Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape

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

Collision-free motion of two robot arms in a common workspace

Collision-free motion of two robot arms in a common workspace is investigated. A collision-free motion is obtained by detecting collisions along the preplanned trajectories using a sphere model for the wrist of each robot and then modifying the paths and/or trajectories of one or both robots to avoid the collision. Detecting and avoiding collisions are based on the premise that: preplanned trajectories of the robots follow a straight line; collisions are restricted to between the wrists of the two robots (which corresponds to the upper three links of PUMA manipulators); and collisions never occur between the beginning points or end points on the straight line paths. The collision detection algorithm is described and some approaches to collision avoidance are discussed

An algorithm of avoiding obstacles with intelligent objects

In this research a path planning which is the first step of motion planning in robotic applications, away from an obstacle in an environment where exist many obstacles is developed. Different from the algorithms in literature, a path away from an obstacle is planned without determining the configuration free space in a place that contains many different shaped obstacles with the help of intelligent objects that are created object oriented programming(OOP). With the help of this developed algorithm not only the probable paths but also finding the shortest path and correcting it with the help of intelligent objects are evaluated at the same time. This algorithm is so profound that it can form the basic principles of many original Works with the additional in future works

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered