Enhancing vibration control in cable-tip-mass systems using asymmetric peak detector boundary control

In this study, a boundary controller based on a peak detector system has been designed to reduce vibrations in the cable–tip–mass system. The control procedure is built upon a recent modification of the controller, incorporating a non-symmetric peak detector mechanism to enhance the robustness of the control design. The crucial element lies in the identification of peaks within the boundary input signal, which are then utilized to formulate the control law. Its mathematical representation relies on just two tunable parameters. Numerical experiments have been conducted to assess the performance of this novel approach, demonstrating superior efficacy compared to the boundary damper control, which has been included for comparative purposes"This work has been funded by the Generalitat de Catalunya through the research projects 2021-SGR-01044."Peer ReviewedPostprint (published version

A computational geometric approach for an ensemble-based topological entropy calculation in two and three dimensions

From the stirring of dye in viscous fluids to the availability of essential nutrients spreading over the surface of a pond, nature is rife with examples of mixing in two-dimensional fluids. The long-time exponential growth rate of a thin filament of dye stretched by the fluid is a well-known proxy for the quality of mixing in two dimensions. This growth rate in turn gives a lower bound on the flow's topological entropy, a measure quantifying the complexity of chaotic dynamics. In the real-world study of mixing, topological entropy may be hard to compute; the velocity field may not be known or may be expensive to recover or approximate, thus limiting our knowledge of the governing system and underlying mechanics driving the mixing. Central to this study are two questions: \emph{How can stretching rates in two-dimensional planar flows best be computed using only trajectory data?}, and \emph{Can a method for computing stretching rates in higher dimensions from only trajectory data be developed?}. In this spirit, we introduce the Ensemble-based Topological Entropy Calculation (E-tec), a method to derive a lower-bound on topological entropy that requires only finite number of system trajectories, like those obtained from ocean drifters, and no detailed knowledge of the velocity field. E-tec is demonstrated to be computationally more efficient than other competing methods in two dimensions that accommodate trajectory data. This is accomplished by considering the evolution of a ``rubber band" wrapped around the data points and evolving with their trajectories. E-tec records the growth of this band as the collective motion of trajectories strike, deform, and stretch it. This exponential growth rate acts as a lower bound on the topological entropy. In this manuscript, I demonstrate convergence of E-tec's approximation with respect to both the number of trajectories (ensemble size) and the duration of trajectories in time. Driving the efficiency of E-tec in two dimensions is the use of computational geometry tools. Not only this, by computing stretching rates in this new computational geometry framework, I extend E-tec to three dimensions using two methods. First, I consider a two-dimensional rubber sheet stretched around a collection of points in a three-dimensional flow. Similar to the band-stretching component of two-dimensional E-tec, a three-dimensional triangulation is used to record the growth of the sheet as it is stretched and deformed by points evolving in time. Second, I calculate the growth rates of one-dimensional rubber strings as they are stretched by the edges of this dynamic, moving triangulation

Modeling and Direct Adaptive Robust Control of Flexible Cable-Actuated Systems

Cable-actuated systems provide an effective method for precise motion transmission over various distances in many robotic systems. In general, the use of cables has many potential advantages such as high-speed manipulation, larger payloads, larger range of motion, access to remote locations and applications in hazardous environments. However, cable flexibility inevitably causes vibrations and poses a concern in high-bandwidth, high-precision applications

An Adaptive Tracking Algorithm for Robotics and Computer Vision Application

We provided a vision-controlled robotics manipulation system with a robust, accurate algorithm to predict the translational motion of a 3-D object; hence, making it possible to continuously point the video camera at the moving object. The real time video images are fed to a PVM-1 (a pyramid-based image processor) for image processing and moving object detection. The measured object coordinates are continuously fed to our algorithm for track smoothing and prediction. In this study, we examined several tracking algorithms and adopted an optimal α - β filter for tracking purposes and the α - β -γ filter as part of the initialization procedure. The optimum gains for these 6lkm are based on the Tracking Index principle which in its turn is based on the measurement noise variance and the object dynamics. We derived an expression for the noise variance corresponding to our application. As for the object dynamics, we developed an adaptive method (using the α - β -γ filter mentioned above) for inferring object dynamics in an iterative learning process that results in an accurate estimate of the Tracking Index. The accuracy of our algorithm realizes that of the Kalman filter but is much simpler computationally

