Search Results (41)

Autonomous navigation in mining environments is challenged by complex wheel–terrain interaction, traction losses caused by slip dynamics, and sensor limitations. This paper investigates the effectiveness of Deep Reinforcement Learning (DRL) techniques for the trajectory tracking control of skid-steer mobile robots operating under terra-mechanical constraints. Four state-of-the-art DRL algorithms, i.e., Proximal Policy Optimization (PPO), Deep Deterministic Policy Gradient (DDPG), Twin Delayed DDPG (TD3), and Soft Actor–Critic (SAC), are selected to evaluate their ability to generate stable and adaptive control policies under varying environmental conditions. To address the inherent partial observability in real-world navigation, this study presents an original approach that integrates Long Short-Term Memory (LSTM) networks into DRL-based controllers. This allows control agents to retain and leverage temporal dependencies to infer unobservable system states. The developed agents were trained and tested in simulations and then assessed in field experiments under uneven terrain and dynamic model parameter changes that lead to traction losses in mining environments, targeting various trajectory tracking tasks, including lemniscate and squared-type reference trajectories. This contribution strengthens the robustness and adaptability of DRL agents by enabling better generalization of learned policies compared with their baseline counterparts, while also significantly improving trajectory tracking performance. In particular, LSTM-based controllers achieved reductions in tracking errors of 10%, 74%, 21%, and 37% for DDPG-LSTM, PPO-LSTM, TD3-LSTM, and SAC-LSTM, respectively, compared with their non-recurrent counterparts. Furthermore, DDPG-LSTM and TD3-LSTM reduced their control effort through the total variation in control input by 15% and 20% compared with their respective baseline controllers, respectively. Findings from this work provide valuable insights into the role of memory-augmented reinforcement learning for robust motion control in unstructured and high-uncertainty environments. Full article

This paper presents the design and implementation of a Model-based Predictive Control (MPC) strategy integrated within a modular multilayer architecture for a three-wheeled omnidirectional mobile robot, the Robotino 4 from Festo. The implemented architecture is organized into three hierarchical layers to support modularity and system scalability. The upper layer is responsible for trajectory planning. This planned trajectory is forwarded to the intermediate layer, where the MPC computes the optimal velocity commands to follow the reference path, taking into account the kinematic model and actuator constraints of the robot. Finally, these velocity commands are processed by the lower layer, which uses three independent PID controllers to regulate the individual wheel speeds. To evaluate the proposed control scheme, it was implemented in MATLAB R2024a using a lemniscate trajectory as the reference. The MPC problem was formulated as a quadratic optimization problem that considered the three states: the global position coordinates and orientation angle. The simulation included state estimation errors and motor dynamics, which were experimentally identified to closely match real-world behavior. The simulation and experimental results demonstrate the capability of the MPC to track the lemniscate trajectory efficiently. Notably, the close agreement between the simulated and experimental results validated the fidelity of the simulation model. In a real-world scenario, the MPC controller enabled simultaneous regulation of both the position and orientation, which offered a greater performance compared with approaches that assume a constant orientation. Full article

In this work, we explore the impact of integral operators such as the Libera and Alexander operators on specific families of analytic functions introduced in the literature and find some of their remarkable results. Using techniques from differential subordination and convolution theory, we establish results concerning the radius of convexity and convolution properties for these function classes. Additionally, we investigate how these integral operators influence the geometric properties of functions in $\mathcal{BS}\left(\mu \right)$ and $\mathcal{KS}\left(\mu \right)$, leading to new insights into their structural behavior. Full article

The dynamics of plasmon polaritons (PPs) in a periodic lattice of dispersed nanorings (NRs) with embedded quantum nanoemitters (NEs) arranged according to the Cassini–Bernoulli lemniscate (LB) is studied. The field structure and the dynamics of the NE (quantum polarization) depend significantly on the plasma frequency ${\omega }_p$ of the NR. We show that in the vicinity of the intersection of the LB branches (a region of high emitter density) located in the nanoring gaps, there is a significant enhancement of the optical field intensity and quantum correlations in the emitter subsystem. This effect may allow the coherent amplification of terahertz PPs (studied recently via free-electron-stimulated emission) in a lattice of NRs with the emission of embedded NEs. Full article

In this article, a new subclass of starlike functions is defined by using the technique of subordination and introducing a novel generalized domain. This domain is obtained by taking the composition of trigonometric $\sin e$ function and the well known curve called lemniscate of Bernoulli which is the image of open unit disc under a function $g\left(\xi \right)=\sqrt{1+\xi }$. This domain is characterized by its pleasing geometry which exhibits symmetric about the real axis. For this newly defined subclass, we investigate the sharp upper bounds for its first four coefficients, as well as the second and third order Hankel determinants. Full article

This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity, k-starlikeness, k-uniform convexity, pre-starlikeness, lemniscate starlikeness, and convexity, and under which exponential starlikeness and convexity are obtained. By combining methods from complex analysis, inequalities, and functional analysis, the article advances the theory of Bessel functions and hypergeometric functions. The established results could be useful in approximation theory and bounding the behavior of functions. Full article

