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In this paper, we present a novel RRT*-based strategy for generating kinodynamically feasible paths that satisfy temporal logic specifications. Our approach integrates a robustness metric for Linear Temporal Logics (LTL) with the system's motion constraints, ensuring that the resulting trajectories are both optimal and executable. We introduce a cost function that recursively computes the robustness of temporal logic specifications while penalizing time and control effort, striking a balance between path feasibility and logical correctness. We validate our approach with simulations and real-world experiments in complex environments, demonstrating its effectiveness in producing robust and practical motion plans. This work represents a significant step towards expanding the applicability of motion planning algorithms to more complex, real-world scenarios.

Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class of incremental Lyapunov functions, an incremental stability notion known as Incremental Input-to-State practical Stability ({\delta}-ISpS). Using Gaussian Process, we learn the unknown dynamics of a class of control systems. We then present a backstepping control design scheme that provides state-feedback controllers that render the partially unknown control system {\delta}-ISpS. To show the effectiveness of the proposed controller, we implement it in two case studies., Comment: 15 page, 4 figures

We propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured porous media, we applied it to a real experimental dataset in which brine is injected at a constant pressure drop into a CO2 saturated naturally fractured shale core plug. The exact spatial positions of natural fractures and the dynamic in-situ distribution of fluids were imaged using a CT-scan setup. To model the targeted system, we followed a domain decomposition approach for matrix and fractures and a multi-network architecture for the separate calculation of water saturation and pressure. The flow equations in the matrix, fractures and interplay between them were solved during training. Prior to fully-coupled simulations, we proposed pre-training the model. This aided in a more efficient and successful training of the coupled system. Both for the synthetic and experimental inverse problems, we determined flow parameters within the matrix and the fractures. Multiple random initializations of network and system parameters were performed to assess the uncertainty and uniqueness of the results. The results confirmed the precision of the inverse calculated parameters in retrieving the main flow characteristics of the system. The consideration of multiscale matrix-fracture impacts is commonly overlooked in existing workflows. Accounting for them led to several orders of magnitude variations in the calculated flow properties compared to not accounting for them. To the best of our knowledge, the proposed PINNs-based workflow is the first to offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements., Comment: 47 pages of paper, including 19 figures

In modern robotics, addressing the lack of accurate state space information in real-world scenarios has led to a significant focus on utilizing visuomotor observation to provide safety assurances. Although supervised learning methods, such as imitation learning, have demonstrated potential in synthesizing control policies based on visuomotor observations, they require ground truth safety labels for the complete dataset and do not provide formal safety assurances. On the other hand, traditional control-theoretic methods like Control Barrier Functions (CBFs) and Hamilton-Jacobi (HJ) Reachability provide formal safety guarantees but depend on accurate knowledge of system dynamics, which is often unavailable for high-dimensional visuomotor data. To overcome these limitations, we propose a novel approach to synthesize a semi-supervised safe visuomotor policy using barrier certificates that integrate the strengths of model-free supervised learning and model-based control methods. This framework synthesizes a provably safe controller without requiring safety labels for the complete dataset and ensures completeness guarantees for both the barrier certificate and the policy. We validate our approach through distinct case studies: an inverted pendulum system and the obstacle avoidance of an autonomous mobile robot., Comment: First two authors have contributed equally. 8 Pages, 3 figures

In the fast-evolving field of Generative AI, platforms like MidJourney, DALL-E, and Stable Diffusion have transformed Text-to-Image (T2I) Generation. However, despite their impressive ability to create high-quality images, they often struggle to generate accurate text within these images. Theoretically, if we could achieve accurate text generation in AI images in a ``zero-shot'' manner, it would not only make AI-generated images more meaningful but also democratize the graphic design industry. The first step towards this goal is to create a robust scoring matrix for evaluating text accuracy in AI-generated images. Although there are existing bench-marking methods like CLIP SCORE and T2I-CompBench++, there's still a gap in systematically evaluating text and typography in AI-generated images, especially with diffusion-based methods. In this paper, we introduce a novel evaluation matrix designed explicitly for quantifying the performance of text and typography generation within AI-generated images. We have used letter by letter matching strategy to compute the exact matching scores from the reference text to the AI generated text. Our novel approach to calculate the score takes care of multiple redundancies such as repetition of words, case sensitivity, mixing of words, irregular incorporation of letters etc. Moreover, we have developed a Novel method named as brevity adjustment to handle excess text. In addition we have also done a quantitative analysis of frequent errors arise due to frequently used words and less frequently used words. Project page is available at: https://github.com/Abhinaw3906/ABHINAW-MATRIX.

