John H. Crews

Design optimization of a shape memory alloy–actuated robotic catheter

In this article, we present a method for optimizing the design of a shape memory alloy–actuated robotic catheter. Highly maneuverable robotic catheters have the potential to revolutionize the treatment of cardiac diseases such as atrial fibrillation. To operate effectively, the catheter must navigate within the confined spaces of the heart, motivating the need for a tight bending radius. The design process is complicated by the shape memory alloy’s hysteretic relationships between strain, stress, and temperature. This article addresses the modeling and optimization of both a single-tendon and antagonistic tendon robotic catheter using COMSOL Multiphysics Modeling and Simulation software. Several design variables that affect the actuator behavior are considered; these include the shape memory alloy tendon radius and its prestrain, the shape memory alloy tendon offset from the neutral axis of the flexible beam, the flexible beam radius and elastic modulus, and the thermal boundary condition between the shape memory alloy tendon and the beam. A genetic algorithm is used to optimize the radius of curvature of the two catheter designs. Both a single-crystal and polycrystalline models are implemented in COMSOL and are experimentally validated.

INDIRECT INTELLIGENT SLIDING MODE CONTROL OF A SHAPE MEMORY ALLOY ACTUATED FLEXIBLE BEAM USING HYSTERETIC RECURRENT NEURAL NETWORKS.

This paper introduces an indirect intelligent sliding mode controller (IISMC) for shape memory alloy (SMA) actuators, specifically a flexible beam deflected by a single offset SMA tendon. The controller manipulates applied voltage, which alters SMA tendon temperature to track reference bending angles. A hysteretic recurrent neural network (HRNN) captures the nonlinear, hysteretic relationship between SMA temperature and bending angle. The variable structure control strategy provides robustness to model uncertainties and parameter variations, while effectively compensating for system nonlinearities, achieving superior tracking compared to an optimized PI controller.

Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys

The homogenized energy model is a unified framework for modeling hysteresis in ferroelectric, ferromagnetic, and ferroelastic materials. The homogenized energy model framework combines energy analysis at the lattice level with stochastic homogenization techniques, based on the assumption that quantities such as interaction and coercive fields are manifestations of underlying densities, to construct macroscopic material models. In this article, we focus on the homogenized energy model for shape memory alloys. Specifically, we develop techniques for estimating model parameters based on attributes of measured data. Both the local (mesoscopic) and macroscopic models are described, and the model parameters’ relationship to the material’s response is discussed. Using these relationships, techniques for estimating model parameters are presented. The techniques are applied to constant-temperature stress–strain and resistance–strain data. These estimates are used in two manners. In one method, the estimates are considered fixed and only the homogenized energy model density functions are optimized. For SMA, the HEM incorporates densities for the interaction and relative stress (the width of the hysteresis loop). In the second method, the estimates are included in the optimization algorithm. Both cases are compared to experimental data at various temperatures, and the optimized model parameters are compared to the initial estimates.

Inversion algorithms for the homogenized energy model for hysteresis in ferroelectric and shape memory alloy compounds

Ferroelectric and ferromagnetic materials have the advantage of broadband and dual actuator and sensor capabilities. Ferroelastic compounds such as shape memory alloys have large energy densities and are biocompatible. However, to take full advantage of these properties, it is necessary to employ models and control designs that account for the rate-dependent hysteresis, creep, and constitutive nonlinearities inherent to the materials. Inverse compensation is one technique that achieves this purpose. We present an inversion algorithm based on a binary search of a discretized input grid and apply this to the homogenized energy model for modeling hysteresis. The inversion algorithm is shown to provide a reasonable balance between accuracy and computational speed. Numerical examples are presented for three specific cases of the homogenized energy model.

Quantification of parameter and model uncertainty for shape memory alloy bending actuators

In this article, we employ a Bayesian framework to estimate parameter and model uncertainty for shape memory alloy bending actuators. The Bayesian framework provides parameter densities, instead of ordinary least-squares optimal point estimates. Bayes’ rule relates a posterior parameter density to a prior density and likelihood. However, the posterior density is difficult to calculate directly for high-dimensional parameter spaces. Markov chain Monte Carlo methods overcome this difficulty indirectly by creating a Markov chain whose stationary density is the posterior. In this article, we utilize the Delayed Rejection Adaptive Metropolis algorithm for estimating parameter uncertainty. The shape memory alloy bending actuator is modeled using the homogenized energy framework, a computationally efficient and accurate model for various transductive materials. The model is summarized, and techniques for estimating the heat transfer parameters are presented. An algorithmic approach to quantifying uncertainty is useful for numerous reasons. The anticipated use is to quantify uncertainty for robust control algorithms. Robust control is an area of considerable research for smart materials such as shape memory alloy; however, the source of uncertainty is rarely quantified. The methods employed here would greatly aid in the design of robust controllers.

