Abraham K. Ishihara

Increasing viscosity and inertia using a robotically controlled pen improves handwriting in children.

The aim of this study was to determine the effect of mechanical properties of the pen on quality of handwriting in children. A total of 22 school-aged children, aged 8 to 14 years, wrote in cursive using a pen attached to a robot. The robot was programmed to increase the effective weight (inertia) and viscosity of the pen. Speed, frequency, variability, and quality of the 2 handwriting samples were compared. Increased inertia and viscosity improved handwriting quality in 85% of children (P ≤ .05). Handwriting quality did not correlate with changes in speed, suggesting that improvement was not due to reduced speed. Measures of movement variability remained unchanged, suggesting improvement was not due to mechanical smoothing of pen movement by the robot. Because improvement was not explained by reduced speed or mechanical smoothing, we conclude that children alter handwriting movements in response to pen mechanics. Altered movement could be caused by changes in sensory feedback.

Time Delay Margin Computation via the Razumikhin Method for an Adaptive Control System

We present a time delay margin estimation technique for an adaptive controller with sigma modification of an unknown plant. The time delay is assumed to enter at the input to the plant. We use the Razumikhin method, a subset of the more general LyapunovKrasovskii method, in which we analyze the stability of the solution of the retarded functional differential equation. Using this technique, we are able to compute an estimate of the time delay margin in which we conclude that for all delays less than this margin, the system is guaranteed to be semi-globally uniformly bounded. We also derive time delay margin landscapes that describe regions in the parameter space (learning rates, gains, etc.) for which the system is guaranteed to be bounded. We present simulation examples that illustrate the method.

Adaptive Backstepping Design for a Longitudinal UAV Model Utilizing a Fully Tuned Growing Radial Basis Function Network

Classical Radial Basis Function (RBF) neural network controller designs typically fix the number of basis functions and tune only the weights. In this paper we present a backstepping neural network controller algorithm in which all RBF parameters, including centers, variances and weight matrices are tuned online. By using a Lyapunov approach, tuning rules for updating the RBF parameters are derived and a stability and robustness analysis is presented. Additionally, we incorporate the ability to append RBF neurons such that both tracking performance and computational cost can be optimized. The condition for adding a neuron is based on a sliding RMS error window. In addition to the theoretical results, we present the controller implemented in several simulations of an auto landing sequence for a unmanned aerial vehicle (UAV) model.

Time Delay Margin Estimation for Adaptive Outer-Loop Longitudinal Aircraft Control

Metrics for adaptive control currently do not exist. Time delay margin is a viable candidate. In this paper we present a method to determine the time-delay margin of a nonlinear adaptive outer-loop control system for a longitudinal aircraft model. The control architecture is based on backstepping and the time-delay margin estimation approach for relevant the delay differential equations is based on the Razumikhin method.

Neural Network Robot Control with Noisy Learning

Abstract Neural network based control of a serial-link robotic manipulator is considered subject to a signal dependent noise (SDN) model corrupting the training signal. A radial basis function (RBF) network is utilized in the feedforward control to approximate the unknown inverse dynamics. The weights are adaptively adjusted according to a gradient descent plus a regulation term (Narendras e -modification). A typical quadratic stochastic Lyapunov function is constructed which shows under certain noise models it is not necessary to employ quartic Lyapunov functions as is typically carried out in stochastic adaptive backstepping designs. Bounds on the feedback gains, and learning rate parameters are derived that guarantee the origin of the closed loop system is semi-globally, uniformly bounded in expectation (SGUBE).

Feedback Error Learning with basis function networks

In this paper, we examine the stability properties of Feedback Error Learning, a model for biological control systems. We consider a specific model for cerebellar learning during fast voluntary movements. We assume that the feedforward approximation is represented by a basis function network. We establish local stability regions and compute explicit bounds on the feedback gain matrices.

