Performance Analysis of Series Elastic Actuator based on Maximum Torque Transmissibility

The use of the Series Elastic Actuator (SEA) system as an actuator system equipped with a compliant element has contributed not only to advances in human interacting robots but also to a wide range of improvements in the robotics area. Nevertheless, there are still limitations in its performance; the elastic spring that is adopted to provide compliance is considered to limit the actuator performance thus lowering the frequency bandwidth of force/torque generation, and the bandwidth decreases even more when it is supposed to provide large torque. This weakness is in turn owing to the limitations of motor and motor drives such as torque and velocity limits. In this paper, mathematical tools to analyze the impact of these limitations on the performance of SEA as a transmission system are provided. A novel criterion called Maximum Torque Transmissibility (MTT)is defined to assess the ability of SEA to fully utilize maximum continuous motor torque. Moreover, an original frequency bandwidth concept, maximum torque frequency bandwidth, which can indicate the maximum frequency up to which the SEA can generate the maximum torque, is proposed based on the proposed MTT. The proposed MTT can be utilized as a unique criterion of the performance, and thus various design parameters including the load condition, mechanical design parameters, and controller parameters of a SEA can be evaluated with its use. Experimental results under various conditions verify that MTT can precisely indicate the limitation of the performance of SEA, and that it can be utilized to accurately analyze the limitation of the controller of SEA

Representations of integral quadratic polynomials

In this paper, we study the representations of integral quadratic polynomials. Particularly, it is shown that there are only finitely many equivalence classes of positive ternary universal integral quadratic polynomials, and that there are only finitely many regular ternary triangular forms. A more general discussion of integral quadratic polynomials over a Dedekind domain inside a global field is also given

Towards Accurate Force Control of Series Elastic Actuators Exploiting a Robust Transmission Force Observer

This paper develops an accurate force control algorithm for series elastic actuators (SEAs) based on a novel force estimation scheme, called transmission force observer (TFOB). The proposed method is designed to improve an inferior force measurement of the SEA caused by nonlinearities of the elastic transmission and measurement noise and error of its deformation sensor. This paper first analyzes the limitation of the conventional methods for the SEA transmission force sensing and then investigates its stochastic characteristics, which indeed provide the base to render the accurate force control performance incorporated with the TFOB. In particular, a tuning parameter is introduced from holistic closed-loop system analyses in the frequency domain. This gives a guideline to attain optimum performance of the force-controlled SEA system. The proposed algorithm is experimentally verified in an actual SEA hardware setup

Black Hole Entropy and Exclusion Statistics

We compute the entropy of systems of quantum particles satisfying the fractional exclusion statistics in the space-time of 2+1 dimensional black hole by using the brick-wall method. We show that the entropy of each effective quantum field theory with a Planck scale ultraviolet cutoff obeys the area law, irrespective of the angular momentum of the black hole and the statistics interpolating between Bose-Einstein and Fermi-Dirac statistics.Comment: REVTeX file, 12 page

The Effect of Anisotropic Extra Dimension in Cosmology

We consider five dimensional conformal gravity theory which describes an anisotropic extra dimension. Reducing the theory to four dimensions yields Brans-Dicke theory with a potential and a hidden parameter $z$ which implements the anisotropy between the four dimensional spacetime and the extra dimension. We find that a range of value of the parameter $z$ can address the current dark energy density compared to the Planck energy density. Constraining the parameter $z$ and the other cosmological model parameters using the recent observational data consisting of the Hubble parameters, type Ia supernovae, and baryon acoustic oscillations, together with the Planck or WMAP 9-year data of the cosmic microwave background radiation, we find $z>-2.05$ for Planck data and $z>-2.09$ for WMAP 9-year data at 95\% confidence level. We also obtained constraints on the rate of change of the effective Newtonian constant~($G_{\rm eff}$) at present and the variation of $G_{\rm eff}$ since the epoch of recombination to be consistent with observation.Comment: Revised version. arXiv admin note: text overlap with arXiv:1512.0054

