Investigations into an optimal approach for on-line robot trajectory planning and control.

The purpose of this thesis is to present a comprehensive and practical approach for the time-optimal motion planning and control of a general purpose industrial manipulator. In particular, the case of point-to-point path unconstrained motions is considered, with special emphasis towards strategies suitable for efficient on-line implementations. From a dynamic model description of the plant, and using an advanced graphical robotics simulation environment, the control algorithms are formulated. Experimental work is then conducted to verify the proposed algorithms, by interfacing the industrial manipulator to the master controller, implemented on a personal computer. The full rigid-body non-linear dynamics of the open-chain manipulator have been accommodated into the modelling, analysis and design of the control algorithms. For path unconstrained motions, this leads to a model-based regulating strategy between set points, which combines conventional trajectory planning and subsequent control tracking stages into one. Theoretical insights into these two robot motion disciplines are presented, and some are experimentally demonstrated on a CRS A251 industrial arm. A critical evaluation of current approaches which yield optimal trajectory planning and control of robot manipulators is undertaken, leading to the design of a control solution which is shown to be a combination of Pontryagin's Maximum Principle and state-space methods of design. However, in a real world setting, consideration of the relationship between optimal control and on-line viability highlights the need to approximate manipulator dynamics by a piecewise linear and decoupled function, hence rendering a near-time-optimal solution in feedback form. The on-line implementation of the proposed controller is presented together with a comparison between simulation and experimental results. Furthermore, these are compared with measurements from the industrial controller. It is shown that the model-based near-optimal-time feedback control algorithms allow faster manipulator motions, with an average speed-up of 14%, clearly outperforming current industrial controller practices in terms of increased productivity. This result was obtained by setting an acceptable absolute error limit on the target location of the joint (position and velocity) to within [2.0E-02 rad, 8.7E-03 rad/s], when the joint was regarded at rest

One-loop non-renormalization results in EFTs

In Effective Field Theories (EFTs) with higher-dimensional operators many anomalous dimensions vanish at the one-loop level for no apparent reason. With the use of supersymmetry, and a classification of the operators according to their embedding in super-operators, we are able to show why many of these anomalous dimensions are zero. The key observation is that one-loop contributions from superpartners trivially vanish in many cases under consideration, making supersymmetry a powerful tool even for non-supersymmetric models. We show this in detail in a simple U(1) model with a scalar and fermions, and explain how to extend this to SM EFTs and the QCD Chiral Langrangian. This provides an understanding of why most "current-current" operators do not renormalize "loop" operators at the one-loop level, and allows to find the few exceptions to this ubiquitous rule.Comment: Corrections made in Sec. 3.2 and Fig.

The renormalized Hamiltonian truncation method in the large ETE_T expansion

Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in Refs. [1-3]. The method is general but as an example we calculate the exact $g^2$ and some of the $g^3$ contributions for the $\phi^4$ theory in two dimensions. The coefficients of the local expansion calculated in Ref. [1] are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.Comment: JHEP version, typos fixed in Appendix and eq. (23

Renormalization of dimension-six operators relevant for the Higgs decays h→γγ,γZh\rightarrow \gamma\gamma,\gamma Z

The discovery of the Higgs boson has opened a new window to test the SM through the measurements of its couplings. Of particular interest is the measured Higgs coupling to photons which arises in the SM at the one-loop level, and can then be significantly affected by new physics. We calculate the one-loop renormalization of the dimension-six operators relevant for $h\rightarrow \gamma\gamma, \gamma Z$, which can be potentially important since it could, in principle, give log-enhanced contributions from operator mixing. We find however that there is no mixing from any current-current operator that could lead to this log-enhanced effect. We show how the right choice of operator basis can make this calculation simple. We then conclude that $h\rightarrow \gamma\gamma, \gamma Z$ can only be affected by RG mixing from operators whose Wilson coefficients are expected to be of one-loop size, among them fermion dipole-moment operators which we have also included.Comment: 21 pages. Improved version with h -> gamma Z results added and structure of anomalous-dimension matrix determined further. Conclusions unchange