Quantification of parameter uncertainty for robust control of shape memory alloy bending actuators

In this paper, we employ Bayesian parameter estimation techniques to derive gains for robust control of smart materials. Specifically, we demonstrate the feasibility of utilizing parameter uncertainty estimation provided by Markov chain Monte Carlo (MCMC) methods to determine controller gains for a shape memory alloy bending actuator. We treat the parameters in the equations governing the actuators temperature dynamics as uncertain and use the MCMC method to construct the probability densities for these parameters. The densities are then used to derive parameter bounds for robust control algorithms. For illustrative purposes, we construct a sliding mode controller based on the homogenized energy model and experimentally compare its performance to a proportional-integral controller. While sliding mode control is used here, the techniques described in this paper provide a useful starting point for many robust control algorithms.

Stress, strain, and resistance behavior of two opposing shape memory alloy actuator wires for resistance-based self-sensing applications

Shape memory alloy actuator wires undergo a significant (∼4%) contraction and a corresponding change in resistance because of a temperature- and load-induced phase transformation. When a restoring force such as a pre-stretched bias spring is placed in series with a shape memory alloy wire, the system becomes an actuator that can generate a repeatable force. Simultaneously, the resistance of the wire can be correlated to strain and enable self-sensing, eliminating the need for external feedback sensors. The self-sensing task, however, is complicated in applications requiring multiple coupled wires, for example, advanced two-dimensional or three-dimensional positioning. The presence of coupled (passive or active) actuator wires with nonlinear, hysteretic force–displacement characteristics has a strong impact on an individual wire’s resistance behavior that has not been systematically studied to date. This article expands upon previous work that studied a single-shape memory alloy–spring system by adding a second opposing shape memory alloy wire and focusing on the resistance to strain mapping that is crucial for self-sensing applications. Systematic stress–strain and resistance–strain experiments are presented alongside physics-based modeling results that help to identify several sources of hysteresis in the resistance–strain behavior and facilitate intelligent calibration schemes for multifunctional self-sensing and actuation applications.

Development of Robust Control Algorithms for Shape Memory Alloy Bending Actuators

In this paper, we present a systematic approach to developing robust control algorithms for a single-tendon shape memory alloy (SMA) bending actuator. Parameter estimation and uncertainty quantification are accomplished using Bayesian techniques. Specifically, we utilize Markov Chain Monte Carlo (MCMC) methods to estimate parameter uncertainty. The Bayesian parameter estimation results are used to construct a sliding mode control (SMC) algorithm where the bounds on uncertainty are used to guarantee controller robustness. The sliding mode controller utilizes the homogenized energy model (HEM) for SMA. The inverse HEM compensates for hysteresis and converts a reference bending angle to a reference temperature. Temperature in the SMA actuator is estimated using an observer, and the sliding mode controller ensures that the observer temperature tracks the reference temperature. The SMC is augmented with proportional-integral (PI) control on the bending angle error.© 2012 ASME

Design and Control of a Shape Memory Alloy Actuated Robotic Catheter

This paper details the development of a Neural Network (NN) controller for a Shape Memory Alloy (SMA) actuated catheter, with potential application to tele-operated cardiac ablation procedures. The robotic catheter prototype consists of a central tubular structure actuated by four SMA tendons. A dual-camera imaging system provides position feedback of the catheter tip. Open loop bending responses are obtained and associated nonlinearities are identified. A NN controller is designed using time-shifted input-output maps generated from randomized open loop measurements. The tracking performance of this NN controller is compared with PI/PID controllers for various reference trajectories.Copyright

Modeling and Bayesian parameter estimation for shape memory alloy bending actuators

In this paper, we employ a homogenized energy model (HEM) for shape memory alloy (SMA) bending actuators. Additionally, we utilize a Bayesian method for quantifying parameter uncertainty. The system consists of a SMA wire attached to a flexible beam. As the actuator is heated, the beam bends, providing endoscopic motion. The model parameters are fit to experimental data using an ordinary least-squares approach. The uncertainty in the fit model parameters is then quantified using Markov Chain Monte Carlo (MCMC) methods. The MCMC algorithm provides bounds on the parameters, which will ultimately be used in robust control algorithms. One purpose of the paper is to test the feasibility of the Random Walk Metropolis algorithm, the MCMC method used here.