Title
Passive Implementation for a Class of Static Nonlinear Environments in Haptic Display

Abstract
This paper derives conditions for the absence of oscillations for a parameterized class of nonlinear environments. This class includes discrete-time environments that can exhibit non-passive behavior. The motivation for considering non-passive discrete-time environments is based on the fact that an interesting class of passive continuous-time environments have non-passive discrete-time counterparts. A design methodology is introduced that provides relationships between the haptic device, virtual coupling and maximum negative stiffness exhibited by the environment.

Source: ICRA '99

Title
Computational Delay and Free Mode Environment Design for Haptic Display

Abstract
This paper develops a technique for the design of haptic systems that guarantees the absence of oscillations. Valid components of the haptic system are general devices, virtual couplings and virtual environments, linear or nonlinear, however the current work focuses on linear components. Once developed, the method will be applied to a haptic system to investigate stability conditions for passive environments versus those for non-passive environments. Examples of computational delay and free mode environment design will be developed as meaningful design problems that fall into the category of non-passive environments.

Source: IMECE '99

Title
Guaranteed Stability of Haptic Systems with Nonlinear Virtual Environments

Abstract
Design of haptic systems that guarantee stable interaction is a challenging task. Virtual environments are typically highly nonlinear - resulting in a non-passive discrete-time model. This paper will investigate how nonlinear mass/spring/damper virtual environments can be designed to guarantee the absence of oscillations and other chaotic behavior in the signal presented to the human operator. In particular, delayed and non-delayed implementation of the environment is considered, revealing a non-intuitive result with regard to the allowable local stiffness.

Source: IEEE '99

Title
Using a Wavelet Network to Characterize Real Environments for Haptic Display

Abstract
This paper will introduce a framework for characterizing real environments, using recorded force/displacement data, for use in haptic display. Steps in the framework include data acquisition, identification, model verification, and implementation. Identification and implementation will be developed in detail. After obtaining a conceptual understanding of the roles data acquisition and model verification play in the process, the methods used in this paper will be described. To meet the requirement for the identification stage, a proven technique in nonlinear system identification will be adopted. This technique, called wavelet network, will provide a tool that is capable of identifying environments with significant nonlinear features. A theoretical development along with experimental results will be presented using a spring attached to a wall. This environment exhibits a linear region with a single nonlinearity. The wavelet network was chosen because it was designed specifically for use with problems of high input dimension. Therefore, it is the expectation that the procedure will be useful in identifying environments of varying complexity. Currently, the technique can be used to identify static nonlinear environments. Work is being done to extend its capabilities to handle dynamic environments.

Source: IMECE '98

Title
Wavelet Networks for Characterization and Implementation of Environments

Abstract
This thesis will introduce a framework for characterizing real objects, using recorded force/displacement data, for use in haptic display. Steps in the framework include data acquisition, identification, model verification, and implementation. Identification and implementation will be developed in detail. After obtaining a conceptual understanding of the role data acquisition and model verification play in the process, the methods used in this paper will be described. To meet the requirement for the identification stage, a proven technique in nonlinear system identification will be adopted. This technique, the wavelet network, will provide a tool that is capable of identifying environments with significant nonlinear features. A theoretical development along with experimental results will be presented using several real objects. These environments exhibit linear regions with significant nonlinearities. The wavelet network was chosen because it was designed specifically for use with problems of high input dimension. Therefore, it is the expectation that the procedure will be useful in identifying environments of varying complexity. Currently, the technique can be used to identify static nonlinear environments.

Source: Masters Thesis, Northwestern University, 1998

Title
Passive Implementation of Multibody Simulations for Haptic Display

Abstract
The development of complex virtual environment simulations is a challenging problem in haptic display. Due to the dynamic interactions between the human operator, mechanism, sensors, actuators and physics-based simulation, provision of stability guarantees is both an interesting theoretical question and an important practical concern. Most existing virtual environments rely on the careful tuning of environment and control parameters to ensure stability. Whenever changes are made to the environment (such as changing the length of an object), these parameters have to be re-tuned. While merely annoying for relatively simple environments, this process becomes impractical for complex ones.

The focus of this work is the development of a software architecture that permits the simulation of complex multibody environments on a haptic display. This architecture separates the haptic display from the simulation, such that stability of the haptic display is not strongly dependent on simulation parameters. These simulations exhibit vastly improved stability properties compared to previous implementations. Since the haptic display and virtual environment are still weakly connected, guidelines for the design of virtual environments are presented.

