The results show the ability of the time reversal technique to focalize impulsive waves back at the origin, even in the case of obstacles to the wave propagation.
In both cases we assume that the robot knows some a priori response to low level sensors (i.e. to contact sensors in the case of obstacles or to proximity target sensors in the case of targets) and has to learn the response to high level stimuli (i.e. distance sensors or visual input).
The proposed methodology is also extended to the case of obstacles that are moving in the workspace with a priori known trajectories.
It is a continuation of the preceding studies of a single-notch diffraction focused on the manifestation of the trapped mode and resonance transmission effects in the case of several obstacles.
The previous study by Warren et al. [68] shows that in the case of impassable obstacles, the pedestrian makes gradual turns when walking in the environment by changing his heading direction over several steps rather than abrupt switching direction.
The optimal trajectory, which corresponds to the minimum cost, is determined in the case of presence of obstacles in the environment, and the robot can move towards the target optimally, without colliding with obstacles.
In the case of a spherical obstacle, the point at which the boundary layer separates from the rear surface of the sphere shifts backward when the boundary layer becomes turbulent, away from the equator Q in Figure 15 and toward P′, and the eddies attached to the sphere therefore become smaller.
In the case of BlaBlaCar, the obstacle of distance is removed.
In this section, we state some lemmas which have been proved in the case of one-phase obstacle problem (see [9]).
As in the case of a circular obstacle, we can see a great accuracy between the numerical solution and the exact one, even if using only 12 cubic boundary elements for the boundary discretization.
