Autonomous and semi-autonomous robots play significant roles in space and terrestrial exploration, even more in unfavorable and dangerous environments. Although recent advances allow robots to evolve ...in many such environments, one of the most important problems remains the establishment of collision-free trajectories in static or partially (temporal) static environments. This paper presents a different approach to address this problem, proposing a methodology based on homotopy continuation methods (HCM) capable of generating collision-free trajectories in two and three dimensions. The basic idea behind the proposal relies on the construction of a nonlinear equation representing the map of the environment, making it possible to apply HCM methods to obtain collision-free paths. A series of simulations are presented to show the effectiveness of the method avoiding circular, semi-rectangular, spherical shaped and semi-parallelepipeds obstacles.
This article utilizes perturbation method (PM) to find an analytical approximate solution for the Quasi-Steady-State Michaelis-Menten problem. From the comparison of Figures and absolute error ...values, between approximate and numerical solutions, it is shown that the obtained solutions are accurate, and therefore, they explain the general behaviour of the Michaelis-Menten mechanism.
This article introduces two approximations that allow the evaluation of Fresnel integrals without the need for using numerical algorithms. These equations accomplish the characteristic of being ...continuous in the same interval as Fresnel. Both expressions have been determined applying the least squares method to suitable expressions. Accuracy of equations improves as x increases; as for small values of x, it is possible to achieve an absolute error less than 8×10-5. To probe the efficiency of the equations, two case studies are presented, both applied in the optics field. The first case is related to the semi-infinite opaque screen for Fresnel diffraction. In this case study Fresnel integrals are evaluated with the proposed equations to calculate the irradiance distribution and the Cornu spiral for diffraction computations of the Fresnel diffraction; obtained results show a good accuracy. The second case is related to the double aperture problem for Fresnel diffraction.
In this paper, it is shown that an extension of the formulas used to calculate the parameters of the one-dimensional canonical piecewise-linear model leads to a generalized methodology which can be ...also applicable to two dimensions. The proposal is based on an approach by which a two-dimensional function is reconstructed by the collection of parallel projections of one-dimensional functions. In order to verify the performance of this proposal, numerical simulations are contrasted to those obtained from the standard high-level canonical piecewise-linear methodology. The comparison reveals that our proposal allows the construction of the function not only requiring a shorter run time but also demanding less memory.
In the present work, we introduce an improved version of the hyperspheres path tracking method adapted for piecewise linear (PWL) circuits. This enhanced version takes advantage of the PWL ...characteristics from the homotopic curve, achieving faster path tracking and improving the performance of the homotopy continuation method (HCM). Faster computing time allows the study of complex circuits with higher complexity; the proposed method also decrease, significantly, the probability of having a diverging problem when using the Newton–Raphson method because it is applied just twice per linear region on the homotopic path. Equilibrium equations of the studied circuits are obtained applying the modified nodal analysis; this method allows to propose an algorithm for nonlinear circuit analysis. Besides, a starting point criteria is proposed to obtain better performance of the HCM and a technique for avoiding the reversion phenomenon is also proposed. To prove the efficiency of the path tracking method, several cases study with bipolar (BJT) and CMOS transistors are provided. Simulation results show that the proposed approach can be up to twelve times faster than the original path tracking method and also helps to avoid several reversion cases that appears when original hyperspheres path tracking scheme was employed.
In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a ...cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to 179.99999999∘ yielding a relative error of 0.01222747.
The three juvenile phases of the spiny lobster Panulirus argus (algal phase: 5–15 mm carapace length, CL; postalgal phase: 15–45 mm CL, and subadults: 45–80 mm CL) occur in the reef lagoon at Puerto ...Morelos, Mexico. The algal phase abounds in this lagoon, which is covered by extensive seagrass–algal meadows, but the density of postalgal and subadult juveniles is low, owing to the scarcity of crevice-type shelters suitable for these phases. The feeding ecology of the three juvenile phases was investigated to examine whether spatial or temporal differences in food intake, diet composition, or nutritional condition occurred among phases and could partially account for the low abundance of the larger juveniles. Juveniles were collected by divers at night, from January to November 1995, throughout the mid-lagoon and back-reef zones. Percent stomach fullness, relative weight of the digestive gland (RWDG, an index of nutritional condition), percent frequency of occurrence and percent volume of food categories in the diet were compared between sexes, juvenile phases, molt stages (postmolt, intermolt, premolt), seasons, and sampling zones (mid-lagoon and back-reef zones). Significant differences in stomach fullness occurred only among molt stages, mainly because postmolt individuals had emptier stomachs. The main food categories in all juvenile phases were crustaceans (mostly hermit crabs and brachyurans) and gastropods, but the food spectrum was wide, including many other animal taxa as well as plant matter. In June 1995, the epibenthic macrofauna was sampled in five sites in the lagoon that differed in their amount of vegetation. The most abundant taxa in all sites were decapods and gastropods, but density and diversity measures showed that the distribution of these potential prey taxa for juvenile P. argus was rather patchy. Diet overlap in juvenile lobsters was high between sexes, juvenile phases, sampling zones, seasons, and molting stages, indicating that all juveniles fed on the same general food categories throughout time. The only factor that affected the RWDG was the juvenile phase. RWDG was significantly lower in subadults than in algal and postalgal phases, suggesting a poorer nutritional condition in the largest juveniles. This may be related to the scarcity of suitable shelters for large juveniles throughout the lagoon, which may preclude subadults from exploiting food resources in areas of the lagoon where shelter is limited.
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