Miracle-dz/UniFAR-FTUs huggingface dataset:
Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval. 2010 Mathematics Subject Classification: 26E70; 34N05; 49K05; 49K21.
Non-Minimal Solvers for Relative Pose Estimation with a Known Relative Rotation Angle

Knowing the relative rotation angle improves relative pose estimation accuracy. We consider the problem of computing relative motion from a non-minimal number of correspondences with a known relative rotation angle. While several solvers for minimum correspondences have been proposed, no non-minimal solver for this problem currently exists. In this work, we propose two non-minimal solvers for this problem. The first solver solves the problem using convex relaxation and semidefinite programming, yielding certifiable solutions. The second method approaches the problem through local eigenvalue optimization with random initialization. Increasing the number of initial guesses lowers the chances of missing the correct solution. We conduct experiments on synthetic and real data, confirming our methods' advantages over competing methods.
Clustering Mechanism in Particle Swarm Optimization Algorithm for Data Aggregation

Wireless Sensor Networks (WSNs) consist of numerous sensor nodes with distinct resources working together to achieve a common objective efficiently. A critical issue is extending the network lifetime of WSNs, especially for data transfer, as sensor nodes depend on their internal batteries to carry out essential functions and communicate with one another. Efficient energy use per sensor is essential for ensuring the overall energy efficiency of the network. Clustering has been the most energy-efficient approach but lacking a method for selecting the most effective cluster head results in decreased data aggregation efficiency, leading to the increased power consumption of sensor nodes. The project aims to enhance energy efficiency and extend network service life by using Particle Swarm optimization (PSO) for clustering in WSNs. PSO is used to select the cluster head based on member node distance from the base station and remaining energy. The proposed PSO technique was tested against Low Energy Adaptive Clustering Hierarchy (LEACH), Stable Election Protocol (SEP), Zonal Stable Election Protocol Z-SEP, and Extended Stable Election Protocol (EZ-SEP) and found to be more effective in reducing energy usage and prolonging the network’s lifespan. The recommended technique can extend the service life of WSNs and reduce energy consumption, ultimately leading to more cost-effective and eco-friendly solutions for various applications such as environmental monitoring, surveillance, and healthcare.
Convergent Second-Order Methods for Min-Max Optimizations

We address the use of second-order methods to solve optimizations of the form\begin{equation*}\mathop {\min }\limits_{u \in \mathcal{U}} \mathop {\max }\limits_{d \in \mathcal{D}} f(u,d),\tag{1}\end{equation*}for a twice continuously differentiable function $f:\mathcal{U} \times \mathcal{D} \to \mathbb{R}$ and sets $\mathcal{U} \subset {\mathbb{R}^{{n_u}}},\mathcal{D} \subset {\mathbb{R}^{{n_d}}}$. This type of optimization arises in numerous applications, including robust machine learning [1], model predictive control [2], [3], and in reformulating stochastic programming as a min-max optimizations [4], [5]. When the sets $\mathcal{U}$ and $\mathcal{D}$ are compact and convex and the function f (u, d) is convex with respect to u and concave with respect to d, the min and max in (1) commute [6] and the optimization becomes relatively simple. However, we are especially interested here in problems for which such assumptions do not hold, the min and max do not commute, and for which the optimizations may have local optima that are not global.In this talk, we address the design of algorithms to solve nonconvex-nonconcave min-max optimizations like (1) using second order methods. These algorithms modify the Hessian matrix to obtain a search direction that can be seen as the solution to a quadratic program that locally approximates the min-max problem. We show that by selecting this type of modification appropriately, the only stable points of the resulting iterations are local min-max points. For min-max model predictive control problems, these algorithms leads to computation times that scale linearly with the horizon length.For more information please see the main tutorial paper [7].
Contact-Based Pose Estimation of Workpieces for Robotic Setups

This paper presents a method for contact-based pose estimation of workpieces using a collaborative robot. The proposed pose estimation exploits positions and surface normal vectors along an arbitrary path on an object with known geometry, where surface normal vectors are estimated based on contact forces measured by the robot. When data is only available along a single path, it is difficult to find initial correspondences between source data (recorded points and normal vectors) and target data (CAD of an object); hence, a novel weighted incremental spatial search approach for generating correspondences based on point pair features is proposed. Subsequently, robust pose estimation is employed to reduce the effect of erroneous correspondences. The proposed pose estimation is verified in simulation on three paths on two objects and with different levels of noise on the source data to quantify the robustness of the algorithm. Finally, the method is experimentally validated to provide an average pose rotation and translation accuracy of $\mathbf{0.55}^{\circ}$ and 0.51 mm, respectively, when using the robust estimation cost function Geman-McClure.
Controlling a Double-Pendulum Crane by Combining Reinforcement Learning and Conventional Control

