A two-dimensional (2-D) inverse synthetic aperture radar (ISAR) return signal model that employs stepped frequency (SF) modulation is developed. The geometry of the examined ISAR scenario is described by analytical geometrical equations. The target to be imaged is represented by a rectangular grid of point scatterers, moving along a rectilinear trajectory at constant speed, without any rotational motion. Thus, the inverse synthetic aperture results from the translational motion of the target for a short period of time. The process of ISAR signal modelling through coherent summation of the SF-modulated signals reflected from different point scatterers of the target is thoroughly described. Moreover, an efficient ISAR image reconstruction approach, including cross-correlation-based range compression and fast-Fourier-transform-based azimuth compression, is presented through analytical mathematical expressions. Numerical simulations are carried out for various SF ISAR scenarios and high-resolution ISAR images are obtained by applying the proposed ISAR image reconstruction approach. Simulation results (ISAR images and corresponding entropy values) indicate the validity of the proposed 2-D SF ISAR return signal model and the efficiency of the proposed imaging algorithms. Finally, a numerical simulation result is illustrated, which shows the comparison of the performance of the proposed ISAR image reconstruction algorithms based on SF and linear frequency modulation waveforms. It is shown that the two waveforms attain almost the same ISAR image resolution.

Robotic waste sorting systems offer a scalable and consistent alternative to manual sorting for Construction and Demolition Waste (CDW) by reducing labor-intensive tasks and exposure to hazardous conditions, while enabling the extraction of high-purity materials (e.g., polymers) from the waste streams. Despite advancements in perception systems, manipulation and planning remain significant bottlenecks, limiting widespread adoption due to high complexity and cost. This paper introduces RaapWaste, a robot- and application-agnostic planning framework specifically designed for waste sorting, addressing challenges in motion planning, scheduling, and real-world integration. Built on open-source resources, RaapWaste employs a modular and flexible architecture, enabling integration of diverse planning techniques and scheduling strategies. The framework aims to simulate the performance of real-world sorting equipment (e.g., robots, grippers). To evaluate its effectiveness, we conducted simulations with articulated and delta robots, as well as real-world tests on CDW sorting. Metrics such as the Sorting Throughput (ST) and Sorting Ratio (SR) reveal the RaapWaste’s capability across different waste sorting cases. In simulation, the delta robot achieved an SR exceeding 95%, while the UR5e showed consistent performance. In real-world CDW experiments, the system achieved a peak SR of 99% and maintained 80% using the SPT scheduler.

We consider the problem of radiation from a vertical short (Hertzian) dipole above flat lossy ground, which represents the well-known “Sommerfeld radiation problem” in the literature. The problem is formulated in a novel spectral domain approach, and by inverse three-dimensional Fourier transformation the expressions for the received electric and magnetic (EM) field in the physical space are derived as one-dimensional integrals over the radial component of wavevector, in cylindrical coordinates. This formulation appears to have inherent advantages over the classical formulation by Sommerfeld, performed in the spatial domain, since it avoids the use of the so-called Hertz potential and its subsequent differentiation for the calculation of the received EM field. Subsequent use of the stationary phase method in the high frequency regime yields closed-form analytical solutions for the received EM field vectors, which coincide with the corresponding reflected EM field originating from the image point. In this way, we conclude that the so-called “space wave” in the literature represents the total solution of the Sommerfeld problem in the high frequency regime, in which case the surface wave can be ignored. Finally, numerical results are presented, in comparison with corresponding numerical results based on Norton’s solution of the problem.