behavior of a robot. The constraint-based approaches are intermediate level languages, promising a higher, more declarative level of programming than trajectory-based approaches, while being more tractable computationally than motion planning. This paper considers a numerical algorithm for solution of differential systems subject to algebraic inequality constraints. These are the mathematical structures behind the constraint-based approach. Our approach is based on a principle of 'least constraint', consisting of a dynamic integration of the equations of motion coupled with invocation of a control mechanism to ensure that the robot trajectory avoids all constraint boundaries. This is achieved by minimization of a barrier function defined using buffer zones near the constraint boundaries. Determination of the buffer zones is done dynamically, corresponding to a local planning strategy.

We describe a new approach to the problem of motion planning for mobile robots on natural, nonhomogenous terrain. Our approach computes a multiresolution representation of the terrain using wavelets, and hierarchically plans the path through sections which are well approximated on coarser levels and relatively smooth. Unlike most methods, the hierarchical approximation errors are used explicitly in a cost function to distinguish preferred terrain sections. The error is computed using the corresponding wavelet coefficients. The path planning algorithm uses a new nonscalar path cost measure based on the sorted terrain costs along the path. This measure can be incorporated into standard global path search algorithms and yields intuitively good paths. Additional constraints for specific robots can be integrated into this approach for efficient hierarchical motion planning on rough terrain. We present experimental results for real terrain data.

Robotic tasks usually require some collision free motions, and there has been considerable work in methods for collision avoidance. However, noise in the sensor data, movement of the obstacles, and incomplete or inaccurate model of the surroundings all may lead to unexpected collisions. Detecting such collisions is necessary before recovery and/or replanning may take place. A means of detecting a collision, as well as the position of the collision on the manipulator has been developed. The detection scheme combines information from observed disturbance torques to detect collision and infer the location of contact with the environment. Knowledge of contact position allows for a more intelligent and less error-prone recovery scheme. A simulation using a three DOF manipulator shows that the collision identification and localization scheme is feasible and robust with respect to noise.

We introduce a formalism for the systematic construction of performance measures for robot manipulators in a unified framework based on differential geometry. We show how known measures arise naturally in our formalism and we construct some new measures. The new measures presented here are the effective inertia on workspace and the kinematic and dynamic anisotropy measures for redundant manipulators.>

We investigate two new classes of performance measures. The first class quantifies the ability of a redundant manipulator to reconfigure itself while keeping the end-effector at a fixed position. The second measures the nonlinearity of the manipulator. We derive these measures using the differential-geometric formalism we introduced previously (1993).>

Describes class of spherically symmetric, high degree of freedom robots called "platonic beasts". A robot in this family is kinematically equivalent to a symmetric polyhedron, such as one of the platonic solids, with identical multi-purpose limbs attached to its vertices. The symmetry and regularity of the design have several advantages including robustness to toppling, novel gaits such as the rolling gait, and fault tolerance. The authors describe the design, simulation, and construction of a prototype platonic beast robot that the authors have built in their lab. The robot has four limbs, each with three degrees of freedom, and is controlled by a network of four embedded 32-bit microcontrollers. The authors also discuss the general features of these robots, including locomotion using the rolling gait and the implications of its novel features.>

Investigates the construction of performance measures for robot manipulators with closed kinematic loops. For such systems, the equations for the forward kinematics and the constraints can not be solved explicitly in general. The authors extend a formalism introduced by them previously (1993, 1994) based on the construction of an "induced" metric tensor on the work space of the manipulator, to include systems with constraints (which may be non-holonomic). As an example of an application the authors compute the generalized Yoshikawa measure for a planar five-link closed linkage chain, which they use to compute some optimal postures.>

Describes the computation of derivatives of functions defined on a robot's kinematic quantities using the efficient adjoint technique for automatic differentiation. Implemented software called RAD (Robot Automated Differentiation), which can generate optimized C programs for computing these quantities from concise descriptions of the robot and the required kinematic quantities, is also described. In addition to automatic differentiation, the RAD software provides a symbolic formulation of the kinematics and simplification of trigonometric algebraic expressions using Mathematica and pattern matching. The authors illustrate the utility of the software with a 2-link robot and a PUMA robot.

The kinematic singularities of robot manipulators are studied from the point of view of the theory of singularities. The notion of a 'generic' kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator, is examined. For three-joint robots, an equivalent algebraic condition for genericity using the Jacobian determinants is derived. This condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. Orientation and translation singularities of manipulators are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation singularities of the eight possible topologies of three-joint robots are studied and the conditions on the link parameters for nongenericity are determined.>

For pt.I see Cornell Computer Science Tech. Report (1989). A fully algorithmic, combinatorially precise approach to designing devices so that they are easy to assemble and (optional) hard to disassemble is presented. The analysis can be used to validate good designs and can be iterated to generate improved designs. The approach is based on an algorithm for predicting the motion of flexible objects in contact. Such objects are intended to model snap-fastener-type devices, which are very useful in assembly design. The authors describe the algorithm, its implementation in a system for predicting and analyzing the motion of snap-fastener-type devices, and experiments run using the system to analyze and design particular devices. The issues discussed include: the relevance of the approach to engineering, the computational methods employed, the algebraic techniques for predicting motions in contact with rotational compliance, and issues of robustness and stability of the geometric and algebraic algorithms. Subtle mechanical difficulties arise in predicting motions under rotational compliance. The authors discuss these problems and their solutions.>

The singularities of the differential kinematic map, i.e. of the manipulator Jacobian, are considered. The authors first examine the notion of a generic kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator. For three-joint robots, an equivalent condition for genericity using determinants is derived. The condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators, i.e. manipulators that an be separated into a three-joint translating part and a three-joint orienting part. The results are illustrated by analyzing the singularities of two classes of three-joint positioning robots.>

This paper describes an environment developed for interactive computer graphic simulation of robotic applications. The goals of this environment are to make the development of application programs easier and to allow the same models to be used by a variety of application programs. In this environment, standard models of work cells, robots, sensors, and other entities can be created. These models can be extended to include user-defined properties of individual entities. Functions are provided to access the data in these models, to manipulate the data with computer graphic animation, and to perform other simulation tasks.