Query: Modeling paddle-aided stair-climbing for a mobile robot based on eccentric paddle mechanism

Relevant passages:
RHex: A Simple and Highly Mobile Hexapod Robot <=SEP=> In this paper, the authors describe the design and control of RHex, a power autonomous, untethered, compliant-legged hexapod robot. RHex has only six actuators—one motor located at each hip—achieving mechanical simplicity that promotes reliable and robust operation in real-world tasks. Empirically stable and highly maneuverable locomotion arises from a very simple clock-driven, openloop tripod gait. The legs rotate full circle, thereby preventing the common problem of toe stubbing in the protraction (swing) phase. An extensive suite of experimental results documents the robot’s significant “intrinsic mobility”—the traversal of rugged, broken, and obstacle-ridden ground without any terrain sensing or actively controlled adaptation. RHex achieves fast and robust forward locomotion traveling at speeds up to one body length per second and traversing height variations well exceeding its body clearance.

Track--Stair Interaction Analysis and Online Tipover Prediction for a Self-Reconfigurable Tracked Mobile Robot Climbing Stairs <=SEP=> This paper analyzes track-stair interactions and develops an online tipover prediction algorithm for a self-reconfigurable tracked mobile robot climbing stairs, which is vulnerable to tipping-over. Tipover prediction and prevention for a tracked mobile robot in stair climbing are intractable problems because of the complex track--stair interactions. Unlike the wheeled mobile robots, which are normally assumed to obey the nonholonomic constraints, slippage is unavoidable for a tracked mobile robot, especially in stair climbing. Furthermore, the track-stair interactive forces are complicated, which may take the forms of grouser-tread hooking force, track--stair edge frictional force, grouser-riser clutching force, and even their compositions. In this paper, the track--stair interactions are analyzed systematically, and tipover stability criteria are derived for a tracked mobile robot climbing stairs. An online tipover prediction algorithm is also developed, which forms an essential part for autonomous and semiautonomous stair-climbing control. The effectiveness of the proposed algorithms are verified by experiments.

Multi-Modal Locomotion Robotic Platform Using Leg-Track-Wheel Articulations <=SEP=> Other than from its sensing and processing capabilities, a mobile robotic platform can be limited in its use by its ability to move in the environment. Legs, tracks and wheels are all efficient means of ground locomotion that are most suitable in different situations. Legs allow to climb over obstacles and change the height of the robot, modifying its viewpoint of the world. Tracks are efficient on uneven terrains or on soft surfaces (snow, mud, etc.), while wheels are optimal on flat surfaces. Our objective is to work on a new concept capable of combining different locomotion mechanisms to increase the locomotion capabilities of the robotic platform. The design we came up with, called AZIMUT, is symmetrical and is made of four independent leg-track-wheel articulations. It can move with its articulations up, down or straight, allowing the robot to deal with three-dimensional environments. AZIMUT is also capable of moving sideways without changing its orientation, making it omnidirectional. By putting sensors on these articulations, the robot can also actively perceive its environment by changing the orientation of its articulations. Designing a robot with such capabilities requires addressing difficult design compromises, with measurable impacts seen only after integrating all of the components together. Modularity at the structural, hardware and embedded software levels, all considered concurrently in an iterative design process, reveals to be key in the design of sophisticated mobile robotic platforms.

Autonomous Stair Climbing for Tracked Vehicles <=SEP=> In this paper, we present an algorithm for autonomous stair climbing with a tracked vehicle. The proposed method achieves robust performance under real-world conditions, without assuming prior knowledge of the stair geometry, the dynamics of the vehicle’s interaction with the stair surface, or lighting conditions. Our approach relies on fast and accurate estimation of the robot’s heading and its position relative to the stair boundaries. An extended Kalman filter is used for quaternion-based attitude estimation, fusing rotational velocity measurements from a 3-axial gyroscope, and measurements of the stair edges acquired with an onboard camera. A twotiered controller, comprised of a centeringand a headingcontrol module, utilizes the estimates to guide the robot fast, safely, and accurately upstairs. Both the theoretical analysis and implementation of the algorithm are presented in detail, and extensive experimental results demonstrating the algorithm’s performance are described.

Dante II: Technical Description, Results, and Lessons Learned <=SEP=> Dante II is a unique walking robot that provides important insight into high-mobility robotic locomotion and remote robotic exploration. Dante II’s uniqueness stems from its combined legged and rappelling mobility system, its scanning-laser rangefinder, and its multilevel control scheme. In 1994 Dante II was deployed and successfully tested in a remote Alaskan volcano, as a demonstration of the fieldworthiness of these technologies. For more than five days the robot explored alone in the volcano crater using a combination of supervised autonomous control and teleoperated control. Human operators were located 120 km distant during the mission. This article first describes in detail the robot, support systems, control techniques, and user interfaces. We then describe results from the battery of field tests leading up to and including the volcanic mission. Finally, we put forth important lessons which comprise the legacy of this project. We show that framewalkers are appropriate for rappelling in severe terrain, though tether systems have limitations. We also discuss the importance of future “autonomous” systems to realize when they require human support rather than relying on humans for constant oversight. KEY WORDS—rappelling, walking robot, supervised autonomy, behavior-based control, terrain visualization, volcano exploration

Improving Indoor Localization Using Convolutional Neural Networks on Computationally Restricted Devices <=SEP=> Indoor localization is one of the key enablers for various application and service areas that rely on precise locations of people, goods, and assets, ranging from home automation and assisted living to increased automation of production and logistic processes and wireless network optimization. Existing solutions provide various levels of precision, which also depends on the complexity of the indoor radio environment. In this paper, we propose two methods for reducing the localization error in indoor non-line-of-sight (NLoS) conditions using raw channel impulse response (CIR) information obtained from ultra-wide band radios requiring no prior knowledge about the radio environment. The methods are based on NLoS channel classification and ranging error regression models, both using convolutional neural networks (CNNs) and implemented in the TensorFlow computational framework. We first show that NLoS channel classification using raw CIR data outperforms existing approaches that are based on derived input signal features. We further demonstrate that the predicted NLoS channel state and predicted ranging error information, used in combination with least squares (LS) and weighted LS location estimation algorithms, significantly improve indoor localization performance. We also evaluate the computational performance and suitability of the proposed CNN-based algorithms on various computing platforms with a wide range of different capabilities and show that in a distributed localization system, they can also be used on computationally restricted devices.

Emotion recognition in the wild from videos using images <=SEP=> This paper presents the implementation details of the proposed solution to the Emotion Recognition in the Wild 2016 Challenge, in the category of video-based emotion recognition. The proposed approach takes the video stream from the audio-video trimmed clips provided by the challenge as input and produces the emotion label corresponding to this video sequence. This output is encoded as one out of seven classes: the six basic emotions (Anger, Disgust, Fear, Happiness, Sad, Surprise) and Neutral. Overall, the system consists of several pipelined modules: face detection, image pre-processing, deep feature extraction, feature encoding and, finally, an SVM classification. 
 This system achieves 59.42% validation accuracy, surpassing the competition baseline of 38.81%. With regard to test data, our system achieves 56.66% recognition rate, also improving the competition baseline of 40.47%.

Centroidal Voronoi Tessellations: Applications and Algorithms <=SEP=> A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods for computing these tessellations, provide some analyses concerning both the tessellations and the methods for their determination, and, finally, present the results of some numerical experiments.

Capturing Regional Variation with Distributed Place Representations and Geographic Retrofitting <=SEP=> Dialects are one of the main drivers of language variation, a major challenge for natural language processing tools. In most languages, dialects exist along a continuum, and are commonly discretized by combining the extent of several preselected linguistic variables. However, the selection of these variables is theorydriven and itself insensitive to change. We use Doc2Vec on a corpus of 16.8M anonymous online posts in the German-speaking area to learn continuous document representations of cities. These representations capture continuous regional linguistic distinctions, and can serve as input to downstream NLP tasks sensitive to regional variation. By incorporating geographic information via retrofitting and agglomerative clustering with structure, we recover dialect areas at various levels of granularity. Evaluating these clusters against an existing dialect map, we achieve a match of up to 0.77 V-score (harmonic mean of cluster completeness and homogeneity). Our results show that representation learning with retrofitting offers a robust general method to automatically expose dialectal differences and regional variation at a finer granularity than was previously possible.

