Warren Robinett

Memristor-CMOS hybrid integrated circuits for reconfigurable logic

Hybrid reconfigurable logic circuits were fabricated by integrating memristor-based crossbars onto a foundry-built CMOS (complementary metal-oxide-semiconductor) platform using nanoimprint lithography, as well as materials and processes that were compatible with the CMOS. Titanium dioxide thin-film memristors served as the configuration bits and switches in a data routing network and were connected to gate-level CMOS components that acted as logic elements, in a manner similar to a field programmable gate array. We analyzed the chips using a purpose-built testing system, and demonstrated the ability to configure individual devices, use them to wire up various logic gates and a flip-flop, and then reconfigure devices.

Writing to and reading from a nano-scale crossbar memory based on memristors

We present a design study for a nano-scale crossbar memory system that uses memristors with symmetrical but highly nonlinear current-voltage characteristics as memory elements. The memory is non-volatile since the memristors retain their state when un-powered. In order to address the nano-wires that make up this nano-scale crossbar, we use two coded demultiplexers implemented using mixed-scale crossbars (in which CMOS-wires cross nano-wires and in which the crosspoint junctions have one-time configurable memristors). This memory system does not utilize the kind of devices (diodes or transistors) that are normally used to isolate the memory cell being written to and read from in conventional memories. Instead, special techniques are introduced to perform the writing and the reading operation reliably by taking advantage of the nonlinearity of the type of memristors used. After discussing both writing and reading strategies for our memory system in general, we focus on a 64 x 64 memory array and present simulation results that show the feasibility of these writing and reading procedures. Besides simulating the case where all device parameters assume exactly their nominal value, we also simulate the much more realistic case where the device parameters stray around their nominal value: we observe a degradation in margins, but writing and reading is still feasible. These simulation results are based on a device model for memristors derived from measurements of fabricated devices in nano-scale crossbars using Pt and Ti nano-wires and using oxygen-depleted TiO(2) as the switching material.

Implementation of flying, scaling and grabbing in virtual worlds

In a virtual world viewed with a head-mounted display, the user may wish to perform certain actions under the control of a manual input device. The most important of these actions are flying through the world, scaling the world, and grabbing objects. This paper shows how these actions can be precisely specified with Frame-to-frame invariants, and how the code to implement the actions can bc dcrivcd from the invariants by algebraic manipulation. INTRODUCTION Wearing a Head-Mounted Display (HMD) gives a human user the scnsalion of being inside a three-dimensional. computersimulated world. Because the HMD rcplaccs the sights and sounds of the real world with a computer-gencratcd virtual world, this synthesizccl world is called virtual reality. The virtual world surrounding the user is dcfincd by a graphics database called a model, which gives the colors and coordinates for each of the polygons making up the virtual world. The polygons making up the virtual world arc normally grouped into cntitics called obj,jccfs, each of which has its own location and orientation. The human being wearing the HMD is called the user, and also has a location and orientation within the virtual world. To turn the data in the model into the illusion of a surrounding virtual world, the HMD system requires certain hardware components. The tracker measures the position and orientation of the user’s head and hand. The graphics engine gcncratcs the images seen by the user, which arc then displayed on the HMD. The manual input device allows the user to use gcslurcs of the hand to cause things to happen in the virtual world. BASIC ACTIONS An aclinn changes ~hc state of the virtual world or the user’s viewpoint wiLhin it under control of a gcsturc of the hand, as mcasurcd by the manual input d&cc. The hand gesture initiates and tcrminatcs the action, and the changing position Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. Q 1992 ACM 0-89791-471-6/92/000310189...

A computational model for the stereoscopic optics of a head-mounted display

1.50 and orientation of the hand during the gesture is also used to control what happens as the action progresses. The manual input device may be a hand-held manipulandum with pushbuttons on it, or it may be an instrumented glove. In either case, the position and orientation of the input device must be measured by the tracker to enable manual control of actions. The input device must also allow the user to signal to the system to start and stop actions, and to select among alternative actions. Certain fundamental manually-controlled actions may be implemented for any virtual world. These actions involve changing the location, orientation or scale of either an object or a user, as shown in Table 1.

The Visual Display Transformation for Virtual Reality

For stereoscopic photography or telepresence, orthostereoscopy occurs when the perceived size, shape, and relative position of objects in the three-dimensional scene being viewed match those of the physical objects in front of the camera. In virtual reality, the simulated scene has no physical counterpart, so orthostereoscopy must be defined in this case as constancy, as the head moves around, of the perceived size, shape, and relative positions of the simulated objects. Achieving this constancy requires that the computational model used to generate the graphics matches the physical geometry of the head-mounted display being used. This geometry includes the optics used to image the displays and the placement of the displays with respect to the eyes. The model may fail to match the geometry because model parameters are difficult to measure accurately, or because the model itself is in error. Two common modeling errors are ignoring the distortion caused by the optics and ignoring the variation in interpupillary distance across different users. A computational model for the geometry of a head-mounted display is presented, and the parameters of this model for the VPL EyePhone are calculated.

