Slower Visuomotor Corrections with Unchanged Latency are Consistent with Optimal Adaptation to Increased Endogenous Noise in the Elderly

We analyzed age-related changes in motor response in a visuomotor compensatory tracking task. Subjects used a manipulandum to attempt to keep a displayed cursor at the center of a screen despite random perturbations to its location. Cross-correlation analysis of the perturbation and the subject response showed no age-related increase in latency until the onset of response to the perturbation, but substantial slowing of the response itself. Results are consistent with age-related deterioration in the ratio of signal to noise in visuomotor response. The task is such that it is tractable to use Bayesian and quadratic optimality assumptions to construct a model for behavior. This model assumes that behavior resembles an optimal controller subject to noise, and parametrizes response in terms of latency, willingness to expend effort, noise intensity, and noise bandwidth. The model is consistent with the data for all young (n = 12, age 20–30) and most elderly (n = 12, age 65–92) subjects. The model reproduces the latency result from the cross-correlation method. When presented with increased noise, the computational model reproduces the experimentally observed age-related slowing and the observed lack of increased latency. The model provides a precise way to quantitatively formulate the long-standing hypothesis that age-related slowing is an adaptation to increased noise

A Generalized Frequency Weighting Framework for LQG Compensator Design

This paper specifies methods enabling specific types of frequency domain loopshaping in the LQG framework. It gives the augmented state and observation equations for a general system with colored sensor or motor noise, sensor and actuator dynamics, and frequency weight on the control and performance costs. The performance weights are useful in design for dealing with the effects of many challenges facing control designers other than colored control and performance in the narrow sense, through shaping the sensitivity and loop gain

Visuomotor Optimality and its Utility in Parametrization of Response

We present a method of characterizing visuomotor response by inferring subject-specific physiologically meaningful parameters within the framework of optimal control theory. The characterization of visuomotor response is of interest in the assessment of impairment and rehabilitation, the analysis of man-machine systems, and sensorimotor research. We model visuomotor response as a Linear Quadratic Gaussian (LQG) controller, a Bayesian optimal state estimator in series with a linear quadratic regulator. Subjects used a modified computer mouse to attempt to keep a displayed cursor at a fixed desired location despite a Gaussian random disturbance and simple cursor dynamics. Nearly all subjects' behavior was consistent with the hypothesized optimality. Experimental data was used to fit an LQG model whose assumptions are simple and consistent with other sensorimotor work. The parametrization is parsimonious and yields quantities of clear physiological meaning: noise intensity, level of exertion, delay, and noise bandwidth. Inferred control cost and noise intensity varied significantly across subjects. Response variations were consistent with changes in exerted effort. This is a novel example of the role of optimal control theory in explaining variance in human visuomotor response. We also present technical improvements on the use of LQG in human operator modeling

Bayesian And Quadratic Methods In System Identification And Iterative Learning Control

The theme of this thesis is the automated creation, updating, and exploitation of models using quadratic and Bayesian approaches when uncertainty modeling is feasible, and the design of dynamical systems that use feedback principles when tractable models of uncertainty are absent. The first chapter describes the 2005 Cornell RoboCup system. I led the mechanical design team and designed local control algorithms for a system where precise traction models were unavailable. The second chapter presents an optimal control based model for response in a visuomotor task. Its utility is in parametrization of human subject response. This work uses optimality as a structural assumption to guide system identification in terms of physiologically meaningful parameters. The third chapter demonstrates that elderly impairment in a visuomotor task is not due to increased latency, and is consistent with optimal response to increased cortical disorder. This uses both model-free cross-correlation analysis, and the previous optimal control based system identification work. The fourth chapter describes a reduced impedance actuator designed for stroke rehabilitation robotics, in which precise models of patient behavior are unavailable. In this case, we exploit basic feedback control principles to guide electromechanical design, thereby achieving the desired impedance reduction without large size and cost. The fifth chapter presents a recursive algorithm for identification of state- and input

A Simple Learning Strategy for High-Speed Quadrocopter Multi-Flips

We describe a simple and intuitive policy gradient method for improving parametrized quadrocopter multi-flips by combining iterative experiments with information from a first-principles model. We start by formulating an N-flip maneuver as a five-step primitive with five adjustable parameters. Optimization using a low-order first-principles 2D vertical plane model of the quadrocopter yields an initial set of parameters and a corrective matrix. The maneuver is then repeatedly performed with the vehicle. At each iteration the state error at the end of the primitive is used to update the maneuver parameters via a gradient adjustment. The method is demonstrated at the ETH Zurich Flying Machine Arena testbed on quadrotor helicopters performing and improving on flips, double flips and triple flips

A simple learning strategy for high-speed quadrocopter multi-flips

Abstract-We describe a simple and intuitive policy gradient method for improving parametrized quadrocopter multi-flips by combining iterative experiments with information from a first-principles model. We start by formulating an N-flip maneuver as a five-step primitive with five adjustable parameters. Optimization using a low-order first-principles 2D vertical plane model of the quadrocopter yields an initial set of parameters and a corrective matrix. The maneuver is then repeatedly performed with the vehicle. At each iteration the state error at the end of the primitive is used to update the maneuver parameters via a gradient adjustment. The method is demonstrated at the ETH Zurich Flying Machine Arena testbed on quadrotor helicopters performing and improving on flips, double flips and triple flips

Time series data.

<p>Representative time series data: All elderly subjects, trial 7. Note identical and two of the outlying elderly subjects, 19 and 22.</p

Typical spectral fit.

<p>This shows representative spectral fits for young (left) and elderly (right) subjects. Discrete data points are circles, and lines are fits. They were selected by choosing the trials with median fit cost from each group. The top panel is the magnitude of the closed loop transfer function compared to the experimental cross spectrum of and . The next panel is the phase of the same quantity. It decreases, wrapping around, as the effects of latency and limited bandwidth build up. The bottom panel is the fitted and observed power spectral density of the control input . The apparent overfitting is due to the model fitting process' knowledge of the perturbation, and the dominance of the low frequency behavior by response to the known perturbation rather than endogenous noise.</p

Relationship of to input velocity.

<p>The left panel shows that among a uniformly healthy young population whose multiplicative noise characteristics can be expected to be uniform, a relationship between the control cost/multiplicative noise parameter and observed RMS exists as expected. Data points from outlying subjects 1 and 10 are shown with triangles and omitted from the displayed empirical least-squares linear fit. The increase in this parameter at any given level of RMS for the elderly is shown in the right frame. This is consistent with increased noise.</p