Sky Detection in Hazy Image <=SEP=> Sky detection plays an essential role in various computer vision applications. Most existing sky detection approaches, being trained on ideal dataset, may lose efficacy when facing unfavorable conditions like the effects of weather and lighting conditions. In this paper, a novel algorithm for sky detection in hazy images is proposed from the perspective of probing the density of haze. We address the problem by an image segmentation and a region-level classification. To characterize the sky of hazy scenes, we unprecedentedly introduce several haze-relevant features that reflect the perceptual hazy density and the scene depth. Based on these features, the sky is separated by two imbalance SVM classifiers and a similarity measurement. Moreover, a sky dataset (named HazySky) with 500 annotated hazy images is built for model training and performance evaluation. To evaluate the performance of our method, we conducted extensive experiments both on our HazySky dataset and the SkyFinder dataset. The results demonstrate that our method performs better on the detection accuracy than previous methods, not only under hazy scenes, but also under other weather conditions.

A Study and Comparison of Sentiment Analysis Methods for Reputation Evaluation <=SEP=> The aim of this paper is to study and compare some of the methods used to evaluate the reputation of items using sentiment analysis. We explain the challenge of the increasing amount of data available on the Internet and the role of sentiment analysis in mining this information. We classify recent solutions into different categories based on techniques, document approach, and rating methods. We present six methods corresponding to different categories and analyze them based on the technique used, advances and results.

Target Detection in SFCW Ground Penetrating Radar with C3 Algorithm and Hough Transform based on GPRMAX Simulation and Experimental Data <=SEP=> We perform target detection in B-scan images obtained using stepped frequency continuous wave (SFCW) ground-penetrating radar (GPR) simulation with Matlab and the open-source software for electromagnetic propagation simulation gprMax and using experimental data from measurements available on the Web. We perform hyperbola detection and target depth estimation using the Hough transform. Additionally, we reduce the complexity of Hough transform using the Column-Connection Clustering (C3) algorithm. The results show that gprMax can be used with SFCW modulated signals, besides its use with conventional impulse signals (impulse GPR). The proposed combination of C3 and Hough transform shows very good detection capability. These algorithms are also tested on experimental GPR data available on the Web to show their applicability in real soil conditions. Mean subtraction method and Singular Value Decomposition (SVD) algorithms are used to reduce the effects of the ground reflected wave.

StackMap: Low-Latency Networking with the OS Stack and Dedicated NICs <=SEP=> StackMap leverages the best aspects of kernel-bypass networking into a new low-latency Linux network service based on the full-featured TCP kernel implementation, by dedicating network interfaces to applications and offering an extended version of the netmap API as a zero-copy, lowoverhead data path while retaining the socket API for the control path. For small-message, transactional workloads, StackMap outperforms baseline Linux by 4 to 80 % in latency and 4 to 391 % in throughput. It also achieves comparable performance with Seastar, a highly-optimized user-level TCP/IP stack for DPDK.

Kalman filters improve LSTM network performance in problems unsolvable by traditional recurrent nets <=SEP=> The long short-term memory (LSTM) network trained by gradient descent solves difficult problems which traditional recurrent neural networks in general cannot. We have recently observed that the decoupled extended Kalman filter training algorithm allows for even better performance, reducing significantly the number of training steps when compared to the original gradient descent training algorithm. In this paper we present a set of experiments which are unsolvable by classical recurrent networks but which are solved elegantly and robustly and quickly by LSTM combined with Kalman filters.

Free-form deformation of solid geometric models <=SEP=> A technique is presented for deforming solid geometric models in a free-form manner. The technique can be used with any solid modeling system, such as CSG or B-rep. It can deform surface primitives of any type or degree: planes, quadrics, parametric surface patches, or implicitly defined surfaces, for example. The deformation can be applied either globally or locally. Local deformations can be imposed with any desired degree of derivative continuity. It is also possible to deform a solid model in such a way that its volume is preserved.The scheme is based on trivariate Bernstein polynomials, and provides the designer with an intuitive appreciation for its effects.

