Fast Marching Methods in path and motion planning: improvements and high-level applications

Mención Internacional en el título de doctorPath planning is defined as the process to establish the sequence of states a system must go through in order to reach a desired state. Additionally, motion planning (or trajectory planning) aims to compute the sequence of motions (or actions) to take the system from one state to another. In robotics path planning can refer for instance to the waypoints a robot should follow through a maze or the sequence of points a robotic arm has to follow in order to grasp an object. Motion planning is considered a more general problem, since it includes kinodynamic constraints. As motion planning is a more complex problem, it is often solved in a two-level approach: path planning in the first level and then a control layer tries to drive the system along the specified path. However, it is hard to guarantee that the final trajectory will keep the initial characteristics. The objective of this work is to solve different path and motion planning problems under a common framework in order to facilitate the integration of the different algorithms that can be required during the nominal operation of a mobile robot. Also, other related areas such as motion learning are explored using this framework. In order to achieve this, a simple but powerful algorithm called Fast Marching will be used. Originally, it was proposed to solve optimal control problems. However, it has became very useful to other related problems such as path and motion planning. Since Fast Marching was initially proposed, many different alternative approaches have been proposed. Therefore, the first step is to formulate all these methods within a common framework and carry out an exhaustive comparison in order to give a final answer to: which algorithm is the best under which situations? This Thesis shows that the different versions of Fast Marching Methods become useful when applied to motion and path planning problems. Usually, high-level problems as motion learning or robot formation planning are solved with completely different algorithms, as the problem formulation are mixed. Under a common framework, task integration becomes much easier bringing robots closer to everyday applications. The Fast Marching Method has also inspired modern probabilistic methodologies, where computational cost is enormously improved at the cost of bounded, stochastic variations on the resulting paths and trajectories. This Thesis also explores these novel algorithms and their performance.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Carlos Balaguer Bernaldo de Quirós.- Secretario: Antonio Giménez Fernández.- Vocal: Isabel Lobato de Faria Ribeir

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

Motion planning using fast marching squared method

Robotic motion planning have been, and still is, a very intense research field. Many problems have been already solved and even real-time, optimal motion planning algorithms have been proposed and successfully tested in real-world scenarios. However, other problems are not satisfactory solved yet and also new motion planning subproblems are appearing. In this chapter we detail our proposed solution for two of these problems with the same underlying method: non-holonomic planning and outdoor motion planning. The first is characterized by the fact that many vehicles cannot move in any direction at any time (car-like robots). Therefore, kinematic constrains need to be taken into account when planning a new path. Outoor motion planning focuses on the problem that has to be faced when a robot is going to work in scenarios with non-flat ground, with different floor types (grass, sand, etc.). In this case the path computed should take into account the capabilities of the robot to properly model the environment. In order to solve these problems we are using the Fast Marching Square method, which has proved to be robust and efficient in the recent past when applied to other robot motion planning subproblems.Publicad

General Path Planning Methodology for Leader-Follower Robot Formations

This paper describes a robust algorithm for mobile robot formations based on the Voronoi Fast Marching path planning method. This is based on the propagation of a wave throughout the model of the environment, the wave expanding faster as the wave's distance from obstacles increases. This method provides smooth and safe trajectories and its computational efficiency allows us to maintain a good response time. The proposed method is based on a local-minima-free planner; it is complete and has an O(n) complexity order where n is the number of cells of the map. Simulation results show that the proposed algorithm generates good trajectories.Comunidad de Madri

Fast methods for Eikonal equations: An experimental survey

Fast methods are very popular algorithms to compute time-of-arrival maps (distance maps measured in time units) solving the Eikonal equation. Since fast marching was proposed in 1995, it has been applied to many different applications, such as robotics, medical computer vision, fluid simulation, and so on. From then on, many alternatives to the original method have been proposed with two main objectives: reducing its computational time and improving its accuracy. In this paper, we collect the main single-threaded approaches, which improve the computational time of the standard fast marching method and study them within a common mathematical framework. Then, they are evaluated using isotropic environments, which are representative of their possible applications. The studied methods are the fast marching method with the binary heap, the fast marching method with Fibonacci heap, the simplified fast marching method, the untidy fast marching method, the fast iterative method, the group marching method, the fast sweeping method, the locking sweeping method, and the double dynamic queue method.This work is funded by the projects: "RoboCity2030-DIH-CM Madrid Robotics Digital Innovation Hub (Robtica aplicada a la mejora de la calidad de vida de los ciudadanos. Fase IV; S2018/NMT-4331), funded by Programas de Actividades I+D en la Comunidad de Madrid and cofunded by Structural Funds of the EU,'' and "Investigacion para la mejora competitiva del ciclo de perforacion y voladura en mineriai y obras subterraneas, mediante la concepcion de nuevas tecnicas de ingenieriai, explosivos, prototipos y herramientas avanzadas (TUNEL).'