Specifically, this thesis presents four distinct results associated with the proposed software architecture. The first result is a detailed passivity analysis of a 1 degree of freedom haptic display, generalizing previous analyses and providing design guidelines for the proposed software architecture. This result also substantiates discrete-time passivity as an exemplar for physics-based simulation methods. The second result is the establishment of a connection between the incremental conservation properties of physics-based numerical methods and discrete-time passivity of their numerical operators. This connection has important implications about which numerical methods are appropriate for use with haptic displays. The third result shows that discrete-time passive numerical operators require the solution of implicit equations. For reasons that are discussed, implicit equations are usually not solvable in real-time, making them difficult to use with haptic displays. The final result is an improved tuning procedure that preserves device passivity even with numerical methods that are not discrete-time passive.

Source: Ph.D. thesis, Northwestern University, December 1998

Title
Minimum mass for haptic display simulations

Abstract
This paper addresses the issue of providing stability guarantees during the implementation of multibody simulations for haptic display. Within the framework of the virtual coupling, we discuss the passivity of the haptic display. Previous work has established that, if the numerical methods used in the virtual environment are discrete time passive, it is possible to decouple the stability of the device from the virtual environment simulation. In the present work, we prove that discrete time passive operators must be implicit, making them unlikely candidates for real time implementation. Given restrictions on environment parameters, however, passivity can sometimes be preserved even when using explicit numerical methods. An important benchmark simulation is that of a point mass, and restrictions take the form of a minimum mass that can be simulated passively. This minimum mass is derived for several simple numerical integrator-virtual coupling pairs.

Source: Proceedings of the 1998 ASME International Mechanical Engineering Congress & Exhibition

Title
Passive Implementation of Multibody Simulations for Haptic Display

Abstract
This paper addresses the issue of providing stability guarantees during the implementation of multibody simulations for haptic display. It introduces the concept of a virtual coupling between the multibody simulation and haptic display hardware. This coupling separates the simulation design process from the sampled- data stability issues that arise during its implementation with a haptic display. Necessary conditions for passivity of a 1-DOF haptic display with a discrete-time passive simulation and an arbitrary virtual coupling are given. The implications of discrete-time passivity on numerical integration and collision response algorithms are also addressed.

Source: IMECE 1997, Dallas, TX

Title
A Survey of Multibody Dynamics for Virtual Environments

Abstract
The field of computational dynamics is surveyed, focusing on issues relevant to the construction of a general purpose simulator with haptic display. The various formalisms available for generating dynamical models will be examined with regard to the form of the equations of motion which they produce. To render the effects of intermittent contact and other transient phenomena as driven by a human haptic explorer, a model is needed which is computationally efficient yet can handle changing kinematic constraints neatly. Models in dependent and independent coordinates produced with the Newton-Euler, Lagrange and Kane formalisms will each be examined in order to provide a vantage point from which an informed selection may be made from among the many tools now available in computational dynamics.

Source: IMECE 1997, Dallas, TX

Title
Stable User-Specific Haptic Rendering of the Virtual Wall

Abstract
Efficient control algorithms are developed to implement stiff virtual walls without chatter. An analysis of the complete coupled system comprising controller, interface device, and user's finger underlies the design of a wall algorithm, thus each virtual wall is tailored to a specific user impedance. The finger is modeled as a static second order impedance with justification drawn from empirical studies of limb dynamics available in the literature and from observations of the disparity in time scales between contact instability and volitional control. Compensation is incorporated for the destabilizing effects of the zero order hold using either model based prediction or design in the digital domain. The destabilizing effects of asynchronous wall on/off switching times and sampling times are tracked by a special watchdog while deadbeat control is used to periodically eliminate these effects. Extensions are discussed including on-the-fly system identification of the user impedance.

Source: IMECE 1996, Atlanta, GA

Title
Toward Guaranteed Stability in the Haptic Display of Virtual Environments

Abstract
A haptic display is a device that allows human operators to manipulate and feel virtual environments. An important issue in the haptic display of virtual environments is stability. Often, unintended oscillations of the human/display system are found to occur. This dissertation addresses the problem of guaranteed stability in the haptic display of virtual environments. The approach taken to this problem is based upon ensuring not only discrete time stability, but also discrete time passivity. The introduction and background of this work are included in Part I.

