Sean B. Andersson

A Tutorial on the Mechanisms, Dynamics, and Control of Atomic Force Microscopes

The atomic force microscope (AFM) is one of the most versatile tools in nanotechnology. For control engineers this instrument is particularly interesting, since its ability to image the surface of a sample is entirely dependent upon the use of a feedback loop. This paper will present a tutorial on the control of AFMs. We take the reader on a walk around the control loop and discuss each of the individual technology components. The major imaging modes are described from a controls perspective and recent advances geared at increasing the performance of these microscopes are highlighted.

Temporal Logic Motion Planning and Control With Probabilistic Satisfaction Guarantees

We describe a computational framework for automatic deployment of a robot with sensor and actuator noise from a temporal logic specification over a set of properties that are satisfied by the regions of a partitioned environment. We model the motion of the robot in the environment as a Markov decision process (MDP) and translate the motion specification to a formula of probabilistic computation tree logic (PCTL). As a result, the robot control problem is mapped to that of generating an MDP control policy from a PCTL formula. We present algorithms for the synthesis of such policies for different classes of PCTL formulas. We illustrate our method with simulation and experimental results.

Motion planning and control from temporal logic specifications with probabilistic satisfaction guarantees

We present a computational framework for automatic deployment of a robot from a temporal logic specification over a set of properties of interest satisfied at the regions of a partitioned environment. We assume that, during the motion of the robot in the environment, the current region can be precisely determined, while due to sensor and actuation noise, the outcome of a control action can only be predicted probabilistically. Under these assumptions, the deployment problem translates to generating a control strategy for a Markov Decision Process (MDP) from a temporal logic formula.We propose an algorithm inspired from probabilistic Computation Tree Logic (PCTL) model checking to find a control strategy that maximizes the probability of satisfying the specification. We illustrate our method with simulation and experimental results.

Localization of a fluorescent source without numerical fitting

We present an algebraic solution to the problem of localizing a single fluorescent particle with sub-diffraction-limit accuracy. The algorithm is derived and its performance studied experimentally. Isolated 20 nm fluorescent beads were imaged using a wide-field microscope at two different positions separated by 100 nm and at a range of signal-to-noise ratios (SNR). The data were analyzed using both the new algorithm and the standard approach of fitting the data to a Gaussian profile. Results indicate that the proposed approach is nearly as accurate as Gaussian fitting across a wide range of SNR while executing over 200 times faster. In addition, the new algorithm is able to localize at lower SNR than the fitting method.

Curve Tracking for Rapid Imaging in AFM

A high-level feedback control approach for rapid imaging in atomic force microscopy is presented. The algorithms are designed for samples which are string-like, such as biopolymers, and for boundaries. Rather than the simple raster-scan pattern, data from the microscope are used in real-time to steer the tip along the sample, drastically reducing the area to be imaged. An order-of-magnitude reduction in the time to acquire an image is possible. The technique is illustrated through simulations and through physical experiments.

Robot phonotaxis with dynamic sound-source localization

We address two key goals pertaining to autonomous mobile robots: one, to develop fast accurate sensory capabilities - at present, the localization of sound sources - and second, the integration of such sensory modules with other robot functions, especially its motor control and navigation. A primary motivation for this work was to devise effective means to guide robotic navigation in environments with acoustic sources. We designed and built a biomimetic sound-source localization apparatus. In contrast to the popular use of time-of-arrival differences in free field microphone arrays, our system is based on the principles observed in nature, where directional acoustic sensing evolved to rely on diffraction about the head with only two ears. In this paper we present an integrated robot phonotaxis system which utilizes the robots movement to resolve frontback localization ambiguity. Our system achieves high angular localization acuity (/spl plusmn/ 2/spl deg/) and it was successfully tested in localizing a single broadband source and moving towards it within a cluttered laboratory environment.

Local raster scanning for high-speed imaging of biopolymers in atomic force microscopy

A novel algorithm is described and illustrated for high speed imaging of biopolymers and other stringlike samples using atomic force microscopy. The method uses the measurements in real-time to steer the tip of the instrument to localize the scanning area over the sample of interest. Depending on the sample, the scan time can be reduced by an order of magnitude or more while maintaining image resolution. Images are generated by interpolating the non-raster data using a modified Kriging algorithm. The method is demonstrated using physical simulations that include actuator and cantilever dynamics, nonlinear tip-sample interactions, and measurement noise as well as through scanning experiments in which a two-axis nanopositioning stage is steered by the algorithm using simulated height data.

Non-raster sampling in atomic force microscopy: A compressed sensing approach

Atomic force microscopy is a powerful tool that has had a tremendous impact in understanding systems with nanometer-scale features. In this work we explore the use of compressed sensing as a means of sampling data and generating an image. Under this approach only a small number of the pixels in an image, typically as few as 10%, need to be sampled to generate an accurate image. We show that when combined with time-optimal control to move the tip of the microscope between measurement locations, the imaging time is comparable to high-speed AFM systems while also greatly reducing the interactions with and force applied to the sample. In addition, the approach can significantly reduce the imaging time in applications such as force mapping in which the tip is moved point-by-point through a sequence of measurement locations rather than continuously scanned as in standard imaging.

A probabilistic approach for control of a stochastic system from LTL specifications

We consider the problem of controlling a continuous-time linear stochastic system from a specification given as a Linear Temporal Logic (LTL) formula over a set of linear predicates in the state of the system. We propose a three-step solution. First, we define a polyhedral partition of the state space and a finite collection of controllers, represented as symbols, and construct a Markov Decision Process (MDP). Second, by using an algorithm resembling LTL model checking, we determine a run satisfying the formula in the corresponding Kripke structure. Third, we determine a sequence of control actions in the MDP that maximizes the probability of following the satisfying run. We present illustrative simulation results.

Fluorochrome-Functionalized Nanoparticles for Imaging DNA in Biological Systems

Attaching DNA binding fluorochromes to nanoparticles (NPs) provides a way of obtaining NPs that bind to DNA through fluorochrome mediated interactions. To obtain a nanoparticle (NP) that bound to the DNA in biological systems, we attached the DNA binding fluorochrome, TO-PRO 1 (TO), to the surface of the Feraheme (FH) NP, to obtain a fluorochrome-functionalized NP denoted TO-FH. When reacted with DNA in vitro, TO-FH formed microaggregates that were characterized by fluorescence, light scattering, and T2 changes. The formation of DNA/TO-FH microaggregates was also characterized by AFM, with microaggregates exhibiting a median size of 200 nm, and consisting of DNA and multiple TO-FH NPs whose individual diameters were only 25-35 nm. TO-FH failed to bind normal cells in culture, but treatment with chemotherapeutic agents or detergents yielded necrotic cells that bound TO-FH and vital fluorochromes similarly. The uptake of TO-FH by HT-29 xenografts (treated with 5-FU and oxaliplatin) was evident by surface fluorescence and MRI. Attaching multiple DNA binding fluorochromes to magnetic nanoparticles provides a way of generating DNA binding NPs that can be used to detect DNA detection by microaggregate formation in vitro, for imaging the DNA of necrotic cells in culture, and for imaging the DNA of a tumor treated with a chemotherapeutic agent. Fluorochrome functionalized NPs are a multimodal (magnetic and fluorescent), highly multivalent (n ≈ 10 fluorochromes/NP) nanomaterials useful for imaging the DNA of biological systems.