Search Results (13)

This paper addresses the real-time trajectory generation problem for hypersonic glide vehicles (HGVs) during atmospheric entry, subject to complex constraints including aerothermal limits, actuator bounds, and no-fly zones (NFZs). To achieve efficient and reliable trajectory planning, a two-phase hp-adaptive sequential convex programming (SCP) framework is proposed. NFZ avoidance is reformulated as a soft objective to enhance feasibility under tight geometric constraints. In Phase I, a shrinking-trust-region strategy progressively tightens the soft trust-region radius by increasing the penalty weight, effectively suppressing linearization errors. A sensitivity-driven mesh refinement method then allocates collocation points based on their contribution to the objective function. Phase II applies residual-based refinement to reduce discretization errors. The resulting reference trajectory is tracked using a linear quadratic regulator (LQR) within a reference-trajectory-tracking guidance (RTTG) architecture. Simulation results demonstrate that the proposed method achieves convergence in only a few iterations, generating high-fidelity trajectories within 2–3 s. Compared to pseudospectral solvers, the method achieves over 12× computational speed-up while maintaining kilometer-level accuracy. Monte Carlo tests under uncertainties confirm a 100% success rate, with all constraints satisfied. These results validate the proposed method’s robustness, efficiency, and suitability for onboard real-time entry guidance in dynamic mission environments. Full article

In this study, we investigated circle design in a bubble chart. The bubble chart that we designed has a unit circle at the center and is surrounded by a series of layered circle rings. In order to add the next layer of circles, there is always a silhouette circle that is tangential to all circles in the newest layer. The extension of the circle is partitioned into two classes: one in which each layer has the same number of circles with the same radii, and another in which the new layer has circles with different radii. We solve this problem geometrically and/or algebraically if the problem is simple and present a heuristic algorithm for solving more complex problems. Full article

Malfatti’s problem is the problem of fitting three circles into a triangle such that they are tangent to each other and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to include T_n = 1 + 2 + … + n circles inside the triangle with special tangency properties among the circles and triangle sides; this problem is referred to as the extended Malfatti problem or the Tri(T_n) problem. In the extended Malfatti problem, the number of circles in the triangle is a triangle number because the tangency properties between the internal circles and the three sides of the triangle have a special type of structure; that is, the corner circle is tangent to two sides of the triangle and two other circles, the boundary circles are tangent to one side of the triangle and four other circles, and the inner circles are always tangent to six other circles. The circles we find in the extended Malfatti problem have the following property: the smallest and largest radii of the circles differ to a great extent. In the study presented herein, we propose algorithms to solve the problem that the tangency properties between the circles and the sides of the triangle are not fixed, so that the number of circles in the triangle is not necessarily a triangle number. The purpose of this change is to attempt to establish the radii of the circles in the triangle within a small range. Full article

Malfatti’s problem involves three circles (called Malfatti circles) that are tangent to each other and two sides of a triangle. In this study, our objective is to extend the problem to find 6, 10, … $\sum _1^{n}i$ (n > 2) circles inside the triangle so that the three corner circles are tangent to two sides of the triangle, the boundary circles are tangent to one side of the triangle, and four other circles (at least two of them being boundary or corner circles) and the inner circles are tangent to six other circles. We call this problem the extended general Malfatti’s problem, or the Tri(T_n) problem, where Tri means that the boundary of these circles is a triangle, and T_n is the number of circles inside the triangle. In this paper, we propose an algorithm to solve the Tri(T_n) problem. Full article