Conscious and unconscious perception: Experiments on visual masking and word recognition <=SEP=> Five experiments are presented which explore the relation of masking to consciousness and visual word processing. In Experiment 1 a single word or blank field was followed by a pattern mask. Subjects had to make one of three decisions: Did anything precede the mask? To which of two probe words was what preceded the mask more similar graphically? To which of two probe words was it more similar semantically? As word-mask stimulus onset asynchrony (SOA) was reduced, subjects reached chance performance on the detection, graphic, and semantic decisions in that order. In Experiment 2, subjects again had to choose which of two words was more similar either graphically or semantically to a nondetectable masked word, but the forced-choice stimuli now covaried negatively on graphic and semantic similarity. Subjects were now unable to choose selectively on each dimension, suggesting that their ability to choose in Experiment 1 was passively rather than intentionally mediated. In Experiment 3 subjects had to make manual identification responses to color patches which were either accompanied or preceded by words masked to prevent awareness. Color-congruent words facilitated reaction time (RT), color-incongruent words delayed RT. Experiment 4 used a lexical decision task where a trial consisted of the critical letter string following another not requiring a response. When both were words they were either semantically associated or not. The first letter string was either left unmasked, energy masked monoptically, or pattern masked dichoptically to prevent awareness. The effect of association was equal in the unmasked and pattern masked cases, but absent with energy masking. In Experiment 5 repeating a word-plus-mask (where the SOA precluded detection) from 1 to 20 times (a) increased the association effect on a subsequent lexical decision, but had no effect on (b) detectability or(c) the semantic relatedness of forced guesses of the masked word. It is proposed that central pattern masking has little effect on visual processing itself (while peripheral energy masking does), but affects availability of records of the results of those processes to consciousness. Perceptual processing itself is unconscious and automatically proceeds to all levels of analysis and redescription available to the perceiver. The general importance of these findings is to cast doubt on the paradigm assumption that representations yielded by perceptual analysis are identical to and directly reflected by phenomenal percepts.

k -Anonymous Data Mining: A Survey <=SEP=> Data mining technology has attracted significant interest as a means of identifying patterns and trends from large collections of data. It is however evident that the collection and analysis of data that include personal information may violate the privacy of the individuals to whom information refers. Privacy protection in data mining is then becoming a crucial issue that has captured the attention of many researchers. In this chapter, we first describe the concept of k-anonymity and illustrate different approaches for its enforcement. We then discuss how the privacy requirements characterized by k-anonymity can be violated in data mining and introduce possible approaches to ensure the satisfaction of k-anonymity in data mining.

Automatic Tempo-based Classification of Argentine Tango Music <=SEP=> Tempo-based classification is a popular technique to classify music, with applications in media-art projects, systematic study of music etc. The success of this technique using dance music genres has typically been found to be over 70%, yet it was mostly evaluated using standardized music genres, such as ballroom music. Argentine tango is a music genre, originating in Buenos Aires at the end of the 19th century, which has gained a lot of popularity since its creation and is currently being danced in social settings all over the world (see side Photo taken in San Francisco, courtesy of Ref. [10]). There are three music types which define the Argentine tango played in social settings; although these types have different meters from one another, their tempi feature variations influenced by the trends of the era of composition and the composersʼ personal style. Therefore, Argentine tango seemingly makes a good, yet interesting candidate to explore for tempo-based classification schemes. In this report, we construct and evaluate an automatic, bayes tempo classifier with application to Argentine tango music, using a library with more than 2,000 pieces. We find that the accuracy of our classifier stands at 79%, which is well within the bound set by similar schemes applied to ballroom music, proving our original point that tempo is a promising feature in the classification of Argentine tango. We also come up with interesting insights about how to improve classification schemes for this particular musical genre.

A rule based bengali stemmer <=SEP=> One of the biggest challenges in doing word lookups is to derive the appropriate base word for any given word in Bengali. The basic concept to the solution of the problem is to eliminate inflections from a given word to derive its stem word. Stemmers attempt to reduce a word to its root form using stemming process, which reduces an inflected or derived word to its stem or root form. Existing works in the literature use lookup tables either for stem words or suffixes, increasing the overheads in terms of memory and time. This paper develops a rule-based algorithm that eliminates inflections stepwise without continuously searching for the desired root in the dictionary. To the best of our knowledge, this paper first investigates that, in Bengali morphology, for a large set of inflections, the stems can be computed algorithmically cutting down the inflections step by step. The proposed algorithm is independent of inflected word lengths and our evaluation shows around 88% accuracy.

Data quality management in the public domain: a case study within the Dutch justice system <=SEP=> The need for anonymity preservation within the justice domain requires the introduction of a trusted third party as an intermediary, while integrating individual databases within its boundaries. After the trusted third party encrypts records, it is no longer possible to perform checks on the data quality and correct data anomalies. Therefore, this research examines the concepts of data quality, data integration, record linkage and trusted third party and, then, combines these with four expert interviews in order to identify ways to assess and improve data quality while linking privacy-sensitive data. Next, the trusted data linkage framework (TDLF) is presented to aid data quality management while combining citizens’ privacy-sensitive data from different organisations. Finally, we evaluate the framework in a case study to demonstrate how the quality of structured judicial data can be managed prior to its encryption, while using multiple databases as sources of data and a different final recipient.