Controlling oscillation is vital for applications in which flexible systems are employed. Many existing control methods rely on knowledge of the system dynamics to mitigate unwanted vibration. However, model-free methods can also be employed to control vibration. One method for model-free control is reinforcement learning (RL). Although the RL agent does not require information about the system to learn a control policy, domain knowledge of dynamics and control can be used to augment the agent and aid in generating an effective control policy. This work analyzes the effectiveness of training RL controllers that operate in combination with conventional controllers. Agents were trained in simulation using a model of a small-scale double-pendulum crane. The effect of the conventional control component on training as well as sensitivity to modeling error are analyzed. Agent transferability is investigated by implementing the simulation-trained controllers on a physical small-scale double-pendulum crane.
Practical Stability Study of Finite Control Set Model Predictive Control for Three-Phase Converters

This paper studies the practical stability of finite control set model predictive control applied to three-phase converters. For current control, the compact set of current control error is determined, according to the upper bound of the error associated with quantizing the output voltage vector. Then, by analyzing the existence of output voltage vectors that lead to the convergence of the current control error, the limitation of the current reference, that is, the practical stability limit, is quantified. The theoretical analysis result provides a reference to the parameter design of inverters. And experiments are presented to verify its effectiveness.
3D-Printed Adaptive Microgripper Driven by Thin-Film NiTi Actuators

Creating microscale actuated mechanisms in 3D space is extremely challenging due to limitations in microfabrication processes. In this work, we present a 3D-printed adaptive microgripper that is driven by thin-film NiTi microactuators with 3D-printed linkage mechanisms. The microgripper's fingers are passively adaptive so that the microgripper can provide conformal gripping on 3D objects. The microgripper can move its fingers by $\mathbf{225}\ \boldsymbol{\mu} \mathbf{m}$ and apply a blocking force of $\mathbf{30}\ \boldsymbol{\mu} \mathbf{N}$ per one finger when 20 mA was applied to the NiTi actuators. The microgripper was also integrated onto a printed circuit board with a current regulating circuit and a 9 V battery. Since the NiTi actuator requires a low voltage for actuation, the microgripper could be integrated with simple and affordable electronics. The fully integrated microgripper system was demonstrated playing with a shape sorting box at the microscale for the first time.
A generic power wheelchair lumped model in the sagittal plane: towards realistic self-motion perception in a virtual reality simulator

This paper presents a generic power wheelchair dynamic model. As a first contribution, this paper proposes to use a generic model composed of a geometric model and a lumped model in order to be compliant with a wide range of existing commercially available wheelchairs. In this model, a set of essential parameters are enough to accurately replicate the dynamic behavior of a wheelchair. As a second contribution, this paper presents an identification method of a n-wheel type power wheelchair. The presented model is restricted to the sagittal plane only, which is sufficient to study the reliability of the identification and validation methods. Moreover, a Motion Cueing Algorithm based on the proposed model controls a simulator mechanical platform. The generic model has been then validated through a user study with 18 able-bodied participants evaluating the self-motion perception with our multisensory power wheelchair driving simulator. Results show that the simplified model is sufficient to provide accurate sensations to the user with respect to their experience while driving a power wheelchair.
Onboard Controller Design for Nano UAV Swarm in Operator-Guided Collective Behaviors

In this paper, we present a swarm of Crazyflie nano-drones. The swarm can show various collective behaviors: Flocking, gradient following, going to a chosen point, formation, and scattered search of the environment. The methodology behind the behaviors is executed entirely on-board. Crazyflies use a common radio channel to share positions with each other. If desired, an operator can use the same channel and start, end, change or guide the collective behaviors online during the flight. We use the virtual force vectors and modify the way they are combined to achieve different behaviors instead of developing unique algorithms for each. This allows us to develop more collective behavior types with less effort. In the results, we show a detailed analysis of the behaviors and assess the coordination and the safety of the agents in addition to the performance as a collective. We conclude that our swarm of 6 Crazyflies was successful in the desired behaviors.
A Novel Optimized Coordination Strategy Between Fast Protection and Multi-port Hybrid DC Circuit Breaker for VSC-Based DC grids