Fixed-wing UAVs have transformed the transportation system with their high flight speed and long endurance, yet their safe operation in increasingly cluttered environments depends heavily on effective collision avoidance techniques. This paper presents a novel method for safely navigating an aircraft along a desired route while avoiding moving obstacles. We utilize a class of control barrier functions (CBFs) based on collision cones to ensure the relative velocity between the aircraft and the obstacle consistently avoids a cone of vectors that might lead to a collision. By demonstrating that the proposed constraint is a valid CBF for the aircraft, we can leverage its real-time implementation via Quadratic Programs (QPs), termed the CBF-QPs. Validation includes simulating control law along trajectories, showing effectiveness in both static and moving obstacle scenarios., Comment: 4 Pages, 3 figures. Presented at CyPhySS, 2024, Bangalore. arXiv admin note: text overlap with arXiv:2303.15871

Hybrid quantum devices enable novel functionalities by combining the benefits of different subsystems. Particularly, point defects in nanomechanical resonators made of diamond or silicon carbide (SiC) have been proposed for precise magnetic field sensing and as versatile quantum transducers. However, the realization of a hybrid system may involve tradeoffs in the performance of the constituent subsystems. In a spin-mechanical system, the mechanical properties of the resonator may suffer from the presence of engineered defects in the crystal lattice. This may severely restrict the performance of the resulting device and needs to be carefully explored. Here, we focus on the impact of defects on high Q nanomechanical string resonators made of pre-stressed 3C-SiC grown on Si(111). We use helium ion implantation to create point defects and study their accumulated effect on the mechanical performance. Using Euler-Bernoulli beam theory, we present a method to determine Young's modulus and the pre-stress of the strings. We find that Young's modulus is not modified by implantation. Under implantation doses relevant for single defect or defect ensemble generation, both tensile stress and damping rate also remain unaltered. For higher implantation dose, both exhibit a characteristic change.

We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the acceptable functionality and define the resilience metric as the maximum disturbance under which the system satisfies the temporal requirements. We fix a parameterized template for the set of disturbances and form a robust optimization problem under the system dynamics and the temporal specifications to find the maximum value of the parameter. Additionally, we introduce two novel classes of specifications: closed and convex finite temporal logics specifications, offering a comprehensive analysis of the resilience metric within these specific frameworks. From a computational standpoint, we present an exact solution for linear systems and exact-time reachability and finite-horizon safety, complemented by an approximate solution for finite-horizon reachability. Extending our findings to nonlinear systems, we leverage linear approximations and SMT-based approaches to offer viable computational methodologies. The theoretical results are demonstrated on the temperature regulation of buildings, adaptive cruise control and DC motors.

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee and performance of safe controllers rely on the construction of valid CBFs. Inspired by universal approximatability, CBFs are represented by neural networks, known as neural CBFs (NCBFs). This paper presents an algorithm for synthesizing formally verified continuous-time neural Control Barrier Functions in stochastic environments in a single step. The proposed training process ensures efficacy across the entire state space with only a finite number of data points by constructing a sample-based learning framework for Stochastic Neural CBFs (SNCBFs). Our methodology eliminates the need for post hoc verification by enforcing Lipschitz bounds on the neural network, its Jacobian, and Hessian terms. We demonstrate the effectiveness of our approach through case studies on the inverted pendulum system and obstacle avoidance in autonomous driving, showcasing larger safe regions compared to baseline methods., Comment: 8 pages, 3 figures

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the TurtleBot, Stoch-Jeep, and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (CBF-QPs). Comparative analysis with the state-of-the-art CBFs highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers., Comment: 13 pages, 16 pages. arXiv admin note: substantial text overlap with arXiv:2209.11524, arXiv:2303.15871, arXiv:2310.10839

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities, prompting interest in their application as black-box optimizers. This paper asserts that LLMs possess the capability for zero-shot optimization across diverse scenarios, including multi-objective and high-dimensional problems. We introduce a novel population-based method for numerical optimization using LLMs called Language-Model-Based Evolutionary Optimizer (LEO). Our hypothesis is supported through numerical examples, spanning benchmark and industrial engineering problems such as supersonic nozzle shape optimization, heat transfer, and windfarm layout optimization. We compare our method to several gradient-based and gradient-free optimization approaches. While LLMs yield comparable results to state-of-the-art methods, their imaginative nature and propensity to hallucinate demand careful handling. We provide practical guidelines for obtaining reliable answers from LLMs and discuss method limitations and potential research directions.

Reinforcement Learning (RL) has progressed from simple control tasks to complex real-world challenges with large state spaces. While RL excels in these tasks, training time remains a limitation. Reward shaping is a popular solution, but existing methods often rely on value functions, which face scalability issues. This paper presents a novel safety-oriented reward-shaping framework inspired by barrier functions, offering simplicity and ease of implementation across various environments and tasks. To evaluate the effectiveness of the proposed reward formulations, we conduct simulation experiments on CartPole, Ant, and Humanoid environments, along with real-world deployment on the Unitree Go1 quadruped robot. Our results demonstrate that our method leads to 1.4-2.8 times faster convergence and as low as 50-60% actuation effort compared to the vanilla reward. In a sim-to-real experiment with the Go1 robot, we demonstrated better control and dynamics of the bot with our reward framework., Comment: 7 pages, 10 figures, Accepted as contributed paper at ICRA 2024

Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis. Herein, we employ neural operators to solve Riemann problems encountered in compressible flows for extreme pressure jumps (up to $10^{10}$ pressure ratio). In particular, we first consider the DeepONet that we train in a two-stage process, following the recent work of \cite{lee2023training}, wherein the first stage, a basis is extracted from the trunk net, which is orthonormalized and subsequently is used in the second stage in training the branch net. This simple modification of DeepONet has a profound effect on its accuracy, efficiency, and robustness and leads to very accurate solutions to Riemann problems compared to the vanilla version. It also enables us to interpret the results physically as the hierarchical data-driven produced basis reflects all the flow features that would otherwise be introduced using ad hoc feature expansion layers. We also compare the results with another neural operator based on the U-Net for low, intermediate, and very high-pressure ratios that are very accurate for Riemann problems, especially for large pressure ratios, due to their multiscale nature but computationally more expensive. Overall, our study demonstrates that simple neural network architectures, if properly pre-trained, can achieve very accurate solutions of Riemann problems for real-time forecasting. The source code, along with its corresponding data, can be found at the following URL: https://github.com/apey236/RiemannONet/tree/main

In this paper, we present a compositional methodology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of "alternating simulation function" to establish a relationship between concrete subsystems and their symbolic models. Assuming some small-gain type conditions, we develop an alternating simulation function between the symbolic models of individual subsystems and those of the nonlinear interconnected impulsive systems. To construct symbolic models of nonlinear impulsive subsystems, we propose an approach that depends on incremental input-to-state stability and forward completeness properties. Finally, we demonstrate the advantages of our framework through a case study.

Autonomy advances have enabled robots in diverse environments and close human interaction, necessitating controllers with formal safety guarantees. This paper introduces an experimental platform designed for the validation and demonstration of a novel class of Control Barrier Functions (CBFs) tailored for Unmanned Ground Vehicles (UGVs) to proactively prevent collisions with kinematic obstacles by integrating the concept of collision cones. While existing CBF formulations excel with static obstacles, extensions to torque/acceleration-controlled unicycle and bicycle models have seen limited success. Conventional CBF applications in nonholonomic UGV models have demonstrated control conservatism, particularly in scenarios where steering/thrust control was deemed infeasible. Drawing inspiration from collision cones in path planning, we present a pioneering CBF formulation ensuring theoretical safety guarantees for both unicycle and bicycle models. The core premise revolves around aligning the obstacle's velocity away from the vehicle, establishing a constraint to perpetually avoid vectors directed towards it. This control methodology is rigorously validated through simulations and experimental verification on the Copernicus mobile robot (Unicycle Model) and FOCAS-Car (Bicycle Model)., Comment: 8 pages, 11 figures, Submitted at American Control Conference (ACC), 2024. arXiv admin note: substantial text overlap with arXiv:2209.11524

Event cameras, also known as neuromorphic cameras, are an emerging technology that offer advantages over traditional shutter and frame-based cameras, including high temporal resolution, low power consumption, and selective data acquisition. In this study, we propose to harnesses the capabilities of event-based cameras to capture subtle changes in the surface of the skin caused by the pulsatile flow of blood in the wrist region. We investigate whether an event camera could be used for continuous noninvasive monitoring of heart rate (HR). Event camera video data from 25 participants, comprising varying age groups and skin colours, was collected and analysed. Ground-truth HR measurements obtained using conventional methods were used to evaluate of the accuracy of automatic detection of HR from event camera data. Our experimental results and comparison to the performance of other non-contact HR measurement methods demonstrate the feasibility of using event cameras for pulse detection. We also acknowledge the challenges and limitations of our method, such as light-induced flickering and the sub-conscious but naturally-occurring tremors of an individual during data capture., Comment: Dataset available at https://doi.org/10.6084/m9.figshare.24039501.v1

In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a compact neural network to adjust the smoothness indicators within the WENO scheme. This modification enhances the accuracy of the numerical results, particularly near abrupt shocks. Unlike previous deep learning-based methods, no additional post-processing steps are necessary for maintaining consistency. We demonstrate the superiority of our new approach using several examples from the literature for the two-dimensional Euler equations of gas dynamics. Through intensive study of these test problems, which involve various shocks and rarefaction waves, the new technique is shown to outperform traditional fifth-order WENO schemes, especially in cases where the numerical solutions exhibit excessive diffusion or overshoot around shocks., Comment: 33 pages, 18 figures

The paper addresses the problem of controller synthesis for control-affine nonlinear systems to meet reach-avoid-stay specifications. Specifically, the goal of the research is to obtain a closed-form control law ensuring that the trajectories of the nonlinear system, reach a target set while avoiding all unsafe regions and adhering to the state-space constraints. To tackle this problem, we leverage the concept of the funnel-based control approach. Given an arbitrary unsafe region, we introduce a circumvent function that guarantees the system trajectory to steer clear of that region. Subsequently, an adaptive funnel framework is proposed based on the target, followed by the construction of a closed-form controller using the established funnel function, enforcing the reach-avoid-stay specifications. To demonstrate the efficacy of the proposed funnel-based control approach, a series of simulation experiments have been carried out., Comment: 8 pages, 3 figures