Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

Trajectory Planning on Grids: Considering Speed Limit Constraints

Trajectory (path) planning is a well known and thoroughly studied field of automated planning. It is usually used in computer games, robotics or autonomous agent simulations. Grids are often used for regular discretization of continuous space. Many methods exist for trajectory (path) planning on grids, we address the well known A* algorithm and the state-of-the-art Theta* algorithm. Theta* algorithm, as opposed to A*, provides ‘any-angle‘ paths that look more realistic. In this paper, we provide an extension of both these algorithms to enable support for speed limit constraints.We experimentally evaluate and thoroughly discuss how the extensions affect the planning process showing reasonability and justification of our approach

Multi-robot team formation control in the GUARDIANS project

Purpose The GUARDIANS multi-robot team is to be deployed in a large warehouse in smoke. The team is to assist firefighters search the warehouse in the event or danger of a fire. The large dimensions of the environment together with development of smoke which drastically reduces visibility, represent major challenges for search and rescue operations. The GUARDIANS robots guide and accompany the firefighters on site whilst indicating possible obstacles and the locations of danger and maintaining communications links. Design/methodology/approach In order to fulfill the aforementioned tasks the robots need to exhibit certain behaviours. Among the basic behaviours are capabilities to stay together as a group, that is, generate a formation and navigate while keeping this formation. The control model used to generate these behaviours is based on the so-called social potential field framework, which we adapt to the specific tasks required for the GUARDIANS scenario. All tasks can be achieved without central control, and some of the behaviours can be performed without explicit communication between the robots. Findings The GUARDIANS environment requires flexible formations of the robot team: the formation has to adapt itself to the circumstances. Thus the application has forced us to redefine the concept of a formation. Using the graph-theoretic terminology, we can say that a formation may be stretched out as a path or be compact as a star or wheel. We have implemented the developed behaviours in simulation environments as well as on real ERA-MOBI robots commonly referred to as Erratics. We discuss advantages and shortcomings of our model, based on the simulations as well as on the implementation with a team of Erratics.</p

Incremental Sampling-based Algorithms for Optimal Motion Planning

During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms have been established so far. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path in the RRT converges almost surely to a non-optimal value. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path in the RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called the RRT$^*$ algorithm, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT$^*$ algorithms is asymptotically within a constant factor of that required by RRT.Comment: 20 pages, 10 figures, this manuscript is submitted to the International Journal of Robotics Research, a short version is to appear at the 2010 Robotics: Science and Systems Conference

ALGORITHM FOR GRAPH VISIBILITY OBTAINMENT FROM A MAP OF NON-CONVEX POLYGONS

Visibility graphs are basic planning algorithms,widely used in mobile robotics and other disciplines. The construction of a visibility graph can be considered a tool based on geometry that provides support to planning strategies in mobile robots. Visually, the method is used to solve that planning, which is quite extended due to the simplicity of operating with polygons, that represent obstacles in the environment. The cost of these algorithms tend to be quite low. The most sensitive issue of obtaining visibility between polygons is in cases in which the polygons are non-convex. In such cases, it is obligatory to know whether the area where one vertex of the polygon is found, is located in a convex or non-convex area, being desirable to distinguish between both situations in a simple way, issue that was not possible up to now. To obtain the visibility of non-convex polygons, the authors have developed a visual and intuitive method which gives the machine the ability to interpret the visibility with a simplicity similar to the human mind

Autonomous robots path planning: An adaptive roadmap approach

Developing algorithms that allow robots to independently navigate unknown environments is a widely researched area of robotics. The potential for autonomous mobile robots use, in industrial and military applications, is boundless. Path planning entails computing a collision free path from a robots current position to a desired target. The problem of path planning for these robots remains underdeveloped. Computational complexity, path optimization and robustness are some of the issues that arise. Current algorithms do not generate general solutions for different situations and require user experience and optimization. Classical algorithms are computationally extensive. This reduces the possibility of their use in real time applications. Additionally, classical algorithms do not allow for any control over attributes of the generated path. A new roadmap path planning algorithm is proposed in this paper. This method generates waypoints, through which the robot can avoid obstacles and reach its goal. At the heart of this algorithm is a method to control the distance of the waypoints from obstacles, without increasing its computational complexity. Several simulations were run to illustrate the robustness and adaptability of this approach, compared to the most commonly used path planning methods