Quickest Paths in Simulations of Pedestrians

This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte

A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations

We present a fast sweeping method for a class of Hamilton-Jacobi equations that arise from time-independent problems in optimal control theory. The basic method in two dimensions uses a four point stencil and is extremely simple to implement. We test our basic method against Eikonal equations in different norms, and then suggest a general method for rotating the grid and using additional approximations to the derivatives in different directions in order to more accurately capture characteristic flow. We display the utility of our method by applying it to relevant problems from engineering

Fast Marching based Rendezvous Path Planning for a Team of Heterogeneous Vehicle

A formulation is developed for deterministically calculating the optimized paths for a multi-agent system consisting of heterogeneous vehicles. The essence of this formulation is the calculation of the shortest time for each agent to reach every grid point from its known initial position. Such arrival time map can be readily assessed using the Fast Marching Method (FMM), a computational algorithm originally designed for solving boundary value problems of the Eikonal equation. Leveraging the FMM method, we demonstrate that the minimal time rendezvous point and paths for all member vehicles can be uniquely determined with minimal computational concerns. To showcase the potential of our method, we use an example of a virtual rendezvous scenario that entails the coordination of a ship, an underwater vehicle, an aerial vehicle, and a ground vehicle to converge at the optimal location within the Tampa Bay area in minimal time. It illustrates the value of the developed framework in efficiently constructing continuous path planning, while accommodating different operational constraints of heterogeneous member vehicles

SLAM and exploration using differential evolution and fast marching

The exploration and construction of maps in unknown environments is a challenge for robotics. The proposed method is facing this problem by combining effective techniques for planning, SLAM, and a new exploration approach based on the Voronoi Fast Marching method. The final goal of the exploration task is to build a map of the environment that previously the robot did not know. The exploration is not only to determine where the robot should move, but also to plan the movement, and the process of simultaneous localization and mapping. This work proposes the Voronoi Fast Marching method that uses a Fast Marching technique on the Logarithm of the Extended Voronoi Transform of the environment"s image provided by sensors, to determine a motion plan. The Logarithm of the Extended Voronoi Transform imitates the repulsive electric potential from walls and obstacles, and the Fast Marching Method propagates a wave over that potential map. The trajectory is calculated by the gradient method

The path to efficiency: fast marching method for safer, more efficient mobile robot trajectories

This article provides a comprehensive view of the novel fast marching (FM) methods we developed for robot path planning. We recall some of the methods developed in recent years and present two improvements upon them: the saturated FM square (FM2) and an heuristic optimization called the FM2 star (FM2*) method. The saturated variation of the existing saturated FM2 provides safe paths that avoid unnecessarily long trajectories (like those computed using the Voronoi diagram). FM2* considerably reduces the computation time. As a result, these methods provide not only a trajectory but also an associated control speed for the robot at each point of the trajectory. The proposed methods are complete; if there is a valid trajectory, it will always be found and will always be optimal in estimated completion time.Comunidad de Madrid. S2009/DPI-1559/ROBOCITY2030 IIPublicad

3D robot formations path planning with fast marching square

This work presents a path planning algorithm for 3D robot formations based on the standard Fast Marching Square (FM2) 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 FM2 algorithm in favour 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 FM2 path planner, is robust enough to manage autonomous movements through an indoor 3D environment.Acknowledgments This work is funded by the project num ber DPI2010-17772, by the Spanish Ministry of Science and Innovation, and also by RoboCity2030-II-CM project (S2009/DPI-1559), funded by Programas de Actividades I+D en la Comunidad de Madrid and co-funded by Structural Funds of the EU.Publicad

Advances in Robot Navigation

Robot navigation includes different interrelated activities such as perception - obtaining and interpreting sensory information; exploration - the strategy that guides the robot to select the next direction to go; mapping - the construction of a spatial representation by using the sensory information perceived; localization - the strategy to estimate the robot position within the spatial map; path planning - the strategy to find a path towards a goal location being optimal or not; and path execution, where motor actions are determined and adapted to environmental changes. This book integrates results from the research work of authors all over the world, addressing the abovementioned activities and analyzing the critical implications of dealing with dynamic environments. Different solutions providing adaptive navigation are taken from nature inspiration, and diverse applications are described in the context of an important field of study: social robotics