The selective and fast isolation of faulty DC lines is the key problem to be urgently solved to ensure the continuous and reliable operation of VSC-based DC grids. As the fault isolation equipment, the multi-port hybrid circuit breaker (MP-HDCB) can realize the selective isolation of the faulty DC line at relatively lower construction cost by cooperating with the fast protection, which shows a wide-spread application prospect in the future large-scale VSC-based DC grid. However, the traditional coordination strategy based on "fast protection acting firstly, and then the MP-HDCB breaking" takes a long time to interrupt the fault current, which is more likely to result the local converter valve blocking and permanent damage to power electronic devices. In order to tackle this problem, a novel optimized coordination strategy is proposed in this paper, which can shorten the overall action time from 6 ms to 3+Δt ms. Firstly, the basic principle of the fast protection, the interruption process of the MP-HDCB and the traditional coordination strategy are introduced in detail. Next, the optimized coordination strategy between the fast protection and the MP-HDCB is redesigned and proposed. Finally, the effectiveness and applicability of the proposed optimized coordination strategy is verified with PSCAD/EMTDC.
Mimicking Real Forces on a Drone Through a Haptic Suit to Enable Cost-Effective Validation

Robots operate under certain forces that affect their behavior. Consider, a drone meant to deliver packages must hold its pose as long as it operates under its weight and wind limits. Validating that such a drone handles external forces correctly is key to ensuring its safety. Nevertheless, validating the system's behavior under the effect of such forces can be difficult and costly. For example, checking the effects of different wind magnitudes may require waiting for the matching outdoor conditions or requiring wind tunnels. Checking the effects of different package sizes and shapes may require many slow and laborious iterations, and validating the combinations of wind gusts and package configurations is often hard to replicate. This work introduces a framework to overcome such challenges by mimicking external forces exercised on a drone with limited cost, setup, and space. The framework consists of a haptic suit device with directional propellers that can be mounted onto a drone, a synthesizer to transform intended forces into setpoints for the suit's directional propellers, and a controller for the suit to meet those setpoints. We conduct a study to assess the framework's capabilities under multiple scenarios involving various forces. Our findings show that the haptic suit framework can recreate real-world forces on the drone with acceptable precision.
Vector Field Aided Trajectory Tracking by a 10-gram Flapping-Wing Micro Aerial Vehicle

Here we describe how a 10-gram Flapping-Wing Micro Aerial Vehicle (FWMAV) was able to perform an automatic trajectory tracking task based on a vector field method. In this study, the desired heading was provided by a vector field which was computed depending on the desired trajectory. The FWMAV's heading was changed by a rear steering mechanism. This rear mechanism simultaneously (i) tenses one wing and relaxes the opposite wing, and (ii) moves the rudder in the same direction as the wing is relaxed. Due to the complex dynamics, system identification methods were used to identify simple linear models using a set of dedicated free flight tests. This yaw and roll simple models help to adjust the yaw controller and the inner loop roll controller. The experimental results obtained here show that a time-independent vector field-based strategy is robust to various initial position and/or speed conditions. The task of tracking circular and 8-shaped trajectories was accomplished successfully over tens of meters.
Relay assisted spectrum sensing in presence of in-phase and quadrature-phase imbalance in multi-channel system

The increasing demand for wireless technology leads to dynamic spectrum access, which is positively accomplished by cognitive radio (CR) technology. For its acceptable efficiency, it needs a robust detection scheme that detects the spectrum holes. This paper investigates a cooperative spectrum sensing method for a relay-based cognitive radio network. In general, a relay is a low-cost device. It is more prone to hardware impairment such as In-phase and Quadrature-phase Imbalance (IQI), which can considerably limit the capabilities of sensing spectrum holes. This work studies the energy detection (ED) based spectrum sensing in multi-channel receiver scenarios affected by IQI. The detection and false alarm probabilities considering Gaussian primary user signal models are derived. Our results are simulation-based and verified with theoretical findings.
Low Reynolds Number Propeller Performance Measurement in Wind Tunnel Test Rig