In Part II, we consider the effect of unilateral nonlinearities on the stability of discrete-time control systems, a problem of some importance in haptic display. For example, a virtual wall is a simple form of unilateral constraint. Sufficient conditions for the stability of linear, shift-invariant systems in feedback with unilateral nonlinearities are derived. The derivation follows a method originally presented by Mitra in which the existence of periodic oscillations is first assumed, then conditions leading to a contradiction are found. The results developed here are presented graphically in the Nyquist plane, allowing direct comparison to other well-known criteria, such as Tsypkin's Condition. It is shown that the new criterion is much less conservative.

In Part III, we show that A-stability relates to the passivity of the discrete time simulation. If A-stable methods are used to map linear time-invariant systems to discrete time, the results will be discrete time passive. Furthermore, the need for real-time simulations of complex dynamic systems in haptic display suggests that simulations may need to be distributed across a network of processors. A parallel simulation structured in a physically meaningful way allows the user to apply the powerful insights and methods of physical network theory. We show that, by modeling junctions in the simulation network using transmission lines, the inherent delays are accommodated, and discrete time passivity is guaranteed.

In conclusion, we are able to construct A-stable simulation networks through the transmission line model and A-stable integration technique. We believe that this is a promising approach to the real-time, A-stable simulation of multibody systems.

Source: Ph.D. Dissertation, Northwestern University, December 1996

Part1 Part2 Part3 Part4 Part5

Title
Stability of Discrete Time Systems with Unilateral Nonlinearities

Abstract
This paper considers the effect of unilateral nonlinearities on the stability of discrete time control systems, a problem of some importance in haptic display. The unilateral nonlinearity is a simple piecewise linear function: f(x) = x for x>=0, f(x) = 0 for x<0. This function plays an important role in the modeling of collisions, and is a part of essentially all implementations of virtual surfaces. The unilateral nonlinearity is, in part, responsible for the instability often seen when haptic display operators contact virtual surfaces.

In this paper, it is shown that an operator contacting a virtual surface via a haptic display can reasonably be modeled as a linear, shift-invariant system (H(z)) in feedback with a unilateral nonlinearity. Conditions for the absence of oscillations in such a system are then derived. The derivation follows a method originally presented by Mitra in which the existence of periodic oscillations is first assumed, then conditions leading to a contradiction are found. This approach is particularly attractive in that it exploits specific properties of the unilateral nonlinearity. The results developed here are presented graphically in the Nyquist plane, allowing direct comparison to other well-known criteria, such as Tsypkin's Condition. It is shown that the new criterion is much less conservative than Tsypkin's Condition.

Source: IMECE 1995, San Francisco, CA

Title
Haptic Perception of Localized Features

Abstract
The perception of localized haptic features (e.g. bumps, scratches, edges, etc.) is an important problem in haptic display. Localized features provide users with landmarks and provide feedback regarding system state and task progression during manipulation. In two separate experiments, I investigated the perception of features created from position-dependent linear damping and stiffness parameters. The aim was to determine which parameters of the features correlated with detectability, in order to design better haptic feedback systems. A secondary goal was to study how the mechanical constraints provided by features influenced performance of a simple positioning task.

In the first experiment, subjects performed a simple positioning task in an environment of non-uniform damping. Damping levels in the target and background regions were systematically varied, and movement times were recorded as a measure of task performance. The most striking result of the experiment was that when the targets were not visible to subjects, performance was very closely correlated with the absolute magnitude of the difference in damping between the target and background damping (i.e. target damping minus the background damping). Performance did not vary with the level of background damping.

In the second experiment, subjects performed a detection task in environments with haptic features generated using position-dependent stiffness. The single most important parameter for feature detectability was shown to be the amplitude of the change in force generated as the feature was traversed. The rate at which the force changed when the feature was traversed (i.e. the feature stiffness) was also shown to be important when detecting features under conditions of large background forces. Large background forces, and especially large background forces that varied with position, were shown to make the detection of features characterized by gradual changes in force more difficult. The same background forces had no effect on detection of features characterized by rapid changes in force.

The results of the two experiments suggest that frequency differences, as well as amplitude differences in resistance force can be used to make foreground-background distinctions, and that one kind of difference can be substituted for the other.

