Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control

Three-Axis Attitude Estimation With a High-Bandwidth Angular Rate Sensor

A continuing challenge for modern instrument pointing control systems is to meet the increasingly stringent pointing performance requirements imposed by emerging advanced scientific, defense, and civilian payloads. Instruments such as adaptive optics telescopes, space interferometers, and optical communications make unprecedented demands on precision pointing capabilities. A cost-effective method was developed for increasing the pointing performance for this class of NASA applications. The solution was to develop an attitude estimator that fuses star tracker and gyro measurements with a high-bandwidth angular rotation sensor (ARS). An ARS is a rate sensor whose bandwidth extends well beyond that of the gyro, typically up to 1,000 Hz or higher. The most promising ARS sensor technology is based on a magnetohydrodynamic concept, and has recently become available commercially. The key idea is that the sensor fusion of the star tracker, gyro, and ARS provides a high-bandwidth attitude estimate suitable for supporting pointing control with a fast-steering mirror or other type of tip/tilt correction for increased performance. The ARS is relatively inexpensive and can be bolted directly next to the gyro and star tracker on the spacecraft bus. The high-bandwidth attitude estimator fuses an ARS sensor with a standard three-axis suite comprised of a gyro and star tracker. The estimation architecture is based on a dual-complementary filter (DCF) structure. The DCF takes a frequency- weighted combination of the sensors such that each sensor is most heavily weighted in a frequency region where it has the lowest noise. An important property of the DCF is that it avoids the need to model disturbance torques in the filter mechanization. This is important because the disturbance torques are generally not known in applications. This property represents an advantage over the prior art because it overcomes a weakness of the Kalman filter that arises when fusing more than one rate measurement. An additional advantage over prior art is that, computationally, the DCF requires significantly fewer real-time calculations than a Kalman filter formulation. There are essentially two reasons for this: the DCF state is not augmented with angular rate, and measurement updates occur at the slower gyro rate instead of the faster ARS sampling rate. Finally, the DCF has a simple and compelling architecture. The DCF is exactly equivalent to flying two identical attitude observers, one at low rate and one at high rate. These attitude observers are exactly of the form currently flown on typical three-axis spacecraft

Isolated effective coherence (iCoh): causal information flow excluding indirect paths

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system causal relations. For instance, electric cortical signals are used for studying functional connectivity between brain areas, their directionality, the direct or indirect nature of the connections, and the spectral characteristics (e.g. which oscillations are preferentially transmitted). The earliest spectral measure of causality was Akaike's (1968) seminal work on the noise contribution ratio, reflecting direct and indirect connections. Later, a major breakthrough was the partial directed coherence of Baccala and Sameshima (2001) for direct connections. The simple aim of this study consists of two parts: (1) To expose a major problem with the partial directed coherence, where it is shown that it is affected by irrelevant connections to such an extent that it can misrepresent the frequency response, thus defeating the main purpose for which the measure was developed, and (2) To provide a solution to this problem, namely the "isolated effective coherence", which consists of estimating the partial coherence under a multivariate auto-regressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest. Simple, realistic, toy examples illustrate the severity of the problem with the partial directed coherence, and the solution achieved by the isolated effective coherence. For the sake of reproducible research, the software code implementing the methods discussed here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the test data as text files, are freely available at: https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherenceComment: 2014-02-21 pre-print, technical report, KEY Institute for Brain-Mind Research, University of Zurich, et a

Innovations orthogonalization: a solution to the major pitfalls of EEG/MEG "leakage correction"

The problem of interest here is the study of brain functional and effective connectivity based on non-invasive EEG-MEG inverse solution time series. These signals generally have low spatial resolution, such that an estimated signal at any one site is an instantaneous linear mixture of the true, actual, unobserved signals across all cortical sites. False connectivity can result from analysis of these low-resolution signals. Recent efforts toward "unmixing" have been developed, under the name of "leakage correction". One recent noteworthy approach is that by Colclough et al (2015 NeuroImage, 117:439-448), which forces the inverse solution signals to have zero cross-correlation at lag zero. One goal is to show that Colclough's method produces false human connectomes under very broad conditions. The second major goal is to develop a new solution, that appropriately "unmixes" the inverse solution signals, based on innovations orthogonalization. The new method first fits a multivariate autoregression to the inverse solution signals, giving the mixed innovations. Second, the mixed innovations are orthogonalized. Third, the mixed and orthogonalized innovations allow the estimation of the "unmixing" matrix, which is then finally used to "unmix" the inverse solution signals. It is shown that under very broad conditions, the new method produces proper human connectomes, even when the signals are not generated by an autoregressive model.Comment: preprint, technical report, under license "Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)", https://creativecommons.org/licenses/by-nc-nd/4.0

The photosynthetic cytochrome c550 from the diatom Phaeodactylum tricornutum

The photosynthetic cytochrome c550 from the marine diatom Phaeodactylum tricornutum has been purified and characterized. Cytochrome c550 is mostly obtained from the soluble cell extract in relatively large amounts. In addition, the protein appeared to be truncated in the last hydrophobic residues of the C-terminus, both in the soluble cytochrome c550 and in the protein extracted from the membrane fraction, as deduced by mass spectrometry analysis and the comparison with the gene sequence. Interestingly, it has been described that the C-terminus of cytochrome c550 forms a hydrophobic finger involved in the interaction with photosystem II in cyanobacteria. Cytochrome c550 was almost absent in solubilized photosystem II complex samples, in contrast with the PsbO and Psb31 extrinsic subunits, thus suggesting a lower affinity of cytochrome c550 for the photosystem II complex. Under iron-limiting conditions the amount of cytochrome c550 decreases up to about 45% as compared to iron-replete cells, pointing to an iron-regulated synthesis. Oxidized cytochrome c550 has been characterized using continuous wave EPR and pulse techniques, including HYSCORE, and the obtained results have been interpreted in terms of the electrostatic charge distribution in the surroundings of the heme centre