Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty.

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models.

Electroosmotic flow analysis of a branched U-turn nanofluidic device.

In this paper, we present the analysis of electroosmotic flow in a branched -turn nanofluidic device, which we developed for detection and sorting of single molecules. The device, where the channel depth is only 150 nm, is designed to optically detect fluorescence from a volume as small as 270 attolitres (al) with a common wide-field fluorescent setup. We use distilled water as the liquid, in which we dilute 110 nm fluorescent beads employed as tracer-particles. Quantitative imaging is used to characterize the pathlines and velocity distribution of the electroosmotic flow in the device. Due to the device's complex geometry, the electroosmotic flow cannot be solved analytically. Therefore we use numerical flow simulation to model our device. Our results show that the deviation between measured and simulated data can be explained by the measured Brownian motion of the tracer-particles, which was not incorporated in the simulation.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models. © 2010 Nagengast et al.

Modelling the entrainment and motion of particles in a gap: Application to abrasive wear

The microscale abrasion or ball-cratering test is being increasingly applied to a wide range of bulk materials and coatings. The response of materials to this test depends critically on the nature of the motion of the abrasive particles in the contact zone: whether they roll and produce multiple indentations in the coating, or slide causing grooving abrasion. Similar phenomena also occur when hard contaminant particles enter a lubricated contact. This paper presents simple quantitative two-dimensional models which describe two aspects of the interaction between a hard abrasive particle and two sliding surfaces. The first model treats the conditions under which a spherical abrasive particle of size d can be entrained into the gap between a rotating sphere of radius R and a plane surface. These conditions are determined by the coefficients of friction between the particle and the sphere, and the particle and the plane, denoted by μs and μp respectively. This model predicts that the values of (μs + μp) and 2μs should both exceed √2d/R for the particles to be entrained into the contact. If either is less than this value, the particle will slide against the sphere and never enter the contact. The second model describes the mechanisms of abrasive wear in a contact when an idealized rhombus-sectioned prismatic particle is located between two parallel plane surfaces separated by a certain distance, which can represent either the thickness of a fluid film or the spacing due to the presence of other particles. It is shown that both the ratio of particle size to the separation of the surfaces and the ratio of the hardnesses of the two surfaces have important influences on the particle motion and hence on the mechanism of the resulting abrasive wear. Results from this model are compared with experimental observations, and the model is shown to lead to realistic predictions. © IMechE 2003.

Time-resolved particle image velocimetry within the nozzle of a drop-on-demand printhead

Time-resolved particle image velocimetry (PIV) has been performed inside the nozzle of a commercially available inkjet print-head to obtain the time-dependent velocity waveform. A printhead with a single transparent nozzle 80 μm in orifice diameter was used to eject single droplets at a speed of 5 m/s. An optical microscope was used with an ultra-high-speed camera to capture the motion of particles suspended in a transparent liquid at the center of the nozzle and above the fluid meniscus at a rate of half a million frames per second. Time-resolved velocity fields were obtained from a fluid layer approximately 200 μm thick within the nozzle for a complete jetting cycle. A Lagrangian finite-element numerical model with experimental measurements as inputs was used to predict the meniscus movement. The model predictions showed good agreement with the experimental results. This work provides the first experimental verification of physical models and numerical simulations of flows within a drop-on-demand nozzle. © 2012 Society for Imaging Science and Technology.

Stabilization of symmetric formations to motion around convex loops

We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms. © 2007 Elsevier B.V. All rights reserved.

Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected, and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant speed around fixed beacons. ©2006 IEEE.

Oscillator models and collective motion: Splay state stabilization of self-propelled particles

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles. © 2005 IEEE.

Static and dynamic errors in particle tracking microrheology.

Particle tracking techniques are often used to assess the local mechanical properties of cells and biological fluids. The extracted trajectories are exploited to compute the mean-squared displacement that characterizes the dynamics of the probe particles. Limited spatial resolution and statistical uncertainty are the limiting factors that alter the accuracy of the mean-squared displacement estimation. We precisely quantified the effect of localization errors in the determination of the mean-squared displacement by separating the sources of these errors into two separate contributions. A "static error" arises in the position measurements of immobilized particles. A "dynamic error" comes from the particle motion during the finite exposure time that is required for visualization. We calculated the propagation of these errors on the mean-squared displacement. We examined the impact of our error analysis on theoretical model fluids used in biorheology. These theoretical predictions were verified for purely viscous fluids using simulations and a multiple-particle tracking technique performed with video microscopy. We showed that the static contribution can be confidently corrected in dynamics studies by using static experiments performed at a similar noise-to-signal ratio. This groundwork allowed us to achieve higher resolution in the mean-squared displacement, and thus to increase the accuracy of microrheology studies.