Discrete-Time Methods for the Analysis of Event Histories <=SEP=> Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use.

Contactless Energy Transfer to a Moving Actuator <=SEP=> In this paper a new topology for contactless energy transfer is proposed and tested that can transfer energy to a moving actuator using inductive coupling. The proposed topology provides long-stroke contactless energy transfer capability in a plane and a short-stroke movement of a few millimeters perpendicular to the plane. In addition, it is tolerant to small rotations. The experimental setup consists of a platform with one secondary coil, which is attached to a linear actuator and a 3-phase brushless electromotor. Underneath the platform is an array of primary coils, which are each connected to a half-bridge square wave power supply. The energy transfer to the electromotor is measured while the platform is moved over the array of primary coils by the linear actuator. The secondary coil moves with a stroke of 18 cm at speeds over 1 m/s, while up to 33 W power is transferred with 90% efficiency

Stereo Acoustic Echo Cancellation Employing Frequency-Domain Preprocessing and Adaptive Filter <=SEP=> This paper proposes a windowing frequency domain adaptive filter and an upsampling block transform preprocessing to solve the stereo acoustic echo cancellation problem. The proposed adaptive filter uses windowing functions with smooth cutoff property to reduce the spectral leakage during filter updating, so the utilization of the independent noise introduced by preprocessing in stereo acoustic echo cancellation can be increased. The proposed preprocessing is operated in short blocks with low processing delay, and it uses frequency-domain upsampling to meet the minimal block length requirement given by the band limit of simultaneous masking. Therefore, the simultaneous masking can be well utilized to improve the audio quality. The acoustic echo cancellation simulations and the audio quality evaluation show that, the proposed windowing frequency domain adaptive filter performs better than the conventional frequency domain adaptive filter in both mono and stereo cases, and the upsampling block transform preprocessing provides better audio quality and stereo acoustic echo cancellation performance than the half-wave preprocessing at the same noise level.

UK Biobank: An Open Access Resource for Identifying the Causes of a Wide Range of Complex Diseases of Middle and Old Age <=SEP=> Cathie Sudlow and colleagues describe the UK Biobank, a large population-based prospective study, established to allow investigation of the genetic and non-genetic determinants of the diseases of middle and old age.

Bayesian Estimation of Beta Mixture Models with Variational Inference <=SEP=> Bayesian estimation of the parameters in beta mixture models (BMM) is analytically intractable. The numerical solutions to simulate the posterior distribution are available, but incur high computational cost. In this paper, we introduce an approximation to the prior/posterior distribution of the parameters in the beta distribution and propose an analytically tractable (closed form) Bayesian approach to the parameter estimation. The approach is based on the variational inference (VI) framework. Following the principles of the VI framework and utilizing the relative convexity bound, the extended factorized approximation method is applied to approximate the distribution of the parameters in BMM. In a fully Bayesian model where all of the parameters of the BMM are considered as variables and assigned proper distributions, our approach can asymptotically find the optimal estimate of the parameters posterior distribution. Also, the model complexity can be determined based on the data. The closed-form solution is proposed so that no iterative numerical calculation is required. Meanwhile, our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm. The good performance of this approach is verified by experiments with both synthetic and real data.

Template Attacks <=SEP=> We present template attacks, the strongest form of side channel attack possible in an information theoretic sense. These attacks can break implementations and countermeasures whose security is dependent on the assumption that an adversary cannot obtain more than one or a limited number of side channel samples. They require that an adversary has access to an identical experimental device that he can program to his choosing. The success of these attacks in such constraining situations is due manner in which noise within each sample is handled. In contrast to previous approaches which viewed noise as a hindrance that had to be reduced or eliminated, our approach focuses on precisely modeling noise, and using this to fully extract information present in a single sample. We describe in detail how an implementation of RC4, not amenable to techniques such as SPA and DPA, can easily be broken using template attacks with a single sample. Other applications include attacks on certain DES implementations which use DPA–resistant hardware and certain SSL accelerators which can be attacked by monitoring electromagnetic emanations from an RSA operation even from distances of fifteen feet.

