Kinematics analysis is a crucial part for multiple joint enabled robot. For Mmathematically moving a multi joined enabled robot, it needs some mathematical calculations to be done that way so the end effector's position can be determined with respect to the other connective joints involved and their respective frames in a specific co-ordinate system. For a locomotive quadruped robot, it is essential to determine two types of kinematics for the robot's leg position on the co-ordinate. For the part of forward kinematics, it measures the position and er can calculate the joint angles by using inverse kinematics. in this study, we mathematically analyze and derived the forward and the inverse kinematics of the quadruped robot and first we have done the simulation with Jupiter notebook in Python environment for the mathematical analysis and verification and also test our kinematics code on a prototype build leg.
The objective of this research is the development of a practical system to manipulate and validate software package specifications. The validation process developed is based on consistency checks. Furthermore, by means of scenarios, the customer will be able to interactively experience the specified system prior to its implementation. Functions, data, and data types constitute the framework of our validation system. The specification of the Graphical Kernel System (GKS) is a typical example of the target software package specifications to be manipulated.
This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit general solution. In this contribution, we introduce the algorithmic verification of nonlinear superposition properties and its implementation. More exactly, for a system of nonlinear ordinary differential equations of first order with a polynomial right-hand side, we check if the differential system admits a general solution by means of a superposition rule and a certain number of particular solutions. It is based on the theory of Newton polytopes and associated symbolic computation. The developed method provides the basis for the identification of nonlinear superpositions within a given system and for the construction of numerical methods which preserve important algebraic properties at the numerical level.
Robotic arms are highly common in various automation processes such as manufacturing lines. However, these highly capable robots are usually degraded to simple repetitive tasks such as pick-and-place. On the other hand, designing an optimal robot for one specific task consumes large resources of engineering time and costs. In this paper, we propose a novel concept for optimizing the fitness of a robotic arm to perform a specific task based on human demonstration. Fitness of a robot arm is a measure of its ability to follow recorded human arm and hand paths. The optimization is conducted using a modified variant of the Particle Swarm Optimization for the robot design problem. In the proposed approach, we generate an optimal robot design along with the required path to complete the task. The approach could reduce the time-to-market of robotic arms and enable the standardization of modular robotic parts. Novice users could easily apply a minimal robot arm to various tasks. Two test cases of common manufacturing tasks are presented yielding optimal designs and reduced computational effort by up to 92%.
Manipulating deformable objects arises in daily life and numerous applications. Despite phenomenal advances in industrial robotics, manipulation of deformable objects remains mostly a manual task. This is because of the high number of internal degrees of freedom and the complexity of predicting its motion. In this paper, we apply the computationally efficient position-based dynamics method to predict object motion and distance to obstacles. This distance is incorporated in a control barrier function for the resolved motion kinematic control for one or more robots to adjust their motion to avoid colliding with the obstacles. The controller has been applied in simulations to 1D and 2D deformable objects with varying numbers of assistant agents, demonstrating its versatility across different object types and multi-agent systems. Results indicate the feasibility of real-time collision avoidance through deformable object simulation, minimizing path tracking error while maintaining a predefined minimum distance from obstacles and preventing overstretching of the deformable object. The implementation is performed in ROS, allowing ready portability to different applications.
Occasional deadline misses are acceptable for soft real-time systems. Quantifying probabilistic and deterministic characteristics of deadline misses is therefore essential to ensure that deadline misses indeed happen only occasionally. This is supported by recent research activities on probabilistic worst-case execution time, worst-case deadline failure probability, the maximum number of deadline misses, upper bounds on the deadline miss probability, and the deadline miss rate. This paper focuses on the deadline miss rate of a periodic soft real-time task in the long run. Our model assumes that this soft real-time task has an arbitrary relative deadline and that a job can still be executed after a deadline-miss until a dismiss point. This model generalizes the existing models that either dismiss a job immediately after its deadline miss or never dismiss a job. We provide mathematical notation on the convergence of the deadline miss rate in the long run and essential properties to calculate the deadline miss rate. Specifically, we use a Markov chain to model the execution behavior of a periodic soft real-time task. We present the required ergodicity property to ensure that the deadline miss rate in the long run is described by a stationary distribution.
Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.
We use Markov categories to develop generalizations of the theory of Markov chains and hidden Markov models in an abstract setting. This comprises characterizations of hidden Markov models in terms of local and global conditional independences as well as existing algorithms for Bayesian filtering and smoothing applicable in all Markov categories with conditionals. We show that these algorithms specialize to existing ones such as the Kalman filter, forward-backward algorithm, and the Rauch-Tung-Striebel smoother when instantiated in appropriate Markov categories. Under slightly stronger assumptions, we also prove that the sequence of outputs of the Bayes filter is itself a Markov chain with a concrete formula for its transition maps. There are two main features of this categorical framework. The first is its generality, as it can be used in any Markov category with conditionals. In particular, it provides a systematic unified account of hidden Markov models and algorithms for filtering and smoothing in discrete probability, Gaussian probability, measure-theoretic probability, possibilistic nondeterminism and others at the same time. The second feature is the intuitive visual representation of information flow in these algorithms in terms of string diagrams.
Mobile edge computing (MEC) is powerful to alleviate the heavy computing tasks in integrated sensing and communication (ISAC) systems. In this paper, we investigate joint beamforming and offloading design in a three-tier integrated sensing, communication and computation (ISCC) framework comprising one cloud server, multiple mobile edge servers, and multiple terminals. While executing sensing tasks, the user terminals can optionally offload sensing data to either MEC server or cloud servers. To minimize the execution latency, we jointly optimize the transmit beamforming matrices and offloading decision variables under the constraint of sensing performance. An alternating optimization algorithm based on multidimensional fractional programming is proposed to tackle the non-convex problem. Simulation results demonstrates the superiority of the proposed mechanism in terms of convergence and task execution latency reduction, compared with the state-of-the-art two-tier ISCC framework.
Object detection is a fundamental task in computer vision and image processing. Current deep learning based object detectors have been highly successful with abundant labeled data. But in real life, it is not guaranteed that each object category has enough labeled samples for training. These large object detectors are easy to overfit when the training data is limited. Therefore, it is necessary to introduce few-shot learning and zero-shot learning into object detection, which can be named low-shot object detection together. Low-Shot Object Detection (LSOD) aims to detect objects from a few or even zero labeled data, which can be categorized into few-shot object detection (FSOD) and zero-shot object detection (ZSD), respectively. This paper conducts a comprehensive survey for deep learning based FSOD and ZSD. First, this survey classifies methods for FSOD and ZSD into different categories and discusses the pros and cons of them. Second, this survey reviews dataset settings and evaluation metrics for FSOD and ZSD, then analyzes the performance of different methods on these benchmarks. Finally, this survey discusses future challenges and promising directions for FSOD and ZSD.
It has been a long time that computer architecture and systems are optimized to enable efficient execution of machine learning (ML) algorithms or models. Now, it is time to reconsider the relationship between ML and systems, and let ML transform the way that computer architecture and systems are designed. This embraces a twofold meaning: the improvement of designers' productivity, and the completion of the virtuous cycle. In this paper, we present a comprehensive review of work that applies ML for system design, which can be grouped into two major categories, ML-based modelling that involves predictions of performance metrics or some other criteria of interest, and ML-based design methodology that directly leverages ML as the design tool. For ML-based modelling, we discuss existing studies based on their target level of system, ranging from the circuit level to the architecture/system level. For ML-based design methodology, we follow a bottom-up path to review current work, with a scope of (micro-)architecture design (memory, branch prediction, NoC), coordination between architecture/system and workload (resource allocation and management, data center management, and security), compiler, and design automation. We further provide a future vision of opportunities and potential directions, and envision that applying ML for computer architecture and systems would thrive in the community.