Massive Photon and Dark Energy

We investigate cosmology of massive electrodynamics and explore the possibility whether massive photon could provide an explanation of the dark energy. The action is given by the scalar-vector-tensor theory of gravity which is obtained by non-minimal coupling of the massive Stueckelberg QED with gravity and its cosmological consequences are studied by paying a particular attention to the role of photon mass. We find that the theory allows cosmological evolution where the radiation- and matter-dominated epochs are followed by a long period of virtually constant dark energy that closely mimics $\Lambda$CDM model and the main source of the current acceleration is provided by the nonvanishing photon mass governed by the relation $\Lambda\sim m^2$. A detailed numerical analysis shows that the nonvanishing photon mass of the order of $\sim 10^{-34}$ eV is consistent with the current observations. This magnitude is far less than the most stringent limit on the photon mass available so far, which is of the order of $m \leq 10^{-27}$eV.Comment: 28 pages, 14 figures, Revised version, accepted for publication in PR

A quantum field theoretical model of neutrino oscillation without external wave packets

We develop a general and consistent model of neutrino oscillation based on the quantum field theoretical description of the neutrino production and detection processes. Emphasis is placed on the locality of the interactions of these processes, where on top of the usual application of the four fermion local Hamiltonian, we assume that weak interactions switched on only when the wave functions of the particles involved are overlapping and switched off upon their separation. A key assumption in our treatment is that the wave packet sizes of the particles, in particular, the neutrino producing source particles and the neutrino absorbing detector particles, are taken to be negligible compared with their mean free path in their respective medium. With this assumption, and taking into considerations of the finite time of neutrino production, neutrino wave packets with well-defined edges are generated. This fact, together with the locality of weak interactions, enable us to relate the propagation time to the propagation distance, thus doing away with the ad hoc time averaging procedure normally employing in derivations of neutrino oscillation formula. No assumptions on the particular forms of particle wave functions; for example, Gaussians, need to be made. A good feature of our approach is that the neutrino oscillation formula is automatically normalised if the in-going states of the production and detection processes are normalised. We also show that causality and unitarity cannot both be satisfied in virtual neutrino models.Comment: 32 pages, 10 figure

Dark aspects of massive spinor electrodynamics

We investigate the cosmology of massive spinor electrodynamics when torsion is non-vanishing. A non-minimal interaction is introduced between the torsion and the vector field and the coupling constant between them plays an important role in subsequential cosmology. It is shown that the mass of the vector field and torsion conspire to generate dark energy and pressureless dark matter, and for generic values of the coupling constant, the theory effectively provides an interacting model between them with an additional energy density of the form $\sim 1/a^6$. The evolution equations mimic $\Lambda$CDM behavior up to $1/a^3$ term and the additional term represents a deviation from $\Lambda$CDM. We show that the deviation is compatible with the observational data, if it is very small. We find that the non-minimal interaction is responsible for generating an effective cosmological constant which is directly proportional to the mass squared of the vector field and the mass of the photon within its current observational limit could be the source of the dark energy.Comment: 15 pages, 1 figure. Accepted for publication in JCA

Neutron Star Structure in Ho\v{r}ava-Lifshitz Gravity

We present interesting aspects of a modified theory of gravity called Ho\v{r}ava-Lifshitz (HL) gravity that can be constrained by the phenomenological and observational prospects in terms of neutron star (NS) structure and equation-of-state models. The deformation in HL gravity from general relativity (GR) can change typical features of the NS structure. In this Letter, we investigate the NS structure by deriving Tolman-Oppenheimer-Volkoff equation in HL gravity. We find that a NS in HL gravity with larger radius and heavier mass than a NS in GR remains stable without collapsing into a black hole.Comment: 6 pages, 4 figures, 1 tabl

Topological quantum phase transitions in the spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings

We examine the topological properties of a spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov-de Gennes (BdG) Hamiltonian by symmetry analysis. We use the Pfaffian invariant $\mathcal{P}$ for the particle-hole symmetry to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, a higher symmetric BdG Hamiltonian is needed to make them topologically stable. The Pfaffian invariant $\mathcal{P}(k_{y})$ and the winding number $\mathcal{W}(k_{y})$ are used in determining the location of the Majorana flat bands