In light of the planar inverse problem of Newtonian Dynamics, we study the monoparametric family of regular orbits $f(r,\theta )=c$ in polar coordinates (where c is the parameter varying along the family of orbits), which are generated by planar potentials $V=V(r,\theta )$. The corresponding family of orbits can be uniquely represented by the “slope function” $\gamma ={\displaystyle \frac{f_{\theta }}{f_r}}$. By using the basic partial differential equation of the planar inverse problem, which combines families of orbits and potentials, we apply a new methodology in order to find specific potentials, e.g., $V=A\left(r\right)+B\left(\theta \right)$ or $V=H\left(\gamma \right)$ and one-dimensional potentials, e.g., $V=A\left(r\right)$ or $V=G\left(\theta \right)$. In order to determine such potentials, differential conditions on the family of orbits $f(r,\theta )$ = c are imposed. If these conditions are fulfilled, then we can find a potential of the above form analytically. For the given families of curves, such as ellipses, parabolas, Bernoulli’s lemniscates, etc., we find potentials that produce them. We present suitable examples for all cases and refer to the case of straight lines. Full article

The main objective of this research is to examine a specific sufficiency criteria for the starlikeness and convexity of order $\delta$, k-uniform starlikeness, k-uniform convexity, lemniscate starlikeness and convexity, exponential starlikeness and convexity, uniform convexity of the Generalized Bessel-Maitland function. Applications of these conclusions to the concept of corollaries are also provided. Additionally, an illustrated representation of these outcomes will be presented. So functional inequalities involving gamma function will be the main research tools of this exploration. The outcomes from this study generalize a number of conclusions from earlier studies. Full article

Suppose that ${\mathcal{A}}_1$ is a class of analytic functions $f:\mathfrak{D}=\{z\in \mathbb{C}:|z|<1\}\to \mathbb{C}$ with normalization $f(0)=1$. Consider two functions ${\mathcal{P}}_l(z)=\sqrt{1+z}$ and ${\mathsf{\Phi }}_{N_e}(z)=1+z-z^3/3$, which map the boundary of $\mathfrak{D}$ to a cusp of lemniscate and to a twi-cusped kidney-shaped nephroid curve in the right half plane, respectively. In this article, we aim to construct functions $f\in {\mathcal{A}}_0$ for which (i) $f(\mathfrak{D})\subset {\mathcal{P}}_l(\mathfrak{D})\cap {\mathsf{\Phi }}_{N_e}(\mathfrak{D})$ (ii) $f(\mathfrak{D})\subset {\mathcal{P}}_l(\mathfrak{D})$, but $f(\mathfrak{D})\not\subset {\mathsf{\Phi }}_{N_e}(\mathfrak{D})$ (iii) $f(\mathfrak{D})\subset {\mathsf{\Phi }}_{N_e}(\mathfrak{D})$, but $f(\mathfrak{D})\not\subset {\mathcal{P}}_l(\mathfrak{D})$. We validate the results graphically and analytically. To prove the results analytically, we use the concept of subordination. In this process, we establish the connection lemniscate (and nephroid) domain and functions, including ${\mathtt{g}}_{\alpha }(z):=\sqrt{1+\alpha z^2}$, $|\alpha |\le 1$, the polynomial ${\mathtt{g}}_{\alpha ,\beta }(z):=1+\alpha z+\beta z^3$, $\alpha ,\beta \in \mathbb{R}$, as well as Lerch’s transcendent function, Incomplete gamma function, Bessel and Modified Bessel functions, and confluent and generalized hypergeometric functions. Full article

The main purpose of this work is to study the third Hankel determinant for classes of Bernoulli lemniscate-related functions by introducing new subclasses of star-like functions represented by $S_{L\lambda }^{*}$ and $R{L}_{\lambda }$. In many geometric and physical applications of complex analysis, estimating sharp bounds for problems involving the coefficients of univalent functions is very important because these coefficients describe the fundamental properties of conformal maps. In the present study, we defined sharp bounds for function-coefficient problems belonging to the family of $S_{L\lambda }^{*}$ and $R{L}_{\lambda }$. Most of the computed bounds are sharp. This study will encourage further research on the sharp bounds of analytical functions related to new image domains. Full article