A Matrix WKB Approach to Feedforward and Feedback Control

We apply a powerful new analytical approximation method, recently developed by the authors, to the design and analysis of feedforward and feedback control systems. This formalism employs a matrix version of the WKB expansion, which is an asymptotic approximation method familiar in quantum mechanics and classical continuum mechanics. Our matrix WKB formalism has proven remarkably useful in approximating and characterizing the long-term dynamics of systems of ODEs (both linear and nonlinear) when there exists a time scale hierarchy. In particular, the linear error dynamics encountered in the analysis and design of controllers for multi-input multi-output systems, is typically formulated as a first-order vector differential equation involving a time-dependent matrix. To illustrate our matrix WKB approach, we consider the feedforward and feedback control of the single link manipulator. The desired trajectory is assumed to vary sinusoidally with time. For sufficiently small expansion parameters, the closed form WKB approximants can be used to determine safe controller parameters. Given a specific time scale hierarchy, we use a theorem reported previously to partition the controller parameter space into three distinct regions in which the system is, respectively: exponentially stable, exponentially unstable, and undecided. The undecided region is a narrow strip about a computable transition hypersurface. This strip can be made progressively narrower by working to a high enough order in the WKB expansion. In the limit of infinitely small expansion parameters, the transition curve tends to the actual stability-instability boundary.© 2006 ASME

Adaptive Control Metrics via the Windowed Laplace Transform

In this paper, we introduce and describe a new type of Joint Time-Frequency Analysis (JTFA), which we call the Windowed Laplace Transform (WLT) method. In addition to general signal processing applications, this new method can be used to extend Nyquists’s classical stability analysis criteria and stability metrics, from LTI to LTV (Linear, TimeVarying) systems a step towards analyzing the more general case of NLTV (Non-Linear, Time Varying) systems. We apply WLT to two LTV models: A simple, exactly solvable 1D toy model, and an MRAC (Model Reference Adaptive Control) innerloop aerodynamic model. The latter is linearized about its reference plant trajectory and ideal neural-network weights. In either model, we assume no physical-layer delays in the system (plant or plantplus-controller), but allow the mathematical (virtual) injection of time delays in order to formulate stability margin metrics. We identify two such metrics: the Extended Phase Margin (EPM), which extends Nyquist’s Phase Margin metric to the LTV case; and the more physically meaningful Time-Delay Margin (TDM), which is defined as the maximal virtually-injected time delay before the EPM metric is driven down to zero. These new ‘quasi-LTI’ stability metrics can be visualized by viewing frames of a time-dependent Nyquist contour as befits a JTFA approach. What is more, it is possible to derive systematically-improvable analytical approximants for our novel EPM and TDM stability margin metrics. In this paper, we analyze a numerical example for each of the two aforementioned LTV models. In subsequent publications, we will present analytical and semi-analytical approximants, proofs of several theorems guaranteeing asymptotic exponential stability, and an extension of our analysis to fully NLTV MRAC schemes all based upon the WLT method and the new EPM and TDM metrics.

Adaptive Feedforward Aircraft Control

In this paper we present a feedforward adaptive control scheme with application to the control of a nonlinear aircraft model with uncertainty in the aerodynamic moment coefficients. The feedforward controller is represented by a basis function network. The learning algorithm consists of a gradient based rule plus e-modification. We prove a theorem which guarantees that the origin of the closed loop system is semi-globally uniformly bounded. We further derive lower bounds on the minimum singular values of the feedback gain matrices that ensure this stability result. Numerous simulation examples are presented that illustrate the performance during abrupt changes in the plant parameters.

Failure Modes in Feedback Error Learning

This paper examines the feedback error learning architecture that has been proposed by Kawato under specific conditions in which learning does not occur. When a robot attempts to learn a novel task in an unknown environment, an approximation of the inverse dynamics of the plant/environment may be required. The novelty of feedback error learning lies in the training signal used to iteratively construct the inverse feedforward controller to achieve this task. We discuss a class of failure modes where the interaction of the learning algorithm and the feedback control leads to poor performance despite repeated practice. We hypothesize that this model could describe motor learning failure commonly seen in childhood movement disorders where a task, such as reaching in a straight path to an intended target, is never learned or improved despite years of repeated practice.