Garrett M. Clayton

A Review of Feedforward Control Approaches in Nanopositioning for High-Speed SPM

Control can enable high-bandwidth nanopositioning needed to increase the operating speed of scanning probe microscopes (SPMs). High-speed SPMs can substantially impact the throughput of a wide range of emerging nanosciences and nanotechnologies. In particular, inversion-based control can find the feedforward input needed to account for the positioning dynamics and, thus, achieve the required precision and bandwidth. This article reviews inversion-based feedforward approaches used for high-speed SPMs such as optimal inversion that accounts for model uncertainty and inversion-based iterative control for repetitive applications. The article establishes connections to other existing methods such as zero-phase-error-tracking feedforward and robust feedforward. Additionally the article reviews the use of feedforward in emerging applications such as SPM-based nanoscale combinatorial-science studies, image-based control for subnanometer-scale studies, and imaging of large soft biosamples with SPMs.

Integrating the Microsoft Kinect With Simulink: Real-Time Object Tracking Example

The introduction of low-cost, relatively high-resolution 3-D sensing systems, like the Microsoft Kinect, has considerable potential in autonomous system applications. One of the impediments to wider Kinect application development is that the available Kinect drivers define C language interfaces. To help fully realize the Kinects potential, the aims of this paper are 1) to develop a “VU-Kinect ” block which provides easy access to the sensors camera and depth image streams, and which enables them to be incorporated seamlessly within a higher level, Simulink-based, image-processing and real-time control strategy; 2) to address implementation issues associated with the Kinect, such as sensor calibration; and 3) to show the utility of both the VU-Kinect block and the Kinect itself through a simple 3-D object tracking example.

Finite-time tracking using sliding mode control

Abstract Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. In this paper, we consider a general class of fully actuated mechanical systems described by Euler–Lagrange dynamics and the class of underactuated systems represented by mobile robot dynamics that are required to reach and maintain the desired trajectory in finite time. An approach known as the terminal sliding mode control (TSMC) involves non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time thus ensuring finite-time tracking. The main advantage of this control scheme is in fast converging times without excessive control effort. Such controllers are known to have singularities in some parts of the state space and, in this paper, we propose a method of partitioning the state space into two regions where the TSMC is bounded and its complement. We show that the region of bounded TSMC is invariant and design an auxiliary sliding mode controller predicated on linear smooth sliding surface for the initial conditions outside this region. Furthermore, we extend these results to address TSMC for underactuated systems characterized by the mobile robot dynamics. We demonstrate the efficacy of our approach by implementing it for a scenario when multiple dynamic agents are required to move in a fixed formation with respect to the formation leader. Finally, we validate our results experimentally using a wheeled mobile robot platform.

Error Analysis for Visual Odometry on Indoor, Wheeled Mobile Robots With 3-D Sensors

The objective of this paper is to improve the visual odometry performance through the analysis of the sensor noise and the propagation of an error through the entire visual odometry system. The visual odometry algorithm is implemented on an indoor, wheeled mobile robot (WMR) constrained to planar motion, and uses an integrated color-depth (RGB-D) camera, and a one-point (1-pt), 3 degree-of-freedom inverse kinematic solution, enabling a closed-form bound on the propagated error. There are three main contributions of this paper. First, feature location errors for the RGB-D camera are quantified. Second, these feature location errors are propagated through the entire visual odometry algorithm. Third, the visual odometry performance is improved by using the predicted error to weight individual 1-pt solutions. The error bounds and the improved visual odometry scheme are experimentally verified on a WMR. Using the error-weighting scheme, the proposed visual odometry algorithm achieves the performance of approximately 1.5% error, without the use of iterative, outlier-rejection tools.

