Topological properties for a perturbed first order sweeping process

In this paper, we consider a perturbed sweeping process for a class of subsmooth moving sets. The perturbation is general and takes the form of a sum of a single-valued mapping and a set-valued mapping. In the first result, we study some topological proprieties of the attainable set, the set-valued mapping considered here is upper semi-continuous with convex values. In the second result, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. Then, we deduce a solution of the time optimality problem.

Chimney Sweeping Robot Based on a Pneumatic Actuator

The need of improving the quality of professions led to the idea of simplification of processes during chimney sweeping. These processes have been essentially the same for tens of years. The goal of this paper is to bring an automation element into the chimney sweeping process, making the job easier for the chimney sweeper. In this paper, an essentially in-pipe robot is presented, which uses brushes to move while simultaneously cleaning the chimney or pipeline. The problem of the robot motion was reduced using an in-pipe robot due to the environments and obstacles that the robot has to face. An approach of using a pneumatic actuator for motion is presented along with the mechanical design. The next part of this paper is focused on the mathematical model of the robot motion, as well as its simulation and testing in the experimental pipeline. The simulations were compared with the experimental measurements and a few analyses were conducted describing the simulation model and its differences with the real robot, as well as considering certain parameters and their impact on the performance of the robot. The results are discussed at the end of the paper.

Search for smart evaders with sweeping agents

Suppose in a given planar circular region, there are smart mobile evaders and we want to find them using sweeping agents. We assume the sweeping agents are in a line formation whose total length is predetermined. We propose procedures for designing a sweeping process that ensures the successful completion of the task, thereby deriving conditions on the sweeping velocity of the linear formation and its path. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. We present results on the search time given the initial conditions.

Modeling of crowds in regions with moving obstacles

<p style='text-indent:20px;'>We present a model of crowd motion in regions with moving obstacles, which is based on the notion of measure sweeping process. The obstacle is modeled by a set-valued map, whose values are complements to <inline-formula><tex-math id="M1">\begin{document}$ r $\end{document}</tex-math></inline-formula>-prox-regular sets. The crowd motion obeys a nonlinear transport equation outside the obstacle and a normal cone condition (similar to that of the classical sweeping processes theory) on the boundary. We prove the well-posedness of the model, give an application to environment optimization problems, and provide some results of numerical computations.</p>