Defect-tolerant interconnect to nanoelectronic circuits: internally redundant demultiplexers based on error-correcting codes

The visual display transformation for virtual reality (VR) systems is typically much more complex than the standard viewing transformation discussed in the literature for conventional computer graphics. The process can be represented as a series of transformations, some of which contain parameters that must match the physical configuration of the system hardware and the users body. Because of the number and complexity of the transformations, a systematic approach and a thorough understanding of the mathematical models involved are essential. This paper presents a complete model for the visual display transformation for a VR system; that is, the series of transformations used to map points from object coordinates to screen coordinates. Virtual objects are typically defined in an object-centered coordinate system (CS), but must be displayed using the screen-centered CSs of the two screens of a head-mounted display (HMD). This particular algorithm for the VR display computation allows multiple users to independently change position, orientation, and scale within the virtual world, allows users to pick up and move virtual objects, uses the measurements from a head tracker to immerse the user in the virtual world, provides an adjustable eye separation for generating two stereoscopic images, uses the off-center perspective projection required by many HMDs, and compensates for the optical distortion introduced by the lenses in an HMD. The implementation of this framework as the core of the UNC VR software is described, and the values of the UNC display parameters are given. We also introduce the vector-quaternion-scalar (VQS) representation for transformations between 3D coordinate systems, which is specifically tailored to the needs of a VR system. The transformations and CSs presented comprise a complete framework for generating the computer-graphic imagery required in a typical VR system. The model presented here is deliberately abstract in order to be general purpose; thus, issues of system design and visual perception are not addressed. While the mathematical techniques involved are already well known, there are enough parameters and pitfalls that a detailed description of the entire process should be a useful tool for someone interested in implementing a VR system.

Synthetic experience: a proposed taxonomy

We describe a family of defect-tolerant demultiplexers based on error-correcting codes. A conventional demultiplexer with a k-bit input address and 2k-bit output may be fortified against certain defect types by widening its address bus to n>k bits to permit an encoded address to be used within the demultiplexer. The redundant address is computed by an encoder that guarantees a minimum Hamming distance d between addresses, which sparsely populate an expanded address space. The increased Hamming distances between addresses are especially tolerant of stuck-open defects (and broken wires, which are equivalent to multiple stuck-open defects). For each address width k, there are a series of demultiplexer designs with increasing internal redundancy, increasing d, and increasing capability for defect tolerance. These circuit designs are especially suitable for nano-scale crossbars; in particular, they may be realized at the interface where the CMOS wires of conventional microelectronics cross nano-wires to form a mixed-scale interconnect crossbar. Thus, a small number (2n) of CMOS wires may be used to control a much larger number (2k) of nano-wires; the family of encoded demultiplexer designs provides a robust interface to the nano-circuitry, giving significant protection from manufacturing mistakes at the cost of a relatively small amount of area overhead . This is a qualitatively new application of error-correcting codes, the analysis of which combines elements of the conventional coding-theoretic notions of full-error and erasure correction. In particular, a code with minimum distance d guarantees tolerance to up to d−1 defects per nano-wire, in analogy to conventional erasure correction.

A memristor-based nonvolatile latch circuit

A taxonomy is proposed to classify all varieties of technologically mediated experience. This includes virtual reality and teleoperation, and also earlier devices such as the microscope and telephone. The model of mediated interaction assumes a sensor-display link from the world to the human, and an action-actuator link going back from the human to the world, with the mediating technology transforming the transmitted experience in some way. The taxonomy is used to classify a number of example systems. Two taxonomies proposed earlier are compared with the ideas presented in this paper. Then the long-term prospects of this field are speculated on, ignoring constraints of cost, effort, or time to develop. Finally, the ultimate limits of synthetic experience are discussed, which derive from properties of the physical universe and the human neural apparatus.

Hybrid CMOS/memristor circuits

Memristive devices, which exhibit a dynamical conductance state that depends on the excitation history, can be used as nonvolatile memory elements by storing information as different conductance states. We describe the implementation of a nonvolatile synchronous flip-flop circuit that uses a nanoscale memristive device as the nonvolatile memory element. Controlled testing of the circuit demonstrated successful state storage and restoration, with an error rate of 0.1%, during 1000 power loss events. These results indicate that integration of digital logic devices and memristors could open the way for nonvolatile computation with applications in small platforms that rely on intermittent power sources. This demonstrated feasibility of tight integration of memristors with CMOS (complementary metal-oxide-semiconductor) circuitry challenges the traditional memory hierarchy, in which nonvolatile memory is only available as a large, slow, monolithic block at the bottom of the hierarchy. In contrast, the nonvolatile, memristor-based memory cell can be fast, fine-grained and small, and is compatible with conventional CMOS electronics. This threatens to upset the traditional memory hierarchy, and may open up new architectural possibilities beyond it.

Resistor-logic demultiplexers for nanoelectronics based on constant-weight codes

This is a brief review of recent work on the prospective hybrid CMOS/memristor circuits. Such hybrids combine the flexibility, reliability and high functionality of the CMOS subsystem with very high density of nanoscale thin film resistance switching devices operating on different physical principles. Simulation and initial experimental results demonstrate that performance of CMOS/memristor circuits for several important applications is well beyond scaling limits of conventional VLSI paradigm.