This paper discusses a particle swarm optimization (PSO)-based motion-planning algorithm in a multiple-vehicle system that minimizes the traveling time of the slowest vehicle by considering, as constraints, the radial and tangential accelerations and maximum linear velocities of all vehicles. A class of continuous-curvature three-degree Bezier curves are selected as the basic shape of the vehicle trajectories to minimize the number of parameters required to express them mathematically. In addition, velocity profile generation using the local minimum of the radial-accelerated linear velocity profile, which reduces the calculation effort, is introduced. A new PSO-based search algorithm, called "particle-group-based PSO," is introduced to find the best combination of trajectories that minimizes the traveling time of the slowest vehicle. A particle group is designed to wrap up a set of particles representing each vehicle. The first and last two control points characterizing a curve are used as the state vector of a particle. Simulation results demonstrating the performance of the proposed method are presented. The main advantage of the proposed method is its minimization of the velocity-profile-generation time, and thereby, its maximization of the search time.
In this paper, the effect of an environmental temperature change on multilayer diffractive optical elements (MLDOEs) is studied in terms of the diffraction efficiency and the polychromatic integral diffraction efficiency (PIDE). The relation between the diffraction efficiency of MLDOEs and environmental temperature is analyzed theoretically, and examples of different MLDOEs are discussed in the visible and infrared wavebands. The result shows that the diffraction efficiency reduction is no more than 5% and the PIDE reduction is less than 1.5% for optical plastic MLDOEs in the visible waveband when the environmental temperature ranges from −62 to 71 • C, and that the decrease of both the diffraction efficiency and PIDE for MLDOEs is more significant in the mid-wave infrared than in the long-wave infrared. The analysis result can be considered during optical engineering design with MLDOEs.
A mathematical model of diffraction efficiency and polychromatic integral diffraction efficiency affected by environment temperature change and incident angle for three-layer diffractive optics with different dispersion materials is put forward, and its effects are analyzed. Taking optical materials N-FK5 and N-SF1 as the substrates of multilayer diffractive optics, the effect on diffraction efficiency and polychromatic integral diffraction efficiency with intermediate materials POLYCARB is analyzed with environment temperature change as well as incident angle. Therefore, three-layer diffractive optics can be applied in more wide environmental temperature ranges and larger incident angles for refractive-diffractive hybrid optical systems, which can obtain better image quality. Analysis results can be used to guide the hybrid imaging optical system design for optical engineers.
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