There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Conventionally, engineers have employed rigid materials to fabricate precise, predictable robotic systems, which are easily modelled as rigid members connected at discrete joints. Natural systems, however, often match or exceed the performance of robotic systems with deformable bodies. Cephalopods, for example, achieve amazing feats of manipulation and locomotion without a skeleton; even vertebrates such as humans achieve dynamic gaits by storing elastic energy in their compliant bones and soft tissues. Inspired by nature, engineers have begun to explore the design and control of soft-bodied robots composed of compliant materials. This Review discusses recent developments in the emerging field of soft robotics.

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Design, fabrication and control of soft robots

This paper reviews the state-of-the art in vibration energy harvesting for wireless, self-powered microsystems. Vibration-powered generators are typically, although not exclusively, inertial spring and mass systems. The characteristic equations for inertial-based generators are presented, along with the specific damping equations that relate to the three main transduction mechanisms employed to extract energy from the system. These transduction mechanisms are: piezoelectric, electromagnetic and electrostatic. Piezoelectric generators employ active materials that generate a charge when mechanically stressed. A comprehensive review of existing piezoelectric generators is presented, including impact coupled, resonant and human-based devices. Electromagnetic generators employ electromagnetic induction arising from the relative motion between a magnetic flux gradient and a conductor. Electromagnetic generators presented in the literature are reviewed including large scale discrete devices and wafer-scale integrated versions. Electrostatic generators utilize the relative movement between electrically isolated charged capacitor plates to generate energy. The work done against the electrostatic force between the plates provides the harvested energy. Electrostatic-based generators are reviewed under the classifications of in-plane overlap varying, in-plane gap closing and out-of-plane gap closing; the Coulomb force parametric generator and electret-based generators are also covered. The coupling factor of each transduction mechanism is discussed and all the devices presented in the literature are summarized in tables classified by transduction type; conclusions are drawn as to the suitability of the various techniques.

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Energy harvesting vibration sources for microsystems applications

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

A nonlinear lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and, in particular, for microrobotic applications requiring accurate position and/or force control. In formulating this model, the authors propose a generalized Maxwell resistive capacitor as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data. Validation is followed by a discussion of model implications for purposes of actuator control.

/pdf/modeling-piezoelectric-stack-actuators-for-control-of-4l2tdqaq4j.pdf

Modeling piezoelectric stack actuators for control of micromanipulation

The paper describes the design and control of a transfemoral prosthesis with powered knee and ankle joints. The initial prototype is a pneumatically actuated powered-tethered device, which is intended to serve as a laboratory test bed for a subsequent self-powered version. The prosthesis design is described, including its kinematic optimization and the design of a three-axis socket load cell that measures the forces and moments of interaction between the socket and prosthesis. A gait controller is proposed based on the use of passive impedance functions that coordinates the motion of the prosthesis with the user during level walking. The control approach is implemented on the prosthesis prototype and experimental results are shown that demonstrate the promise of the active prosthesis and control approach in restoring fully powered level walking to the user.

/pdf/design-and-control-of-a-powered-transfemoral-prosthesis-hsu8pq35hd.pdf

Design and Control of a Powered Transfemoral Prosthesis

This paper describes a control architecture and intent recognition approach for the real-time supervisory control of a powered lower limb prosthesis. The approach infers user intent to stand, sit, or walk, by recognizing patterns in prosthesis sensor data in real time, without the need for instrumentation of the sound-side leg. Specifically, the intent recognizer utilizes time-based features extracted from frames of prosthesis signals, which are subsequently reduced to a lower dimensionality (for computational efficiency). These data are initially used to train intent models, which classify the patterns as standing, sitting, or walking. The trained models are subsequently used to infer the user's intent in real time. In addition to describing the generalized control approach, this paper describes the implementation of this approach on a single unilateral transfemoral amputee subject and demonstrates via experiments the effectiveness of the approach. In the real-time supervisory control experiments, the intent recognizer identified all 90 activity-mode transitions, switching the underlying middle-level controllers without any perceivable delay by the user. The intent recognizer also identified six activity-mode transitions, which were not intended by the user. Due to the intentional overlapping functionality of the middle-level controllers, the incorrect classifications neither caused problems in functionality, nor were perceived by the user.

/pdf/multiclass-real-time-intent-recognition-of-a-powered-lower-21s5mr8je7.pdf

Multiclass Real-Time Intent Recognition of a Powered Lower Limb Prosthesis

This paper describes a powered lower-limb orthosis that is intended to provide gait assistance to spinal cord injured (SCI) individuals by providing assistive torques at both hip and knee joints. The orthosis has a mass of 12 kg and is capable of providing maximum joint torques of 40 Nm with hip and knee joint ranges of motion from 105° flexion to 30 ° extension and 105 ° flexion to 10 ° hyperextension, respectively. A custom distributed embedded system controls the orthosis with power being provided by a lithium polymer battery which provides power for one hour of continuous walking. In order to demonstrate the ability of the orthosis to assist walking, the orthosis was experimentally implemented on a paraplegic subject with a T10 complete injury. Data collected during walking indicates a high degree of step-to-step repeatability of hip and knee trajectories (as enforced by the orthosis) and an average walking speed of 0.8 km/hr. The electrical power required at each hip and knee joint during gait was approximately 25 and 27 W, respectively, contributing to the 117 W overall electrical power required by the device during walking. A video of walking corresponding to the aforementioned data is included in the supplemental material.

/pdf/preliminary-evaluation-of-a-powered-lower-limb-orthosis-to-2b7novppus.pdf

Preliminary Evaluation of a Powered Lower Limb Orthosis to Aid Walking in Paraplegic Individuals

This paper presents a self-contained powered knee and ankle prosthesis, intended to enhance the mobility of transfemoral amputees. A finite-state based impedance control approach, previously developed by the authors, is used for the control of the prosthesis during walking and standing. Experiments on an amputee subject for level treadmill and overground walking are described. Knee and ankle joint angle, torque, and power data taken during walking experiments at various speeds demonstrate the ability of the prosthesis to provide a functional gait that is representative of normal gait biomechanics. Measurements from the battery during level overground walking indicate that the self-contained device can provide more than 4500 strides, or 9 km, of walking at a speed of 5.1 km/h between battery charges.

Michael Goldfarb

Papers

Modeling piezoelectric stack actuators for control of micromanipulation

Design and Control of a Powered Transfemoral Prosthesis

Multiclass Real-Time Intent Recognition of a Powered Lower Limb Prosthesis

Preliminary Evaluation of a Powered Lower Limb Orthosis to Aid Walking in Paraplegic Individuals

Preliminary Evaluations of a Self-Contained Anthropomorphic Transfemoral Prosthesis