英语科技论文写作
论文题目：学生姓名：学号：
Robot formation motion planning
using Fast Marching
Dear Editor,
Cover letter
We would like to submit the enclosed manuscript entitled \Fast Marching\
We are particularly interested in leader-following deformable formations, where the leader can be virtual and tracks a given trajectory, pulling the followers behind it according to nominal geometry specifications (e.g., desired inter-vehicle distances) that can change within a given range so as to accommodate environmental conditions. Leonard and Fiorelli introduced the concept of artificial potential fields between formation vehicles, some of them virtual leaders. The nominal inter-vehicle distance corresponds to minima of the potential functions, representing equilibrium points. We deeply appreciate your consideration of our manuscript, and we look forward to receiving comments from the reviewers. If you have any queries, please don’t hesitate to contact me. Thank you and best regards. Yours sincerely.
Highlight：As stated before, the FM method is based on a potential function without local minima that
provides smooth trajectories. The advantage of using the VFM method, as proposed here, is that each robot, at each time, has one single potential which is attractive to the objective and repulsive from walls, obstacles, and the other robots of the formation, while keeping the desired nominal inter-robot distances.
Robot formation motion planning using Fast
Marching
Abstract: This paper presents the application of the Voronoi FastMarching (VFM) method to path planning of mobile formation robots. The VFM method uses the propagation of awave (FastMarching) operating on the world model to determine a motion plan over a viscosity map (similar to the refraction index in optics) extracted from the updated map model. The computational efficiency of the method allows the planner to operate at high rate sensor frequencies. This method allows us to maintain good response time and smooth and safe planned trajectories. The navigation function can be classified as a type of potential field, but it has no local minima, it is complete (it finds the solution path if it exists) and it has a complexity of order n(O(n)), where n is the number of cells in the environment map. The results presented in this paper show how the proposed method behaves with mobile robot formations and generates trajectories of good quality without problems of local minima when the formation encounters non-convex obstacles.
OCIS codes: (100.0100) Image processing; (100.6890) Three-dimensional image processing
References and links
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1. Introduction
Formation control is currently a topic of vast research in the literature. Different approaches can be classified according to different criteria. Beard et al. [1] consider the different design approaches and classify them into the following three groups. Leader-following,where one vehicle is designated as the leader and the others as followers. The leader posture (position and orientation) is determined by a trajectory to be tracked or by external control objectives (e.g., joy sticked by a human) and the followers must track the leader following some prescribed geometry, possibly dynamically changing over time [2]. Behavioral, where the motion of each vehicle results from a weighted average of several behaviors, ultimately contributing to a desired group behavior [3]. Virtual structure, where the entire formation is treated as a single structure, whose desired motion is translated into the desired motion of each vehicle [4]. Another possible criterion takes into account the rigidity of the formation geometry: some authors specify the full geometry, e.g., the distances and bearings between the vehicles of the formation, and control each vehicle to ensure that these are accurately achieved [5], requiring a coordination architecture to switch between geometries when required by the environmental characteristics (e.g., narrow passages, open spaces) [6]; others see the formation as a dynamic geometry structure, that naturally becomes distorted in the presence of obstacles and/or environmental geometry changes [7].
We are particularly interested in leader-following deformable formations, where the leader can be virtual and tracks a given trajectory, pulling the followers behind it according to nominal geometry specifications (e.g., desired inter-vehicle distances) that can change within a given range so as to accommodate environmental conditions. Leonard and Fiorelli [8] introduced the concept of artificial potential fields between formation vehicles, some of them virtual leaders. The nominal inter-vehicle distance corresponds to minima of the potential functions, representing equilibrium points.
that balance inter-vehicle repulsion, vehicle–obstacle repulsion,and follower–leader attraction. MacArthur and Crane proposed a similar approach but virtual spring-damper systems were used to ‘‘connect’’ the formation vehicles [9]. The drawback of such approaches is the well-known local minima problem of potential fields, that may lead to breaking of the formation in the presence of non-convex shaped obstacles.
In a previous paper [10], we have introduced one possible solution to this problem, where the
followers keep track of the n most recent positions of the leader, and not only its current position, to be dragged away from the obstacle trap. However, this method has not been proven to work for all possible situations.We have also introduced a method to avoid local minima of potential fields for a single vehicle, using the Voronoi Fast Marching (VFM) method and the Fast Marching squared (FM2) method [11–13].
In this paper, we use the FastMarching (FM) algorithm to control a leader–follower deformable formation, where the trajectory of the leader in an environment cluttered by obstacles is computed using the VFM algorithm. Each follower attempts to reach, ateach iteration step, a nominal sub-goal position related to the desired leader trajectory, but takes into account the positions o The other followers and the environmental objects, both seen as obstacles. This influences the metrics used by these algorithms effectively deforming the followers’ trajectories. In this way we ensure that non-convex obstacles do not break the formation and that the inter-vehicle distances are smoothly deformed while the formation moves from open areas to regions with obstacles narrow corridors, and narrow passages.
The paper is organized as follows. In Section 2 the FastMarching method and some of its variants are summarized. Its application to robot formations is described in Section 3. The results of applying the method to two different formation geometries in a diversity of simulation scenarios are presented in Section 4. The paper ends with conclusions and prospects for future work (Section 5). 2. Fast Marching method and Voronoi Fast Marching method 2.1. Introduction to Fast Marching and level sets
The FM algorithm was introduced by Sethian in 1996 and is a numerical algorithm that approximates the viscosity solution of the eikonal equation |?(D(x))| = P(x), (1)i.e., the equation for light propagation in a non-homogeneous medium. The level set {x/D(x) = t} of the solution represents the wave front advancing with a medium velocity P(x), which is the inverse of the medium’s refraction index R(x). Therefore, the eikonal equation can be written as |?(D(x))| = 1/R(x). The resulting function D is a distance function, and if the medium velocity P is constant, it can be seen as the Euclidean distance function to a set of starting points, usually the goal points. If the medium is non-homogeneous and the velocity P is not constant, the function D represents the distance function measured with the metrics P(x) or the arrival time of the wave front to point x. The FM method is used to solve the eikonal equation and is very similar to the Dijkstra algorithm that finds the shortest paths on graphs, though it is applied to continuous media. Using a gradient descent of the distance function D, one is able to extract a good approximation of the shortest path (geodesic) in various settings (Euclidean distance with constant P and a weighted Riemannian manifold with varying P). 2.2. Intuitive introduction to the Fast Marching motion planner
To get a motion planner for mobile robots with desirable properties, such as smoothness and safety,we can think of attractive potentials. In Nature, there are phenomena with a similar behaviour,e.g., electromagnetic waves. If there is an antenna at the goal point that emits an electromagnetic wave, then the robot can drive to the destination by tracing the waves back to the source. In general, the concept of electromagnetic waves is especially interesting, since the potential and its associated vector field have the good properties desired for the trajectory, such as smoothness and the absence of local minima.
This attractive potential still has some problems. The most important one that typically arises in mobile robotics is that optimal motion plans may bring robots too close to obstacles or people, which is not safe. This problem has been treated by