Position Degrees Of Freedom Research Articles

A Relationship Between Spin and Geometry

In physics, spin is often seen exclusively through the lens of its phenomenological character: as an intrinsic form of angular momentum. However, there is mounting evidence that spin fundamentally originates as a quality of geometry, not of dynamics, and recent work further suggests that the structure of non-relativistic Euclidean three-space is sufficient to define it. In this paper, we directly explicate this fundamentally non-relativistic, geometric nature of spin by constructing non-commutative algebras of position operators which subsume the structure of an arbitrary spin system. These “Spin-s Position Algebras” are defined by elementary means and from the properties of Euclidean three-space alone, and constitute a fundamentally new model for quantum mechanical systems with non-zero spin, within which neither position and spin degrees of freedom, nor position degrees of freedom within themselves, commute. This reveals that the observables of a system with spin can be described completely geometrically as tensors of oriented planar elements, and that the presence of non-zero spin in a system naturally generates a non-commutative geometry within it. We will also discuss the potential for the Spin-s Position Algebras to form the foundation for a generalisation to arbitrary spin of the Clifford and Duffin–Kemmer–Petiau algebras.

Motion sensor-based haptic master controller with finger band soft actuator for surgical robots

This paper presents a motion sensor-based haptic master controller capable of static and dynamic force presentation by the newly invented Finger Band Soft Actuator (FBSA). The master controller operates a surgical assist robot using the 6 degrees of freedom position and posture data tracked by an optical motion capture. The haptic force presentation can be realized by the pneumatic pressure of FBSA, which can be highly integrated into the controller mechanism to maintain precise manipulability. The FBSA can present a pressing force of 3.7 N for a small-sized finger and 5.1 N for a large-sized finger at an internal pressure of 60 kPa, and there is a monotonically increasing and decreasing relationship between the air pressure and the pressing force. The effectiveness of haptic force presentation by the FBSA was experimentally evaluated in the master-follower operation of a surgical assist robot. Ten subjects performed the task of pulling a suture thread and controlled the manipulation to achieve the directed tension. The experimental result shows that with the four levels of force presentation scheme by the FBSA, the error between suture tension and target operating force is significantly smaller than without force presentation.

A simple coin for a 2d entangled walk

We analyze the effect of a simple coin operator, built out of Bell pairs, in a 2d Discrete Quantum Random Walk (DQRW) problem. The specific form of the coin enables us to find analytical and closed form solutions to the recursion relations of the DQRW. The coin induces entanglement between the spin and position degrees of freedom, which oscillates with time and reaches a constant value asymptotically. We probe the entangling properties of the coin operator further, by two different measures. First, by integrating over the space of initial tensor product states, we determine the Entangling Power of the coin operator. Secondly, we compute the Generalized Relative Rényi Entropy between the corresponding density matrices for the entangled state and the initial pure unentangled state. Both the Entangling Power and Generalized Relative Rényi Entropy behaves similar to the entanglement with time. Finally, in the continuum limit, the specific coin operator reduces the 2d DQRW into two 1d massive fermions coupled to synthetic gauge fields, where both the mass term and the gauge fields are built out of the coin parameters.

Estimator for Deep-Space Position and Attitude Using X-ray Pulsars

In this article, we develop an algorithm for the estimation of a full six degree of freedom position, navigation, and timing solution in deep space by measuring the time and angle of arrival of x-rays photons from pulsars and other bright stars. We show that for pulsar navigation, the position and attitude determination problems are coupled. This is due in part to the small signal-to-noise ratio of pulsar signals and the fact that x-ray photons emanating from various pulsars and bright stars have no unique identifier that can be used to associate them with their source. To address this challenge, a joint probabilistic data association filter is developed. The filter fuses angular rate measurements from a three-axis rate gyro with time-of-arrival and angle-of-arrival measurements from an x-ray detector. The performance of the filter is validated in simulation, and the tradeoffs associated with detector size and initial conditions are evaluated. Additional validation of the algorithm is performed by playback of data from x-ray detectors on the Chandra spacecraft. The results show that positioning accuracy on the order of 1000 km and attitude accuracies on the order of 5 arcseconds can be achieved.