Iterative image-based modeling and control for higher scanning probe microscope performance

In this article, we develop an image-based approach to model and control the dynamics of scanning probe microscopes (SPMs) during high-speed operations. SPMs are key enabling tools in the experimental investigation and manipulation of nano- and subnanoscale phenomena; however, the speed at which the SPM probe can be positioned over the sample surface is limited due to adverse dynamic effects. It is noted that SPM speed can be increased using model-based control techniques. Modeling the SPM dynamics is, however, challenging because currently available sensing methods do not measure the SPM tip directly. Additionally, the resolution of currently available sensing methods is limited by noise at higher bandwidth. Our main contribution is an iterative image-based modeling method which overcomes these modeling difficulties (caused by sensing limitations). The method is applied to model an experimental scanning tunneling microscope (STM) system and to achieve high-speed imaging. Specifically, we model the STM up to a frequency of 2000 Hz (corresponds to approximately 23 of the resonance frequency of our system) and achieve approximately 1.2% error in 1 nm square images at that same frequency.

Conditions for Image-Based Identification of SPM-Nanopositioner Dynamics

Rather than using external sensors, images of standard calibration samples can be used to model and correct positioning errors caused by dynamics effects in scanning probe microscopes (SPMs). The main contribution of this study is the development of conditions, on the calibration sample and the scan trajectory, that allow for the image based identification of SPM nanopositioner dynamics. The choice of and tradeoff between calibration sample and scan trajectory properties are discussed in the context of a scanning tunneling microscope (STM) example.

HYSTERESIS AND VIBRATION COMPENSATION IN PIEZOELECTRIC ACTUATORS BY INTEGRATING CHARGE CONTROL AND INVERSE FEEDFORWARD1

Abstract In this paper we address the problems of hysteresis and vibrations that limit the accuracy of piezoelectric positioners. It is widely known that the use of charge control significantly reduces hysteresis, thus enabling high-accuracy positioning during low speed operations. However, charge control is unable to reduce vibrations that limit the positioning bandwidth. Our main contribution is to overcome this bandwidth limitation by augmenting charge control with inverse feedforward to compensate for vibrations, resulting in a high-bandwidth, high-accuracy positioning system. We apply this integrated method to a piezoelectric tube actuator and experimental results are presented to illustrate the positioning improvements with the proposed integrated approach.

Range-based control of dual-stage nanopositioning systems.

A novel dual-stage nanopositioner control framework is presented that considers range constraints. Dual-stage nanopositioners are becoming increasingly popular in applications such as scanning probe microscopy due to their unique ability to achieve long-range and high-speed operation. The proposed control approach addresses the issue that some precision positioning trajectories are not achievable through existing control schemes. Specifically, short-range, low-speed inputs are typically diverted to the long-range actuator, which coincidentally has lower positioning resolution. This approach then limits the dual-stage nanopositioners ability to achieve the required positioning resolution that is needed in applications where range and frequency are not inversely correlated (which is a typical, but not always the correct assumption for dual stage systems). The proposed range-based control approach is proposed to overcome the limitations of existing control methods. Experimental results show that the proposed control strategy is effective.

Sliding mode coordination control for multiagent systems with underactuated agent dynamics

In this paper, we develop a new integrated coordinated control and obstacle avoidance approach for a general class of underactuated agents. We use graph-theoretic notions to characterise communication topology in the network of underactuated agents as determined by the information flow directions and captured by the graph Laplacian matrix. Obstacle avoidance is achieved by surrounding the stationary as well as moving obstacles by elliptical or other convex shapes that serve as stable periodic solutions to planar systems of ordinary differential equations and using transient trajectories of those systems to navigate the agents around the obstacles. Decentralised controllers for individual agents are designed using sliding mode control approach and are only based on data communicated from the neighbouring agents. We demonstrate the efficacy of our theoretical approach using an example of a system of wheeled mobile robots that reach and maintain a desired formation. Finally, we validate our results experimentally.

Trajectory Tracking Control of Planar Underactuated Vehicles

This work presents a novel nonlinear trajectory tracking control framework for general planar models of underactuated vehicles with six states and two control inputs. In this framework, feasible state trajectories are derived through utilization of nonholonomic constraints and a transitional trajectory is introduced that reduces the sixth order system into a fourth order error dynamic stabilization problem. A nonlinear sliding mode control law is employed to stabilize the error dynamics. It is shown that the control law is uniformly asymptotically stable if unknown disturbances and modeling uncertainties are bounded. The framework is applied to differential drive mobile robots, air vehicles operating in the vertical plane, and marine vehicles. Simulations are presented for models of in-house mobile robots and surface vessels subject to unknown disturbances.