The objective of the work in this thesis was to to equip the University’s of Beira Interior wind tunnel with a Low Reynolds Number (LRN) Propeller Performance Test Rig. This LRN condition is verified in small Unmanned Aerial Vehicles (UAVs) applications or in the high-altitude airships covered by the project MAAT-Multybody Advanced Airship for Transport. The design, construction and validation of an accurate measuring mechanism was conducted. The test rig was developed to collect performance data of propellers with diameter between 6 to 14 inches (approx. 0.15 to 0.40m), operating at Reynolds number between 30,000 to 300,000 (based on chord at 3/4 of the blade radius). The design chosen for the thrust balance closely resembles the T-shaped pendulum structure originally built in the University of Illinois at Urbana-Champaign (UIUC). Due to the adjustable load cell positioning, this setting allows the use of the full range of the load cell for most thrust levels in the propeller size, relative wind speed and rotation speed ranges. The test rig was completely validated and the experimental procedure was shown herein as well. Furthermore, thrust and torque characteristics of two Aeronaut Carbon Electric were measured. It was shown that as the Reynolds number increases with the increase of propeller RPM, it affects the propellers performance increasing their thrust coefficient and their efficiency. The developed test rig can be used for several purposes, namely: the design of propellers in the UBI’s Department of Aerospace Sciences; the development UAVs, as well as the validation and improvement of numerical tools such as JBLADE.
Direct Adaptive Fuzzy-Based Neural Network Controller for a Human-Driven Knee Joint Orthosis

This paper presents a control error based direct adaptive Neural Network (NN) controller applied to a lower limb knee joint orthosis during flexion/extension movements. The proposed approach requires neither pre-knowledge of the exact human-orthosis system nonlinearities nor it’s exact parameters. Unlike the available NN control approaches that rely on the tracking errors to derive the adaptive weights, our approach represent an alternative way on which we introduce the control error for online updating of the NN weights. A Fuzzy Inference System (FIS) is exploited to estimate the unknown control error. Then, the NN weights are tuned directly using back-propagation algorithm based on a quadratic criterion of the control error independently from the tracking error. In terms of stability, the tracking error has been proved to converge exponentially to an arbitrary small set despite the presence of external disturbances. Simulations are conducted to evaluate the effectiveness of the proposed control approach.
Generalization of Impact Response Factors for Proprioceptive Collaborative Robots

Physical Human-Robot Interaction(pHRI) re-quires taking safety into account from the design board to the collaborative operation of any robot. For collaborative robotic environments, where human and machine are sharing space and interacting physically, the analysis and quantification of impacts becomes very relevant and necessary. Furthermore, analyses of this kind are a valuable source of information for the design of safer, more efficient pHRI. In the definition of the first parameter for dynamic impact analysis, the dynamic impact mitigation capacity was considered for certain configurations of the robot, but the design characteristics of the robot, such as the inertia of actuators, were not included. This paradigm changed when MIT presented the “impact mitigation factor” (IMF) with which, in addition to considering the ability of a certain robot to mitigate impacts for every configuration, it was possible to quantify backdriveability by taking the inertia of actuators into account for the calculation of the factor. However, IMF was proposed as a method to analyse floating robots like. This paper presents the Generalised Impact Absorption Factor (GIAF), suitable for both floating and fixed-base robots. GIAF is a valuable design parameter, as it provides information about the backdriveability of each joint, while allowing the comparison of impact response between floating and fixed-base robotic platforms. In this work, the mathematical definition of GIAF is developed and examples of possible uses of GIAF are presented.
On Legible and Predictable Robot Navigation in Multi-Agent Environments

Legible motion is intent-expressive, which when employed during social robot navigation, allows others to quickly infer the intended avoidance strategy. Predictable motion matches an observer's expectation which, during navigation, allows others to confidently carryout the interaction. In this work, we present a navigation framework capable of reasoning on its legibility and predictability with respect to dynamic interactions, e.g., a passing side. Our approach generalizes the previously formalized notions of legibility and predictability by allowing dynamic goal regions in order to navigate in dynamic environments. This generalization also allows us to quantitatively evaluate the legibility and the predictability of trajectories with respect to navigation interactions. Our approach is shown to promote legible behavior in ambiguous scenarios and predictable behavior in unambiguous scenarios. In a multi-agent environment, this yields an increase in safety while remaining competitive in terms of goal-efficiency when compared to other robot navigation planners in multi-agent environments. The code of this work is made publicly available1.
A Novel Protocol for Fixed-Time Distributed Optimization Over Networks Based on Zero-Gradient-Sum Strategy

Different from existing protocols for achieving fixed-time convergence, a novel fixed-time protocol with an adaptive gain is proposed for solving the distributed optimization problem over networks. Based on the zero-gradient-sum straetgy, the problem will reduced to the fixed-time consensus problem and the convergence time is determined by the frequency of a sine function. Besides, some comments on the practical implementation are also given and it is found that the proposed protocol maintains strong robustness to input saturations. Two illustrative examples are finally provided to validate all the mentioned results.