Key body pose detection and movement assessment of fitness performances

Motion segmentation plays an important role in human motion analysis. Understanding the intrinsic features of human activities represents a challenge for modern science. Current solutions usually involve computationally demanding processing and achieve the best results using expensive, intrusive motion capture devices. In this thesis, research has been carried out to develop a series of methods for affordable and effective human motion assessment in the context of stand-up physical exercises. The objective of the research was to tackle the needs for an autonomous system that could be deployed in nursing homes or elderly people's houses, as well as rehabilitation of high profile sport performers. Firstly, it has to be designed so that instructions on physical exercises, especially in the case of elderly people, can be delivered in an understandable way. Secondly, it has to deal with the problem that some individuals may find it difficult to keep up with the programme due to physical impediments. They may also be discouraged because the activities are not stimulating or the instructions are hard to follow. In this thesis, a series of methods for automatic assessment production, as a combination of worded feedback and motion visualisation, is presented. The methods comprise two major steps. First, a series of key body poses are identified upon a model built by a multi-class classifier from a set of frame-wise features extracted from the motion data. Second, motion alignment (or synchronisation) with a reference performance (the tutor) is established in order to produce a second assessment model. Numerical assessment, first, and textual feedback, after, are delivered to the user along with a 3D skeletal animation to enrich the assessment experience. This animation is produced after the demonstration of the expert is transformed to the current level of performance of the user, in order to help encourage them to engage with the programme. The key body pose identification stage follows a two-step approach: first, the principal components of the input motion data are calculated in order to reduce the dimensionality of the input. Then, candidates of key body poses are inferred using multi-class, supervised machine learning techniques from a set of training samples. Finally, cluster analysis is used to refine the result. Key body pose identification is guaranteed to be invariant to the repetitiveness and symmetry of the performance. Results show the effectiveness of the proposed approach by comparing it against Dynamic Time Warping and Hierarchical Aligned Cluster Analysis. The synchronisation sub-system takes advantage of the cyclic nature of the stretches that are part of the stand-up exercises subject to study in order to remove out-of-sequence identified key body poses (i.e., false positives). Two approaches are considered for performing cycle analysis: a sequential, trivial algorithm and a proposed Genetic Algorithm, with and without prior knowledge on cyclic sequence patterns. These two approaches are compared and the Genetic Algorithm with prior knowledge shows a lower rate of false positives, but also a higher false negative rate. The GAs are also evaluated with randomly generated periodic string sequences. The automatic assessment follows a similar approach to that of key body pose identification. A multi-class, multi-target machine learning classifier is trained with features extracted from previous motion alignment. The inferred numerical assessment levels (one per identified key body pose and involved body joint) are translated into human-understandable language via a highly-customisable, context-free grammar. Finally, visual feedback is produced in the form of a synchronised skeletal animation of both the user's performance and the tutor's. If the user's performance is well below a standard then an affine offset transformation of the skeletal motion data series to an in-between performance is performed, in order to prevent dis-encouragement from the user and still provide a reference for improvement. At the end of this thesis, a study of the limitations of the methods in real circumstances is explored. Issues like the gimbal lock in the angular motion data, lack of accuracy of the motion capture system and the escalation of the training set are discussed. Finally, some conclusions are drawn and future work is discussed

Behavior finding: Morphogenetic Designs Shaped by Function

Evolution has shaped an incredible diversity of multicellular living organisms, whose complex forms are self-made through a robust developmental process. This fundamental combination of biological evolution and development has served as an inspiration for novel engineering design methodologies, with the goal to overcome the scalability problems suffered by classical top-down approaches. Top-down methodologies are based on the manual decomposition of the design into modular, independent subunits. In contrast, recent computational morphogenetic techniques have shown that they were able to automatically generate truly complex innovative designs. Algorithms based on evolutionary computation and artificial development have been proposed to automatically design both the structures, within certain constraints, and the controllers that optimize their function. However, the driving force of biological evolution does not resemble an enumeration of design requirements, but much rather relies on the interaction of organisms within the environment. Similarly, controllers do not evolve nor develop separately, but are woven into the organism’s morphology. In this chapter, we discuss evolutionary morphogenetic algorithms inspired by these important aspects of biological evolution. The proposed methodologies could contribute to the automation of processes that design “organic” structures, whose morphologies and controllers are intended to solve a functional problem. The performance of the algorithms is tested on a class of optimization problems that we call behavior-finding. These challenges are not explicitly based on morphology or controller constraints, but only on the solving abilities and efficacy of the design. Our results show that morphogenetic algorithms are well suited to behavior-finding