Recent interest in high-speed scanning probe microscopy for high-throughput applications including video-rate atomic force microscopy and probe-based nanofabrication has sparked attention on the development of high-bandwidth flexure-guided nanopositioning systems (nanopositioners). Such nanopositioners are designed to move samples with sub-nanometer resolution with positioning bandwidth in the kilohertz range. State-of-the-art designs incorporate uniquely designed flexure mechanisms driven by compact and stiff piezoelectric actuators. This paper surveys key advances in mechanical design and control of dynamic effects and nonlinearities, in the context of high-speed nanopositioning. Future challenges and research topics are also discussed.

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Abstract-An XYZ nanopositioner is designed for fast the atomic force microscopy. The first resonant modes of the device are measured at 8.8, 8.9, and 48.4 kHz along the X-, Y-, and Z-axes, respectively, which are in close agreement to the finite-element simulations. The measured travel ranges of the lateral and vertical axes are 6.5 μm × 6.6 μm and 4.2 μm, respectively. Actuating the nanopositioner at frequencies beyond 1% of the first resonance of the lateral axes causes mechanical vibrations that result in degradation of the images generated. In order to improve the lateral scanning bandwidth, controllers are designed using the integral resonant control methodology to damp the resonant modes of the nanopositioner and to enable fast actuation. Due to the large bandwidth of the designed nanopositioner, a field programmable analog array is used for analog implementation of the controllers. Highresolution images are successfully generated at 200-Hz line rate with 200×200 pixel resolution in closed loop.Index Terms-Field-programmable analog array (FPAA), flexure-guided positioners, high-speed atomic force microscope (AFM), integral resonant control (IRC), nanopositioner, piezoelectric actuators.

Tracking of triangular or sawtooth waveforms is a major difficulty for achieving high-speed operation in many scanning applications such as scanning probe microscopy. Such non-smooth waveforms contain high order harmonics of the scan frequency that can excite mechanical resonant modes of the positioning system, limiting the scan range and bandwidth. Hence, fast raster scanning often leads to image distortion. This paper proposes analysis and design methodologies for a nonlinear and smooth closed curve, known as Lissajous pattern, which allows much faster operations compared to the ordinary scan patterns. A simple closed-form measure is formulated for the image resolution of the Lissajous pattern. This enables us to systematically determine the scan parameters. Using internal model controllers (IMC), this non-raster scan method is implemented on a commercial atomic force microscope driven by a low resonance frequency positioning stage. To reduce the tracking errors due to actuator nonlinearities, higher order harmonic oscillators are included in the IMC controllers. This results in significant improvement compared to the traditional IMC method. It is shown that the proposed IMC controller achieves much better tracking performances compared to integral controllers when the noise rejection performances is a concern.

Soft robotics has experienced an exponential growth in publications in the last two decades. [1] Unlike rigid conventional manipulators, [2,3] soft robots based on hydrogels, [4,5] electroactive polymers, [6,7] and elastomers [7-9] are physically resilient and can adapt to delicate objects and environments due to their conformal deformation. [10,11] They also show increased safety and dexterity can be lightweight and used within constrained environments with restricted access. [12,13] Many soft robots have a biologically inspired design coming from snakes, [14-17] worms, [18-20] fishes, [21-24] manta rays, [25,26] and tentacles. [27-29] The scope of applications includes minimally invasive surgery, [30,31] rehabilitation, [32,33] elderly assistance, [34] safe human-robot interaction, [35,36] and handling of fragile materials. [37,38] Important features of soft robotics design, fabrication, modeling, and control are covered in the soft robotics toolkit. [39,40] The building blocks of soft robots are the soft actuators. The most popular category of soft actuator is the soft fluidic actuator (SFA), where actuation is achieved using hydraulics or pneumatics. [8,41] These actuators are usually fabricated with silicone rubbers following a 3D molding process, [42] although directly 3D printing the soft actuators is also possible. [43,44] Silicone rubber is a highly flexible/extensible elastomer with high-temperature resistance, lowtemperature flexibility, and good biocompatibility. [45] Elastomers can withstand very large strains over 500% with no permanent deformation or fracture. [46] For relatively small strains, simple linear stress-strain relationships can be used, and two of the following parameters can be used to describe the elastic properties: bulk compressibility, shear modulus, tensile modulus (Young's modulus of elasticity), or Poisson's ratio. [45] For large deformations, nonlinear solid mechanic models using hyperelasticity should be considered. [8,32,47-50] Due to the strong nonlinearities in SFAs and their complex geometries, analytical modeling is challenging. [51] A brief review of the analytical methods for modeling of soft robotic structures is provided in the following. 1.1. Analytical Modeling of Soft Actuators The majority of soft/continuum robots with bending motion can be approximated as a series of mutually tangent constant curvature sections, i.e., piecewise constant curvature. [52] This is a result of the fact that the internal potential energy is uniformly distributed along each section for pressure-driven robots. [53] This approach has also been validated using Hamilton's principle by Gravagne et al. [54] As discussed by Webster and Jones, [52] the kinematics of continuum robots can be separated into robotspecific and robot-independent components in this approach. The robot specific mapping transforms the input pressures P or actuator space q to the configuration space κ, ϕ, l, and the robot-independent mapping goes from the configuration space to the task space x. The actuator space contai...