Formation of a Morphogen Gradient - Acceleration by Quantum Walks

The establishment of graded concentration distributions of certain signalling molecules, called morphogens, is crucial for the successful embryonic development of multicellular organisms. The morphogen system that has been studied in the greatest detail is the Bicoid (Bcd) gradient established during the early embryonic development of fruit flies and provides the embryo cells with the necessary positional information for the proper implementation of the body plan of the organism. Both continuous as well as discrete-state classical random-walk models fail to provide a completely satisfactory explanation of the dynamics of Bcd gradient formation within the developmentally relevant timescales. By presuming the existence of an arbitrary chirality degree of freedom that characterizes each Bcd molecule, we here therefore develop a discrete-time quantum walk model of the process. Our approach is based on the recent suggestion that high temperatures and random interactions need not necessarily destroy many-body quantum coherence. In this way we are led to a system of non-classical master equations bearing an interference term that can be numerically solved on a computer. Our analysis predicts a large value of diffusion rate for the Bcd system in the very early nuclear division cycles that needs to be verified experimentally. Additionally, with the chirality and position degrees of freedom at our disposal entanglement shows up as a natural consequence in the system. Taking inspiration from a very recent demonstration of the existence of entanglement phenomenon in a hot, strongly-interacting atomic system, the discussion takes the point of view that the emergence of geometry in the embryo system is consequence of quantum entanglement that needs further understanding and analysis.

Enhanced non-Markovian behavior in quantum walks with Markovian disorder

Non-Markovian quantum effects are typically observed in systems interacting with structured reservoirs. Discrete-time quantum walks are prime example of such systems in which, quantum memory arises due to the controlled interaction between the coin and position degrees of freedom. Here we show that the information backflow that quantifies memory effects can be enhanced when the particle is subjected to uncorrelated static or dynamic disorder. The presence of disorder in the system leads to localization effects in 1-dimensional quantum walks. We shown that it is possible to infer about the nature of localization in position space by monitoring the information backflow in the reduced system. Further, we study other useful properties of quantum walk such as entanglement, interference and its connection to quantum non-Markovianity.

Dynamics of a novel robotic leg based on the Peaucellier–Lipkin mechanism on linear paths during the transfer phase

This article deals with the kinematics and dynamics of a novel leg based on the Peaucellier–Lipkin mechanism, which is better known as the straight path tracer. The basic Peaucellier–Lipkin linkage with 1 degree of freedom was transformed into a more skillful mechanism, through the addition of 4 more degrees of freedom. The resulting 5-degree-of-freedom leg enables the walking machine to move along paths that are straight lines and/or concave or convex curves. Three degrees of freedom transform the leg in relation to a reachable center of rotation that the machine walks around. Once the leg is transformed, the remaining 2 degrees of freedom position the foot at a desirable Cartesian point during the transfer or support phase. We analyzed the direct and inverse kinematics developed for the leg when the foot describes a straight line and found some interesting relationships among the motion parameters. The dynamic model equations of motion for the leg were derived from the Lagrangian dynamic formulation to calculate the required torques during a particular transfer phase.

Modeling of two-plate capacitive position sensing systems for high precision planar three DOF measurement

This paper investigates the issues associated with the use of two-plate capacitive sensors for the measurement of coupled linear and angular motions, particularly those of three planar degrees of freedom (DOF) micro/nano positioners. Commonly, such sensors are employed for the measurement of linear motions, and angular motion could introduce non-linearities in the capacitance response. An analytic model of a general three sensor system is developed, together with its linearization, which transform the position and orientation (pose) of the end effector of a planar positioner to the capacitance of each sensor. The sensitivities of pose estimations to capacitance non-linearity and parameter variation are analyzed, which further leads to the identification of optimized sensor positioning strategies. The response of a single sensor to tilt is investigated, and experimentation is performed to determine the magnitude of non-linear effects, and its subsequent impact on the three DOF position estimation.

Quantum walk, entanglement and thermodynamic laws

We consider a special dynamics of a quantum walk (QW) on a line. The walker, initially localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is performed and the state resulting from this measurement is used to start a second QW evolution to achieve a second asymptotic stationary state. In previous works, we developed the thermodynamics associated with the entanglement between the coin and position degrees of freedom in the QW. Here we study the application of the first and second laws of thermodynamics to the process between the two stationary states mentioned above. We show that: (i) the entropy change has upper and lower bounds that are obtained analytically as functions of the initial conditions. (ii) the energy change is associated to a heat-transfer process.

Catheter Position Tracking System Using Planar Magnetics and Closed Loop Current Control

This paper presents an electromagnetic system for five degrees of freedom position and orientation sensing with application in a virtual bronchoscopy system. Planar magnetic source coils were manufactured on printed circuit boards for reproducibility and low-cost manufacturing. The exact magnetic field of each coil is calculated using a filament-based approach. A constant ac current amplifier is used to drive each coil at an independent frequency and a synchronous demodulator calculates each associated magnetic field component using the current waveform as a reference signal. Commercially available search coil sensors are used and a comparison between shielded and unshielded probes is presented. Extensive testing with two separate methods has shown the accuracy of the system to be between 1 and 2 mm. The use of a novel closed loop coil driver has been found to offer excellent magnetic field stability and significant reduction in crosstalk interference.

