We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.

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The ability to plan a multiple-target path that goes through places considered important is desirable for autonomous mobile robots that perform tasks in industrial environments. This characteristic is necessary for inspection robots that monitor the critical conditions of sectors in thermal, nuclear, and hydropower plants. This ability is also useful for applications such as service at home, victim rescue, museum guidance, land mine detection, and so forth. Multiple-target collision-free path planning is a topic that has not been very studied because of the complexity that it implies. Usually, this issue is left in second place because, commonly, it is solved by segmentation using the point-to-point strategy. Nevertheless, this approach exhibits a poor performance, in terms of path length, due to unnecessary turnings and redundant segments present in the found path. In this paper, a multiple-target method based on homotopy continuation capable to calculate a collision-free path in a single execution for complex environments is presented. This method exhibits a better performance, both in speed and efficiency, and robustness compared to the original Homotopic Path Planning Method (HPPM). Among the new schemes that improve their performance are the Double Spherical Tracking (DST), the dummy obstacle scheme, and a systematic criterion to a selection of repulsion parameter. The case studies show its effectiveness to find a solution path for office-like environments in just a few milliseconds, even if they have narrow corridors and hundreds of obstacles. Additionally, a comparison between the proposed method and sampling-based planning algorithms (SBP) with the best performance is presented. Furthermore, the results of case studies show that the proposed method exhibits a better performance than SBP algorithms for execution time, memory, and in some cases path length metrics. Finally, to validate the feasibility of the paths calculated by the proposed planner; two simulations using the pure-pursuit controlled and differential drive robot model contained in the Robotics System Toolbox of MATLAB are presented.

Natural sources of green energy include sunshine, water, biomass, geothermal heat, and wind. These energies are alternate forms of electrical energy that do not rely on fossil fuels. Green energy is environmentally benign, as it avoids the generation of greenhouse gases and pollutants. Various systems and equipment have been utilized to gather natural energy. However, most technologies need a huge amount of infrastructure and expensive equipment in order to power electronic gadgets, smart sensors, and wearable devices. Nanogenerators have recently emerged as an alternative technique for collecting energy from both natural and artificial sources, with significant benefits such as light weight, low-cost production, simple operation, easy signal processing, and low-cost materials. These nanogenerators might power electronic components and wearable devices used in a variety of applications such as telecommunications, the medical sector, the military and automotive industries, and internet of things (IoT) devices. We describe new research on the performance of nanogenerators employing several green energy acquisition processes such as piezoelectric, electromagnetic, thermoelectric, and triboelectric. Furthermore, the materials, applications, challenges, and future prospects of several nanogenerators are discussed.