Action recognition in depth videos using hierarchical gaussian descriptor <=SEP=> In this paper, we propose a new approach based on distribution descriptors for action recognition in depth videos. Our local features are computed from binary patterns which incorporate the shape and motion cues for effective action recognition. Given pixel-level features, our approach estimates video local statistics in a hierarchical manner, where the distribution of pixel-level features and that of frame-level descriptors are modeled using single Gaussians. In this way, our approach constructs video descriptors directly from low-level features without resorting to codebook learning required by Bag-of-features (BoF) based approaches. In order to capture the spatial geometry and temporal order of a video, we use a spatio-temporal pyramid representation for each video. Our approach is validated on six benchmark datasets, i.e. MSRAction3D, MSRGesture3D, DHA, SKIG, UTD-MHAD and CAD-120. The experimental results show that our approach gives good performance on all the datasets. In particular, it achieves state-of-the-art accuracies on DHA, SKIG and UTD-MHAD datasets.

Construction and Evaluation of a User Experience Questionnaire <=SEP=> An end-user questionnaire to measure user experience quickly in a simple and immediate way while covering a preferably comprehensive impression of the product user experience was the goal of the reported construction process. An empirical approach for the item selection was used to ensure practical relevance of items. Usability experts collected terms and statements on user experience and usability, including ‘hard’ as well as ‘soft’ aspects. These statements were consolidated and transformed into a first questionnaire version containing 80 bipolar items. It was used to measure the user experience of software products in several empirical studies. Data were subjected to a factor analysis which resulted in the construction of a 26 item questionnaire including the six factors Attractiveness, Perspicuity, Efficiency, Dependability, Stimulation, and Novelty. Studies conducted for the original German questionnaire and an English version indicate a satisfactory level of reliability and construct validity.

Experiences of integration and performance testing of multilingual OCR for printed Indian scripts <=SEP=> This paper presents integration and testing scheme for managing a large Multilingual OCR Project. The project is an attempt to implement an integrated platform for OCR of different Indian languages. Software engineering, workflow management and testing processes have been discussed in this paper. The OCR has now been experimentally deployed for some specific applications and currently is being enhanced for handling the space and time constraints, achieving higher recognition accuracies and adding new functionalities.

A 5GHz Digital Fractional- $N$ PLL Using a 1-bit Delta–Sigma Frequency-to-Digital Converter in 65 nm CMOS <=SEP=> A highly digital two-stage fractional-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> phase-locked loop (PLL) architecture utilizing a first-order 1-bit <inline-formula> <tex-math notation="LaTeX">$ \Delta \!\Sigma $ </tex-math></inline-formula> frequency-to-digital converter (FDC) is proposed and implemented in a 65nm CMOS process. Performance of the first-order 1-bit <inline-formula> <tex-math notation="LaTeX">$ \Delta \!\Sigma $ </tex-math></inline-formula> FDC is improved by using a phase interpolator-based fractional divider that reduces phase quantizer input span and by using a multiplying delay-locked loop that increases its oversampling ratio. We also describe an analogy between a time-to-digital converter (TDC) and a <inline-formula> <tex-math notation="LaTeX">$ \Delta \!\Sigma $ </tex-math></inline-formula> FDC followed by an accumulator that allows us to leverage the TDC-based PLL analysis techniques to study the impact of <inline-formula> <tex-math notation="LaTeX">$ \Delta \!\Sigma $ </tex-math></inline-formula> FDC characteristics on <inline-formula> <tex-math notation="LaTeX">$ \Delta \!\Sigma $ </tex-math></inline-formula> FDC-based fractional-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> PLL (FDCPLL) performance. Utilizing proposed techniques, a prototype PLL achieves 1 MHz bandwidth, −101.6 dBc/Hz in-band phase noise, and <inline-formula> <tex-math notation="LaTeX">$ {\textrm {1.22 ps}_{\textrm {rms}}}$ </tex-math></inline-formula> (1 kHz–40 MHz) jitter while generating 5.031GHz output from 31.25MHz reference clock input. For the same output frequency, the stand-alone second-stage fractional-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> FDCPLL achieves 1MHz bandwidth, −106.1dBc/Hz in-band phase noise, and <inline-formula> <tex-math notation="LaTeX">$ {\textrm {403 fs}_{\textrm {rms}}}$ </tex-math></inline-formula> jitter with a 500MHz reference clock input. The two-stage PLL consumes 10.1mW power from a 1V supply, out of which 7.1 mW is consumed by the second-stage FDCPLL.