Higgs Inflation as a Mirage

We discuss a simple unitarization of Higgs inflation that is genuinely weakly coupled up to Planckian energies. A large non-minimal coupling between the Higgs and the Ricci curvature is induced dynamically at intermediate energies, as a simple ratio of mass scales. Despite not being dominated by the Higgs field, inflationary dynamics simulates the `Higgs inflation' one would get by blind extrapolation of the low-energy effective Lagrangian, at least qualitatively. Hence, Higgs inflation arises as an approximate `mirage' picture of the true dynamics. We further speculate on the generality of this phenomenon and show that, if Higgs-inflation arises as an effective description, the details of the UV completion are necessary to extract robust quantitative predictions.Comment: 21 pages, 2 figure

Observation of soliton explosions in a passively mode-locked fiber laser

Soliton explosions are among the most exotic dissipative phenomena studied in mode-locked lasers. In this regime, a dissipative soliton circulating in the laser cavity experiences an abrupt structural collapse, but within a few roundtrips returns to its original quasi-stable state. In this work we report on the first observation of such events in a fiber laser. Specifically, we identify clear explosion signatures in measurements of shot-to-shot spectra of an Yb-doped mode-locked fiber laser that is operating in a transition regime between stable and noise-like emission. The comparatively long, all-normal-dispersion cavity used in our experiments also permits direct time-domain measurements, and we show that the explosions manifest themselves as abrupt temporal shifts in the output pulse train. Our experimental results are in good agreement with realistic numerical simulations based on an iterative cavity map.Comment: 5 pages, 5 figures, submitte

On the shape of a pure O-sequence

An order ideal is a finite poset X of (monic) monomials such that, whenever M is in X and N divides M, then N is in X. If all, say t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h=(1,h_1,...,h_e), counting the monomials of X in each degree. Equivalently, in the language of commutative algebra, pure O-sequences are the h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of Richard Stanley's early works in this area, and have since played a significant role in at least three disciplines: the study of simplicial complexes and their f-vectors, level algebras, and matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences. Our work, making an extensive use of algebraic and combinatorial techniques, includes: (i) A characterization of the first half of a pure O-sequence, which gives the exact converse to an algebraic g-theorem of Hausel; (ii) A study of (the failing of) the unimodality property; (iii) The problem of enumerating pure O-sequences, including a proof that almost all O-sequences are pure, and the asymptotic enumeration of socle degree 3 pure O-sequences of type t; (iv) The Interval Conjecture for Pure O-sequences (ICP), which represents perhaps the strongest possible structural result short of an (impossible?) characterization; (v) A pithy connection of the ICP with Stanley's matroid h-vector conjecture; (vi) A specific study of pure O-sequences of type 2, including a proof of the Weak Lefschetz Property in codimension 3 in characteristic zero. As a corollary, pure O-sequences of codimension 3 and type 2 are unimodal (over any field); (vii) An analysis of the extent to which the Weak and Strong Lefschetz Properties can fail for monomial algebras; (viii) Some observations about pure f-vectors, an important special case of pure O-sequences.Comment: iii + 77 pages monograph, to appear as an AMS Memoir. Several, mostly minor revisions with respect to last year's versio

A multi-modal utility to assist powered mobility device navigation tasks

© Springer International Publishing Switzerland 2014. This paper presents the development of a shared control systemfor power mobility device users of varying capability in order toreduce carer oversight in navigation. Weighting of a user’s joystick inputagainst a short-tem trajectory prediction and obstacle avoidancealgorithm is conducted by taking into consideration proximity to obstaclesand smoothness of user driving, resulting in capable users rewardedgreater levels of manual control for undertaking maneuvres that can beconsidered more challenging. An additional optional comparison with aVector Field Histogram applied to leader-tracking provides further activities,such as completely autonomous following and a task for the userto follow a leading entity. Indoor tests carried out on university campusdemonstrate the viability of this work, with future trials at a care homefor the disabled intended to show the system functioning in one of itsintended settings