18 research outputs found
Iterative Machine Learning for Precision Trajectory Tracking with Series Elastic Actuators
When robots operate in unknown environments small errors in postions can lead
to large variations in the contact forces, especially with typical
high-impedance designs. This can potentially damage the surroundings and/or the
robot. Series elastic actuators (SEAs) are a popular way to reduce the output
impedance of a robotic arm to improve control authority over the force exerted
on the environment. However this increased control over forces with lower
impedance comes at the cost of lower positioning precision and bandwidth. This
article examines the use of an iteratively-learned feedforward command to
improve position tracking when using SEAs. Over each iteration, the output
responses of the system to the quantized inputs are used to estimate a
linearized local system models. These estimated models are obtained using a
complex-valued Gaussian Process Regression (cGPR) technique and then, used to
generate a new feedforward input command based on the previous iteration's
error. This article illustrates this iterative machine learning (IML) technique
for a two degree of freedom (2-DOF) robotic arm, and demonstrates successful
convergence of the IML approach to reduce the tracking error.Comment: 9 pages, 16 figure. Submitted to AMC Worksho
Digital control of force microscope cantilevers using a field programmable gate array
This report describes a cantilever controller for magnetic resonance force
microscopy (MRFM) based on a field programmable gate array (FPGA), along with
the hardware and software used to integrate the controller into an experiment.
The controller is assembled from a low-cost commercially available software
defined radio (SDR) device and libraries of open-source software. The
controller includes a digital filter comprising two cascaded second-order
sections ("biquads"), which together can implement transfer functions for
optimal cantilever controllers. An appendix in this report shows how to
calculate filter coefficients for an optimal controller from measured
cantilever characteristics. The controller also includes an input multiplexer
and adder used in calibration protocols. Filter coefficients and multiplexer
settings can be set and adjusted by control software while an experiment is
running. The input is sampled at 64 MHz; the sampling frequency in the filters
can be divided down under software control to achieve a good match with filter
characterisics. Data reported here were sampled at 500 kHz, chosen for acoustic
cantilevers with resonant frequencies near 8 kHz. Inputs are digitized with 12
bits resolution, outputs with 14 bits. The experiment software is organized as
a client and server to make it easy to adapt the controller to different
experiments. The server encapusulates the details of controller hardware
organization, connection technology, filter architecture, and number
representation. The same server could be used in any experiment, while a
different client encodes the particulars of each experiment.Comment: submitted to Review of Scientific Instrument
Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems
This article presents numerical recipes for simulating high-temperature and
non-equilibrium quantum spin systems that are continuously measured and
controlled. The notion of a spin system is broadly conceived, in order to
encompass macroscopic test masses as the limiting case of large-j spins. The
simulation technique has three stages: first the deliberate introduction of
noise into the simulation, then the conversion of that noise into an equivalent
continuous measurement and control process, and finally, projection of the
trajectory onto a state-space manifold having reduced dimensionality and
possessing a Kahler potential of multi-linear form. The resulting simulation
formalism is used to construct a positive P-representation for the thermal
density matrix. Single-spin detection by magnetic resonance force microscopy
(MRFM) is simulated, and the data statistics are shown to be those of a random
telegraph signal with additive white noise. Larger-scale spin-dust models are
simulated, having no spatial symmetry and no spatial ordering; the
high-fidelity projection of numerically computed quantum trajectories onto
low-dimensionality Kahler state-space manifolds is demonstrated. The
reconstruction of quantum trajectories from sparse random projections is
demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity
limit is observed, a deterministic construction for sampling matrices is given,
and methods for quantum state optimization by Dantzig selection are given.Comment: 104 pages, 13 figures, 2 table