The paper presents a novel small-footprint varactor diode-based reconfigurable reflectarray (RRA) design and investigates its power reflection efficiency theoretically and experimentally in a real-life indoor environment. The surface is designed to operate at 865.5 MHz and is intended for simultaneous use with other wireless power transfer (WPT) efficiency-improving techniques that have been recently reported in the literature. To the best of the authors’ knowledge, no RRA intended to improve the performance of antenna-based WPT systems operating in the sub-GHz range has been designed and studied both theoretically and experimentally so far. The proposed RRA is a two-layer structure. The top layer contains electronically tunable phase shifters for the local phase control of an incoming electromagnetic wave, while the other one is fully covered by metal to reduce the phase shifter size and RRA’s backscattering. Each phase shifter is a pair of diode-loaded 8-shaped metallic patches. Extensive numerical studies are conducted to ascertain a suitable set of RRA unit cell parameters that ensure both adequate phase agility and reflection uniformity for a given varactor parameter. The RRA design parameter finding procedure followed in this paper comprises several steps. First, the phase and amplitude responses of a virtual infinite double periodic RRA are computed using full-wave solver Ansys HFSS. Once the design parameters are found for a given set of physical constraints, the phase curve of the corresponding finite array is retrieved to estimate the side lobe level due to the finiteness of the RRA aperture. Then, a diode reactance combination is found for several different RRA reflection angles, and the corresponding RRA radiation pattern is computed. The numerical results show that the side lobe level and the deviation of the peak reflected power angles from the desired ones are more sensitive to the reflection coefficient magnitude uniformity than to the phase agility. Furthermore, it is found that for scanning angles less than 50°, satisfactory reflection efficiency can be achieved by using the classical reactance profile synthesis approach employing the generalized geometrical optics (GGO) approximation, which is in accord with the findings of other studies. Additionally, for large reflection angles, an alternative synthesis approach relying on the Floquet mode amplitude optimization is utilized to verify the maximum achievable efficiency of the proposed RRA at large angles. A prototype consisting of 36 elements is fabricated and measured to verify the proposed reflectarray design experimentally. The initial diode voltage combination is found by applying the GGO-based phase profile synthesis method to the experimentally obtained phase curve. Then, the voltage combination is optimized in real time based on power measurement. Finally, the radiation pattern of the prototype is acquired using a pair of identical 4-director printed Yagi antennas with a gain of 9.17 dBi and compared with the simulated. The calculated results are consistent with the measured ones. However, some discrepancies attributed to the adverse effects of biasing lines are observed. Full article

The paper presents the use of a supervised active learning approach for the solution of a simulation-driven design optimization (SDDO) problem, pertaining to the resistance reduction of a destroyer-type vessel in calm water. The optimization is formulated as a single-objective, single-point problem with both geometrical and operational constraints. The latter also considers seakeeping performance at multiple conditions. A surrogate model is used, based on stochastic radial basis functions with lower confidence bounding, as a supervised active learning approach. Furthermore, a multi-fidelity formulation, leveraging on unsteady Reynolds-averaged Navier–Stokes equations and potential flow solvers, is used in order to reduce the computational cost of the SDDO procedure. Exploring a five-dimensional design space based on free-form deformation under limited computational resources, the optimal configuration achieves a resistance reduction of about 3% at the escape speed and about 6.4% on average over the operational speed range. Full article

We present a multi-objective topology optimization method based on the Non-Sorting Genetic Algorithm II (NSGA-II). The presented approach is a tool for early-stage engineering applications capable of providing insights into the complex relationship between structural features and the performance of a design without a priori assumptions about objective space. Mass reduction, linear elastic deformation, and stationary thermal conduction are considered simultaneously with three additional constraints. The specifically developed genotype-phenotype mapping ensures the practical benefit of obtained design propositions and significantly reduces computational effort to generate a dense set of Pareto solutions. The mapping procedure smooths probabilistically generated structures, removes unconnected material, and refines the spatial discretization for the subsequently used finite element solver. We present sets of Pareto optimal solutions to large three-dimensional design problems with multiple objectives and multiple near-application constraints that are feasible design propositions for engineering design. Geometrical features present in the obtained Pareto set are discussed. Full article

This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved using off-the-shelf optimization solvers. The main motivation for this approach is that Bernstein polynomials possess favorable geometric properties and yield computationally efficient algorithms that enable a trajectory planner to efficiently evaluate and enforce constraints along the vehicles’ trajectories, including maximum speed and angular rates as well as minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties and algorithms, feasibility and safety constraints typically imposed on autonomous vehicle operations can be enforced and guaranteed independently of the order of the polynomials. To support the use of the proposed method we introduce BeBOT (Bernstein/Bézier Optimal Trajectories), an open-source toolbox that implements the operations and algorithms for Bernstein polynomials. We show that BeBOT can be used to efficiently generate feasible and collision-free trajectories for single and multiple vehicles, and can be deployed for real-time safety critical applications in complex environments. Full article