Source: Dissertation, Northwestern University, December 1995

Intro Chapt1 Chapt2 Chapt3 Chapt4 Chapt5 Chapt6 Chapt7

Title
Effects of Non-Uniform Environment Damping on Haptic Perception and Performance of Aimed Movements

Abstract
A set of experiments was conducted to investigate the relationship of environment damping to performance of a Fitts one-shot tapping task, and especially the relationship of environment damping to the haptic perception of target position. In the experiments, subjects were asked to locate a narrow target region that had a different level of viscous damping than the background regions. The task was performed using a one degree-of-freedom manipulandum. Movement time to target was measured as a function of the damping in the target and background regions. Different visual feedback conditions were also tested.

The most striking result of the experiments was that when the targets were not visible to subjects, performance was very closely correlated with the absolute magnitude of the difference in target and environment damping (i.e. target damping minus the background damping). Performance did not vary with the percentage difference between target damping and background damping, nor with the sign of the difference between target and background damping, nor with the level of background damping. When target positions were visible to subjects, performance depended very weakly on the environment damping.

Source: IMECE 1995, San Francisco, CA

Title
A Theoretical and Experimental Investigation into the Factors Affecting the Z- Width of a Haptic Display

Abstract
This thesis addresses some of the issues that come up in the implementation of virtual environments for haptic display. In particular, the concept of "Z-width", or dynamic range of achievable impedances, will be used to evaluate the performance of different device configurations. We suggest that an impedance is achievable if it satisfies a robustness property such as passivity. Several factors affecting Z-Width - sample-and-hold, inherent interface dynamics, displacement sensor quantization, and velocity filtering - are discussed. A set of human subject experiments designed to evaluate these factors are described, and experiemental results are presented. A striking result is that inherent interface damping exerts an overwhelming influence on Z-width. Finally, we discuss the practical difficulties of implementing low impedances with a damped haptic display, introducing the concept of "frequency-dependent damping."

Source: Masters Thesis, Northwestern Univeristy, March 1995

Title
Issues in the Haptic Display of Tool Use

Abstract
Our group is interested in using haptic display for training tool use. Applications include training doctors to use tools during surgery, and training astronauts to use tools during EVA. This paper describes some of the challenges of creating realistic haptic perceptions of tool use. Many of these challenges stem from the importance of unilateral constraints during tool use. Unilateral constraints occur whenever rigid bodies collide, resisting the interpenetration of the bodies, but not holding the bodies together. To identify unilateral constraints, a tool/environment simulation must perform collision detection. To respond properly to a collision, the simulation must estimate the forces that ensue, and integrate the equations of motion. All of these computations must occur in real time, and the simulation as a whole must be stable (to ensure the user's safety). Approaches to these problems are described.

Source: IROS 1995, Pittsburgh, PA

Title
Physics-based Approach to Haptic Display

Abstract
This paper addresses the implementation of complex multiple degree of freedom virtual environments for haptic display. We suggest that a physics-based approach to rigid body simulation is appropriate for hand tool simulation, but that currently available simulation techniques are not sufficient to guarantee successful implementation. We discuss the desirable features of a VE simulation, specifically highlighting the importance of stability guarantees.

Source: ISMRC 1994, Houston, TX

Title
Factors Affecting the Z-Width of a Haptic Display

Abstract
This paper addresses the performance of force-reflecting interfaces ("haptic displays"). We suggest that an important measure of performance is the dynamic range of achievable impedances - "Z-Width" - and that an impedance is achievable if it satisfies a robustness property such as passivity. Several factors affecting Z-Width - sample-and-hold, inherent interface dynamics, displacement sensor quantization, and velocity filtering - are discussed. A set of experiments designed to evaluate these factors is described, and experimental results are presented. A striking result is that inherent interface damping exerts an overwhelming influence on Z-Width.

Source: Proceedings of the IEEE 1994 International Conference on Robotics & Automation, pp. 3205-10, San Diego, CA, May 1994

Title
Passivity Of a Class of Sampled-Data Systems: Application to Haptic Interfaces

Abstract
Passivity of systems comprising a continuous time plant and discrete time controller is considered. This topic is motivated by stability considerations arising in the control of robots and force-reflecting human interfaces ("haptic interfaces"). A necessary and sufficient condition for the passivity of a class of sampled-data systems is derived. An example - implementation of a "virtual wall" via a one degree-of-freedom haptic interface - is presented.

Source: ACC 1994