Brian Armstrong

Single state elastoplastic friction models

For control applications involving small displacements and velocities, friction modeling and compensation can be very important. In particular, the modeling of presliding displacement (motion prior to fully developed slip) can play a pivotal role. In this paper, it is shown that existing single-state friction models exhibit a nonphysical drift phenomenon which results from modeling presliding as a combination of elastic and plastic displacement. A new class of single state models is defined in which presliding is elastoplastic: under loading, frictional displacement is first purely elastic and then transitions to plastic. The new model class is demonstrated to substantially reduce drift while preserving the favorable properties of existing models (e.g., dissipativity) and to provide a comparable match to experimental data.

A New Compuatitional Model of Friction Applied to Haptic Rendering

A time-free, drift-free, multi-dimensional model of friction is introduced. A discrete implementation is developed which exhibits four solution regimes: sticking, creeping, oscillating, and sliding. Its computational solution is efficient to compute online and is robust to noise. It is applied to haptic rendering.

New results in NPID control: Tracking, integral control, friction compensation and experimental results

Nonlinear proportional-integral-derivative (NPID) control is implemented by varying the controller gains as a function of system state. NPID control has been previously described and implemented, and recently a constructive Lyapunov stability proof has been given. Here, NPID control analysis and design methods are extended to tracking, and to systems with state feedback and integral control. Experimental results are presented showing improved tracking accuracy and friction compensation by NPID control.

Elasto-plastic friction model: contact compliance and stiction

The presliding displacement and stiction properties of friction models are investigated. It is found that existing single-state-variable friction models possess either stiction or presliding displacement. Next, those models with continuous states are interpreted as examples of Prandlts elasto-plastic material model. A class of general one-state models is derived that is stable, dissipative and exhibits both stiction and presliding displacement.

PID control in the presence of static friction: a comparison of algebraic and describing function analysis

PID position control in the presence minimal Coulomb friction and non-zero static friction is shown to lead to a frictional limit cycle for all stabilizing combinations of P, I and D parameters. An idealized Coulomb + static friction model, dimensional analysis and the study of all possible solutions of the equations of motion are used to achieve rigorous and general results for this nonlinear problem. The algebraic prediction of stick-slip for this system is contrasted with predictions of the describing function. The predictions of the describing function are shown to be unreliable for this problem of friction and control.

Measurement and correction of microscopic head motion during magnetic resonance imaging of the brain.

Magnetic resonance imaging (MRI) is a widely used method for non-invasive study of the structure and function of the human brain. Increasing magnetic field strengths enable higher resolution imaging; however, long scan times and high motion sensitivity mean that image quality is often limited by the involuntary motion of the subject. Prospective motion correction is a technique that addresses this problem by tracking head motion and continuously updating the imaging pulse sequence, locking the imaging volume position and orientation relative to the moving brain. The accuracy and precision of current MR-compatible tracking systems and navigator methods allows the quantification and correction of large-scale motion, but not the correction of very small involuntary movements in six degrees of freedom. In this work, we present an MR-compatible tracking system comprising a single camera and a single 15 mm marker that provides tracking precision in the order of 10 m and 0.01 degrees. We show preliminary results, which indicate that when used for prospective motion correction, the system enables improvement in image quality at both 3 T and 7 T, even in experienced and cooperative subjects trained to remain motionless during imaging. We also report direct observation and quantification of the mechanical ballistocardiogram (BCG) during simultaneous MR imaging. This is particularly apparent in the head-feet direction, with a peak-to-peak displacement of 140 m.

Prospective motion correction for magnetic resonance spectroscopy using single camera retro‐grate reflector optical tracking

To introduce and evaluate a method of prospective motion correction for localized proton magnetic resonance spectroscopy (1H‐MRS) using a single‐camera optical tracking system.

Target tracking with a network of Doppler radars

By observing a Doppler signal at several points in space, it is possible to determine the position, velocity, and acceleration of a moving target. Parameter identification for a constant-acceleration motion model is studied, and the Cramer-Rao bound on motion parameter uncertainty is obtained for phaseand frequency-based estimation strategies, with the result that the preferred strategy depends upon the sensor/target geometry and target motion. Direct identification of the constant-acceleration trajectory model from the Doppler signal requires a 9-dimensional nonlinear optimization. Exploiting symmetry in the sensing geometry, a novel trajectory representation is presented which reduces the nonlinear optimization to one in 3 dimensions, with additional parameters obtained by linear identification. Baseball tracking using a network of four Doppler radars is experimentally demonstrated.

Nonlinear PID Control with Partial State Knowledge: Damping without Derivatives

Nonlinear PID (NPID) control is implemented by allowing the controller gains to vary as a function of system state. NPID control has been previously described and implemented, and recently a constructive Lyapunov stability proof has been given. The controllers arising with the constructive Lyapunov method will in general depend on knowledge of the full state vector. In the present work, NPID controllers that operate without knowledge of some state variables are demonstrated. A general but conservative design method is presented with an experimental demonstration. For a special case, complete necessary and sufficient conditions are established; for this case, simulation of a robotic force control application demonstrates well-damped control with no requirement for a force-rate signal. The extension to cases of partial state knowledge is important for NPID control, which is most practical when some state variables—particularly rate variables—are poorly known, confounding full-state feedback or other high-damping linear control designs. Extension of NPID control to MIMO systems and computed torque control is also shown.

Discrete-Time Elasto-Plastic Friction Estimation

For control applications involving small displacements and velocities, friction modeling and compensation can be very important, especially around velocity reversal. We previously described single-state friction models that are based on elasto-plastic presliding, something that reduces drift while preserving the favorable properties of existing models (e.g., dissipativity) and that provide a comparable match to experimental data. In this paper, for this class of models, discrete estimation for friction force compensation is derived. The estimator uses only position and velocity (not force) measurements and integrates over space rather than time, yielding a discrete-time implementation that is robust to issues of sample size and sensor noise, reliably renders static friction and is computationally efficient for real-time implementation. Boundedness with respect to all inputs, convergence during steady sliding and dissipativity are established for the discrete-time formulation.