The Fast Marching Method is a very popular algorithm to compute times-of-arrival maps (distances map measured in time units). Since their proposal in 1995, it has been applied to many different applications such as robotics, medical computer vision, fluid simulation, etc. Many alternatives have been proposed with two main objectives: to reduce its computational time and to improve its accuracy. In this paper, we collect the main approaches which improve the computational time of the standard Fast
Path planning is general problem of mobile robots, which has special characteristics when applied to marine applications. In addition to avoid colliding with obstacles, in marine scenarios, environment conditions such as water currents or wind need to be taken into account in the path planning process. In this paper, several solutions based on the Fast Marching Method are proposed. The basic method focus on collision avoidance and optimal planning and, later on, using the same underlying method, the influence of marine currents in the optimal path planning is detailed. Finally, the application of these methods to consider marine robot formations is presented.
This work presents a path planning algorithm for 3D robot formations based on the standard Fast Marching Square (FM 2 ) path planning method. This method is enlarged in order to apply it to robot formations motion planning. The algorithm is based on a leader-followers scheme, which means that the reference pose for the follower robots is defined by geometric equations that place the goal pose of each follower as a function of the leader's pose. Besides, the Frenet-Serret frame is used to control the orientation of the formation. The algorithm presented allows the formation to adapt its shape so that the obstacles are avoided. Additionally, an approach to model mobile obstacles in a 3D environment is described. This model modifies the information used by the FM 2 algorithm in favor of the robots to be able to avoid obstacles. The shape deformation scheme allows to easily change the behaviour of the formation. Finally, simulations are performed in different scenarios and a quantitative analysis of the results has been carried out. The tests show that the proposed shape deformation method, in combination with the FM 2 path planner, is robust enough to manage autonomous movements through an indoor 3D environment.
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