Planning robot formations with fast marching square including uncertainty conditions

This paper presents a novel algorithm to solve the robot formation path planning problem working under uncertainty conditions such as errors the in robot's positions, errors when sensing obstacles or walls, etc. The proposed approach provides a solution based on a leader-followers architecture (real or virtual leaders) with a prescribed formation geometry that adapts dynamically to the environment. The algorithm described herein is able to provide safe, collision-free paths, avoiding obstacles and deforming the geometry of the formation when required by environmental conditions (e.g. narrow passages). To obtain a better approach to the problem of robot formation path planning the algorithm proposed includes uncertainties in obstacles' and robots' positions. The algorithm applies the Fast Marching Square (FM2) method to the path planning of mobile robot formations, which has been proved to work quickly and efficiently. The FM2 method is a path planning method with no local minima that provides smooth and safe trajectories to the robots creating a time function based on the properties of the propagation of the electromagnetic waves and depending on the environment conditions. This method allows to easily include the uncertainty reducing the computational cost significantly. The results presented here show that the proposed algorithm allows the formation to react to both static and dynamic obstacles with an easily changeable behavior.This work is included in the project number DPI2010-17772 funded by the Spanish Ministry of Science and Innovation and has been supported by the CAM Project S2009/DPI-1559/ROBOCITY2030 II, developed by the research team RoboticsLab at the University Carlos III of Madrid.Publicad

Fast Marching-based globally stable motion learning

In this paper, a novel motion learning method is introduced: Fast Marching Learning (FML). While other learning methods are focused on optimising probabilistic functions or fitting dynamical systems, the proposed method consists on the modification of the Fast Marching Square (FM2) path planning algorithm. Concretely, FM2 consists of expanding a wave through the environment with a velocity directly proportional to the distance to the closest obstacle. FML modifies these velocities in order to generalise the taught motions and reproduce them. The result is a deterministic, asymptotically globally stable learning method free of spurious attractors and unpredictable behaviours. Along the paper, detailed analysis of the method, its properties and parameters are carried out. Comparison against a state-of-the-art method and experiments with real data is also included.This work is supported by the Spanish Ministry of Science and Innovation under the projects DPI2010-17772 and CSD2009-00067.Publicad

Performance analysis of fast marching-based motion planning for autonomous mobile robots in ITER scenarios

Operations of transportation in cluttered environments require robust motion planning algorithms. Specially with large and heavy vehicles under hazardous operations of maintenance, such as in the ITER, an international nuclear fusion research project. The load transportation inside the ITER facilities require smooth and optimized paths with safety margin of 30 cm. The transportation is accomplished by large rhombic-like vehicles to exploit its kinematic capabilities. This paper presents the performance analysis of a motion planning algorithm to optimize trajectories in terms of clearance, smoothness and execution time in cluttered scenarios. The algorithm is an upgraded version of a previous one used in ITER, replacing the initialization implemented using Constrained Delaunay Triangulation by the Fast Marching Square. Exhaustive simulated experiments have been carried out in different levels of ITER buildings, comparing the performance of the algorithm using different metrics.This work was supported by the TECHNOFUSION R&D program funded by the Community of Madrid, project DPI2010-17772 funded by the Spanish Ministry of Science. IST activities received financial support from “Fundação para a Ciência e Tecnologia” through project Pest-OE/SADG/LA0010/2013. The views and opinions expressed herein do not necessarily reflect those of the European Commission.Publicad

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

Point-of-care manufacturing: a single university hospital's initial experience

The integration of 3D printing technology in hospitals is evolving toward production models such as point-of-care manufacturing. This study aims to present the results of the integration of 3D printing technology in a manufacturing university hospital.Analysis and interpretation of the data supported by Project PI18/01625 (Ministerio de Ciencia, Innovación y Universidades, Instituto de Salud Carlos III) and European Regional Development Fund (“Una manera de hacer Europa”)