In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position. The problem can be decomposed into two simple sub-problems and can be solved with angle constraints. A polynomial equation of one variable is solved to determine the focal length, and then a geometric approach is used to determine the absolute orientation. The geometric derivations are easy to understand and significantly improve performance. Rewriting the camera model with the known camera position leads to a simpler and more efficient closed form solution, and this gives a single solution, without the multi-solution phenomena of perspective-three-point (P3P) solvers. Experimental results demonstrated that our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, with synthetic data and real images. Full article

A design method was developed for automated, systematic design of hydrokinetic turbine rotor blades. The method coupled a Computational Fluid Dynamics (CFD) solver to estimate the power output of a given turbine with a surrogate-based constrained optimization method. This allowed the characterization of the design space while minimizing the number of analyzed blade geometries and the associated computational effort. An initial blade geometry developed using a lifting line optimization method was selected as the base geometry to generate a turbine blade family by multiplying a series of geometric parameters with corresponding linear functions. A performance database was constructed for the turbine blade family with the CFD solver and used to build the surrogate function. The linear functions were then incorporated into a constrained nonlinear optimization algorithm to solve for the blade geometry with the highest efficiency. A constraint on the minimum pressure on the blade could be set to prevent cavitation inception. Full article

The systematic kinematic analysis method for planar link mechanisms based on their unique procedures can clearly show the analysis process. The analysis procedure is expressed by a combination of many kinds of conversion functions proposed as the minimum calculation units for analyzing a part of the mechanism. When it is desired to perform this systematic kinematics analysis for a specific linkage mechanism, expert researchers can accomplish the analysis by searching for the procedure by themselves, however, it is difficult for non-expert users to find the procedure. This paper proposes the automatic procedure extraction algorithm for the systematic kinematic analysis of closed-loop planar link mechanisms. By limiting the types of conversion functions to only geometric calculations that are related to the two-link chain, the analysis procedure can be represented by only one type transformation function, and the procedure extraction algorithm can be described as a algorithm searching computable 2-link chain. The configuration of mechanism is described as the “LJ-matrix”, which shows the relationship of connections between links with pairs. The algorithm consists of four sub-processes, namely, “LJ-matrix generator”, “Solver process”, “Add-link process”, and “Over-constraint resolver”. Inputting the sketch of the mechanism into the proposed algorithm, it automatically extracts unique analysis procedure and generate a kinematic analysis program as a MATLAB code based on it. Several mechanisms are analyzed as examples to show the usefulness of the proposed method. Full article

The LS89 high pressure axial turbine vane was originally designed and optimized for a downstream isentropic Mach number of 0.9. This profile has been widely used for computational fluid dynamics (CFD) validation in the open literature but very few attempts have been made to improve the already optimized design. This paper presents a sound methodology to design and optimize the LS89 using computer-aided design (CAD) at design conditions. The novelty of the study resides in the parametrization of design space, which is done at the CAD level, and the detailed analysis of the aerodynamic performance of the optimized design. Higher level constraints are imposed on the shape, such as the trailing edge thickness, the axial chord length, and G2 geometric continuity between the suction side and pressure side at the leading edge. The gradients used for the optimization are obtained by applying algorithmic differentiation to the CAD kernel and grid generator and the discrete adjoint method to the CFD solver. A reduction of almost 12% entropy generation is achieved, which is equivalent to a 16% total pressure loss reduction. The entropy generation is reduced while keeping the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by the L-BFGS-B algorithm. The flow is governed by the Reynolds-averaged Navier-Stokes equations and the one-equation transport Spalart-Allmaras turbulence model. The optimal profile is compared and benchmarked against the baseline case. Full article

The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD) workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP) algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier–Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included. Full article