Modeling and Analysis of Coupling Performance Between Passive Magnetic Bearing and Hybrid Magnetic Radial Bearing for Magnetically Suspended Flywheel

In this paper, the design and development of a novel magnetic bearing (MB) system which consists of a passive magnetic bearing (PMB) with two pairs of passive permanent magnet rings and hybrid magnetic radial bearing (HMRB) used in magnetic bearing flywheel (MBFW) of control moment gyroscope (CMG) for agile satellite application are presented. The models of PMB and HMRB are proposed and their performances of force-current, force-position, and torque-angle are analyzed using the equivalent magnetic circuit method, finite element method (FEM), and equivalent magnetic charge method. The coupling forces between x and y position degrees of freedom (DOFs) of the HMRB, between the coil current in x-axis and y-axis, between the radial and the axial position DOF of the HMRB, and the coupling force and torque between the translating motion along the x (or y) axis and the rotary motion around x (or y) axis. These coupling problems of the novel MB system are proposed and clarified in this paper. An example is given to clarify the mathematical models and the coupling problems, and the linearized model is proposed for controller design of the MB system.

UNSUPERVISED MARKERLESS 3-DOF MOTION TRACKING IN REAL TIME USING A SINGLE LOW-BUDGET CAMERA

Motion tracking is a critical task in many computer vision applications. Existing motion tracking techniques require either a great amount of knowledge on the target object or specific hardware. These requirements discourage the wide spread of commercial applications based on motion tracking. In this paper, we present a novel three degrees of freedom motion tracking system that needs no knowledge on the target object and that only requires a single low-budget camera that can be found installed in most computers and smartphones. Our system estimates, in real time, the three-dimensional position of a nonmodeled unmarked object that may be nonrigid, nonconvex, partially occluded, self-occluded, or motion blurred, given that it is opaque, evenly colored, enough contrasting with the background in each frame, and that it does not rotate. Our system is also able to determine the most relevant object to track in the screen. Our proposal does not impose additional constraints, therefore it allows a market-wide implementation of applications that require the estimation of the three position degrees of freedom of an object.

ASYMPTOTIC ENTANGLEMENT IN THE PARAMETRIZED HADAMARD WALK

We study asymptotic entanglement properties of the Hadamard walk with phase parameters on the line using the Fourier representation. We use the von Neumann entropy of the reduced density operator to quantify entanglement between the coin and position degrees of freedom. We investigate obtaining exact expressions for the asymptotic entropy of entanglement, for different classes of initial conditions. We also determine under which conditions the asymptotic entropy of entanglement can be characterized as full, intermediate, or minimum.

Asymptotic evolution of quantum walks on theN-cycle subject to decoherence on both the coin and position degrees of freedom

Consider a discrete-time quantum walk on the $N$-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some new conclusions about the asymptotic behavior of the system. When $N$ is odd, the density matrix of the system tends, in the long run, to the maximally mixed state, independent of the initial state. When $N$ is even, although the behavior of the system is not necessarily asymptotically stationary, in this case too an explicit formulation is obtained of the asymptotic dynamics of the system. Moreover, this approach enables us to specify the limiting behavior of the mutual information, viewed as a measure of quantum entanglement between subsystems (coin and walker). In particular, our results provide efficient theoretical confirmation of the findings of previous authors, who arrived at their results through extensive numerical simulations. Our results can be attributed to an important theorem which, for a generalized random unitary operation, explicitly identifies the structure of all of its eigenspaces corresponding to eigenvalues of unit modulus.

Quantumness in a decoherent quantum walk using measurement-induced disturbance

The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability distribution becomes increasingly Gaussian, with a concomitant fall in the standard deviation, in the former case, but not in the latter. As another example, each step of the quantum walk on a line may be subjected to an arbitrary phase gate, without affecting the position probability distribution, no matter whether the walk is noiseless or noisy. This symmetry, which is absent in the case of noiseless cyclic walk, but is restored in the presence of sufficient noise, serves as an indicator of classicalization, but only in the cyclic case. Here we show that the degree of quantum correlations between the coin and position degrees of freedom, quantified by a measure based on the disturbance induced by local measurements (Luo, Phys. Rev. A 77, 022301 (2008)), provides a suitable measure of classicalization across both type of walks. Applying this measure to compare the two walks, we find that cyclic quantum walks tend to classicalize faster than quantum walks on a line because of more efficient phase randomization due to the self-interference of the two counter-rotating waves. We model noise as acting on the coin, and given by the squeezed generalized amplitude damping (SGAD) channel, which generalizes the generalized amplitude damping channel.