Modeling and control are challenging in unmanned aerial vehicles, especially in quadrotors where there exists high coupling between the position and the orientation dynamics. In simulations, conventional control strategies such as the use of a proportional–integral–derivative (PID) controller under different configurations are typically employed due to their simplicity and ease of design. However, linear assumptions have to be made, which turns into poor performance for practical applications on unmanned aerial vehicles (UAVs). This paper designs and implements a hierarchical cascaded model predictive control (MPC) for three-dimensional trajectory tracking using a quadrotor platform. The overall system consists of two stages: the mission server and the commander stabilizer. Different from existing works, the heavy computational burden is managed by decomposing the overall MPC strategy into two different schemes. The first scheme controls the translational displacements while the second scheme regulates the rotational movements of the quadrotor. For validation, the performance of the proposed controller is compared against that of a proportional–integral–velocity (PIV) controller taken from the literature. Here, real-world experiments for tracking helicoidal and lemniscate trajectories are implemented, while for regulation, an extreme wind disturbance is applied. The experimental results show that the proposed controller outperforms the PIV controller, presenting less signal effort fluctuations, especially in terms of rejecting external wind disturbances. Full article

In this paper, the very fundamental geometrical characteristics of the Mylar balloon like the profile curve, height, volume, arclength, surface area, crimping factor, etc. are recognized as geometrical moments ${\mathcal{I}}_n\left(x\right)$ and ${\mathcal{I}}_n$ and this observation has been used to introduce an infinite family of surfaces ${\mathcal{S}}_n$ specified by the natural numbers $n=0,1,2,\dots$. These surfaces are presented via explicit formulas (through the incomplete Euler’s beta function) and can be identified as an interesting family of balloons. Their parameterizations is achieved relying on the well-known relationships among elliptic integrals, beta and gamma functions. The final results are expressed via the fundamental mathematical constants, such as $\pi$ and the lemniscate constant $\varpi$. Quite interesting formulas for recursive calculations of various quantities related to associated figures modulo four are derived. The most principal results are summarized in a table, illustrated via a few graphics, and some direct relationships with other fundamental areas in mathematics, physics, and geometry are pointed out. Full article

The field of geometric function theory has thoroughly investigated starlike functions concerning symmetric points. The main objective of this work is to derive certain geometric properties, such as the starlikeness of order $\delta$, convexity of order $\delta$, k-starlikeness, k-uniform convexity, lemniscate starlikeness and convexity, exponential starlikeness and convexity, and pre-starlikeness for the Galué type Struve function (GTSF). Furthermore, the conditions for GTSF belonging to the Hardy space are also derived. The results obtained in this work generalize several results available in the literature. Full article

This paper presents a novel approach to address the challenges associated with the trajectory tracking control of wheeled mobile robots (WMRs). The proposed control approach is based on an indirect adaptive control PID using a neural network and discrete extended Kalman filter (IAPIDNN-DEKF). The proposed IAPIDNN-DEKF scheme uses the NN to identify the system Jacobian, which is used for tuning the PID gains using the stochastic gradient descent algorithm (SGD). The DEKF is proposed for state estimation (localization), and the NN adaptation improves the tracking error performance. By augmenting the state vector, the NN captures higher-order dynamics, enabling more accurate estimations, which improves trajectory tracking. Simulation studies in which a WMR is used in different scenarios are conducted to evaluate the effectiveness of the IAPIDNN-DEKF control. In order to demonstrate the effectiveness of the IAPIDNN-DEKF control, its performance is compared with direct adaptive NN (DA-NN) control, backstepping control (BSC) and an adaptive PID. On lemniscate, IAPIDNN-DEKF achieves RMSE values of $0.078769$, $0.12086$ and $0.1672$. On sinusoidal trajectories, the method yields RMSE values of $0.01233$, $0.015138$ and $0.088707$, and on sinusoidal with perturbation, RMSE values are $0.021495$, $0.016504$ and $0.090142$ in x, y and $\theta$, respectively. These results demonstrate the superior performance of IAPIDNN-DEKF for achieving accurate control and state estimation. The proposed IAPIDNN-DEKF offers advantages in terms of accurate estimation, adaptability to dynamic environments and computational efficiency. This research contributes to the advancement of robust control techniques for WMRs and showcases the potential of IAPIDNN-DEKF to enhance trajectory tracking and state estimation capabilities in real-world applications. Full article

The construction of the underwater Internet of Things (UIoT) is crucial to marine resource development, environmental observation, and tactical surveillance. The underwater optical wireless communication (UOWC) system with its large bandwidth and wide coverage facilitates the high-capacity information interconnection within the UIoT networks over short and medium ranges. To enhance the coverage characteristics of the UOWC system, an optimized lemniscate-compensated layout of light-emitting diode (LED) array is proposed in this paper, which can ameliorate the received optical power and reliability at the receiving terminal. Compared with traditional circular and rectangular layouts, the received optical power and bit error rate (BER) performance of the proposed system are analyzed based on the Monte Carlo simulation method. The analysis results show that the proposed LED array achieves a smaller peak power deviation and mean square error of the received optical power under three typical seawater environments. Furthermore, the proposed LED-array scheme supports a better BER performance of the UOWC system. For example, in turbid seawater with a transmission depth of 9.5 m, the BER of the proposed LED array layout is 1 × 10⁻⁷, which is better than the BER of 3.5 × 10⁻⁶ and 1 × 10⁻⁴ under the other two traditional light source layouts. Full article