Quantum walk on the line: Entanglement and nonlocal initial conditions

The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumann entropy of the reduced density operator (entropy of entanglement). In the long time limit, it converges to a well defined value which depends on the initial state. Exact expressions for the asymptotic (long-time) entanglement are obtained for (i) localized initial conditions and (ii) initial conditions in the position subspace spanned by the +1 and -1 position eigenstates.

Precision positioning of a five degree-of-freedom planar motion stage

This paper presents the development of a five degree-of-freedom (DOF) planar motion stage with an integrated surface encoder for position detection. The single-level moving element is levitated by three air-bearings without mechanical contact, and is actuated by three linear motors and three piezoelectric transducer (PZT) actuators. The three linear motors are placed on the stage base to generate movement of the stage in the XYθ z directions (in-plane motion), while the three PZT actuators move the stage in the Zθ x θ y directions (out-of-plane motion). A surface encoder composed of three two-dimensional (2D) angle sensors and a 2D angle grid is employed as the position sensor to detect the five DOF position of the stage for feedback control. Experimental results demonstrate that the surface encoder has a resolution of 30 nm and is suitable for sub-micrometer positioning. It is also confirmed experimentally that the stage can be controlled independently in the five DOFs with a positioning resolution of 50 nm and a settling time of 50 ms.

Quantum random walks do not need a coin toss

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. Our construction eliminates quantum entanglement between the coin and the position degrees of freedom from the algorithm, and the results match those obtained with a quantum coin toss instruction.

RELIABILITY OF AN ACOUSTO-INERTIAL 6-DOF POSITION AND ORIENTATION TRACKING SYSTEM

PURPOSE To establish the reliability of an acousto-inertial six degrees of freedom position and orientation tracking system (Intersence 600) during one-axis and combined-axes neck rotations. METHOD During one-axis rotations, the 2-sonidisc mounting bracket of the Intersense was mounted on the upper part of a rigid box. This upper part could be tilted to simulate lateroflexion and flexion/extension. Axial rotation was simulated by mounting the 2- sonidisc mounting bracket on a circle, which rotated on a protractor. For combined-axes rotations, the same set-up as during one-axis axial rotation was flexed. Intersense results were compared with goniometer results. RESULTS The Intersense 600 was reliable for both one-axis and combined axes rotations. During one-axis rotations, highest mean deviation between Intersense data and goniometer results was 0.64 ± 0.2 degrees for right lateroflexion. During combined axial rotation and flexion, axial rotation was reliable with a mean deviation between Intersense and goniometer results of 0.15 ± 0.2 degrees for left axial rotation and 0.84 ± 0.2 degrees for right axial rotation. Flexion showed high mean deviations between Intersense and goniometer results of −5.52 ± 0.1 degrees, which could be corrected to a mean difference of −1.9 ± 0.2 degrees. Lateroflexion showed a mean deviation of 7.5 ± 2.7 degrees for right lateroflexion and −2.2 ± 2.4 degrees for left lateroflexion. This error could be corrected to a deviation of −2.8 ± 0.8 degrees and −2.3 ± 0.4 degrees respectively. CONCLUSION The Intersense 600 is a reliable measurement method for measuring cervical rotations. One-axis rotations showed only a small deviation with respect to goniometer results. Combined rotations showed also a small deviation with respect to goniometer results. In that case a correction formula was necessary to transform the angles measured in the original co-ordinate system to angles in the tilted co-ordinate system in which the rotation occurs.

Haptic Device Control – Will it Fit Standardized Input Models?

Over recent years a wide variety of interaction devices involving haptic feedback have been brought to the market, but they vary widely in terms of input measures recorded. These range from one dimensional input on a haptic feedback steering wheel to a six degree of freedom position and orientation device and further, to assemblies of such devices. On the surface most of the variations can be accommodated logically with standardized input models combining existing logical input devices and haptic feedback processes as acknowledgement/echos. However it is very uncertain whether such a model can adequately model the system requirements for effective haptic feedback.In this paper we review the input models that have developed over the past 20 years and ask “Is it the end of the road for the conceptual model of input incorporated into the early graphics standards and elaborated over the years?” In addition, to highlight the problems of implementation with haptic interaction, we describe a typical application, the simulation of a collision with a virtual wall.