Super restricted edge connected Cartesian product graphs

An edge-cut F of a connected graph G is called a restricted edge-cut if G−F contains no isolated vertices. The minimum cardinality of all restricted edge-cuts is called the restricted edge-connectivity λ^′(G) of G. A graph G is said to be λ^′-optimal if λ^′(G)=ξ(G), where ξ(G) is the minimum edge-degree of G. A graph is said to be super-λ^′ if every minimum restricted edge-cut isolates an edge. This article gives a sufficient condition for Cartesian product graphs to be super-λ^′. Using this result, certain classes of networks which are recursively defined by the Cartesian product can be simply shown to be super-λ^′.     

Characterizations for restricted graphs of NLC-width 2

In this paper we give a finite forbidden subgraph characterization of graphs defined by NLC-width 2-expressions, by NLCT-width 2-expressions, or by linear NLC-width 2-expressions that have tree-width 1.     

On transitive orientations with restricted covering graphs

We consider the problem of finding a transitive orientation of a comparability graph, such that the edge set of its covering graph contains a given subset of edges. We propose a solution which employs the classical technique of modular tree decomposition. The method leads to a polynomial time algorithm to construct such an orientation or report that it does not exist.     

Algorithms for derivation of structurally stable Hamiltonian signed graphs

A graph S_p,q,n refers to a signed graph with p nodes and q edges with n being the number of negative edges. We introduce two theorems to facilitate identification of the complete set of balanced signed graph configurations for any p-node Hamiltonian signed graph in terms of p, q and n. This allows for the development of computational procedures to efficiently determine the structural stability of a signed graph. This is potentially useful for the planning and analysis of complex situations or scenarios which can be depicted as signed graphs. Through the application of the theorems, the state of balance of a signed graph structure or its affinity towards balance can be determined in a more time-efficient manner compared to any explicit enumeration algorithm.     

Incremental planning using conceptual graphs

Abstract

When performing a planning or design task in many domains it is often difficult to specify in advance what the precise goals are. It is therefore useful to have a system in which the planning process is performed interactively, with the solution approaching the users' intent incrementally through iterations of the planning process. A planning system intended to function in this way must be able to take goal specifications interactively rather than all at once at the beginning of the planning process. The planning process then becomes one of satisfying new goals as they are given by the user, modifying as little as possible the results of previous planning work. Incremental planning is an approach to interactive planning problems that allows a system to create a plan incrementally, modifying a previous plan to satisfy new or more precise goal specifications. In this paper we present an incremental planning system called the general constraint system (GCS) that is based on the conceptual programming environment (CP) developed at New Mexico State University and we show an example of the use of the system for a simple civil engineering design problem     

State agnostic planning graphs: deterministic,non-deterministic,and probabilistic planning

Planning graphs have been shown to be a rich source of heuristic information for many kinds of planners. In many cases, planners must compute a planning graph for each element of a set of states, and the naive technique enumerates the graphs individually. This is equivalent to solving a multiple-source shortest path problem by iterating a single-source algorithm over each source.We introduce a data-structure, the state agnostic planning graph, that directly solves the multiple-source problem for the relaxation introduced by planning graphs. The technique can also be characterized as exploiting the overlap present in sets of planning graphs. For the purpose of exposition, we first present the technique in deterministic (classical) planning to capture a set of planning graphs used in forward chaining search. A more prominent application of this technique is in conformant and conditional planning (i.e., search in belief state space), where each search node utilizes a set of planning graphs; an optimization to exploit state overlap between belief states collapses the set of sets of planning graphs to a single set. We describe another extension in conformant probabilistic planning that reuses planning graph samples of probabilistic action outcomes across search nodes to otherwise curb the inherent prediction cost associated with handling probabilistic actions. Finally, we show how to extract a state agnostic relaxed plan that implicitly solves the relaxed planning problem in each of the planning graphs represented by the state agnostic planning graph and reduces each heuristic evaluation to counting the relevant actions in the state agnostic relaxed plan. Our experimental evaluation (using many existing International Planning Competition problems from classical and non-deterministic conformant tracks) quantifies each of these performance boosts, and demonstrates that heuristic belief state space progression planning using our technique is competitive with the state of the art.     

Distributed minimum dominating set approximations in restricted families of graphs

A dominating set is a subset of the nodes of a graph such that all nodes are in the set or adjacent to a node in the set. A minimum dominating set approximation is a dominating set that is not much larger than a dominating set with the fewest possible number of nodes. This article summarizes the state-of-the-art with respect to finding minimum dominating set approximations in distributed systems, where each node locally executes a protocol on its own, communicating with its neighbors in order to achieve a solution with good global properties. Moreover, we present a number of recent results for specific families of graphs in detail. A unit disk graph is given by an embedding of the nodes in the Euclidean plane, where two nodes are joined by an edge exactly if they are in distance at most one. For this family of graphs, we prove an asymptotically tight lower bound on the trade-off between time complexity and approximation ratio of deterministic algorithms. Next, we consider graphs of small arboricity, whose edge sets can be decomposed into a small number of forests. We give two algorithms, a randomized one excelling in its approximation ratio and a uniform deterministic one which is faster and simpler. Finally, we show that in planar graphs, which can be drawn in the Euclidean plane without intersecting edges, a constant approximation factor can be ensured within a constant number of communication rounds.     

UAV path planning method for avoiding restricted areas

Intelligent Service Robotics - Recently, the industry of drone systems has come into the spotlight because a new potential market has been revealed. A considerable number of drones are deployed...     

一种限制搜索区域的多比例尺最优路径规划算法*

针对现有大区域范围路径规划算法存在的一些问题,提出一种限制搜索区域的多比例尺最优路径规划算法。该算法在进行路径规划时,一方面根据路网的多比例尺信息对路网进行分级,另一方面对搜索区域进行合理限制。测试实验表明此算法可以提高路径规划的效率。     

Causal approximate inversion for control of structurally flexible manipulators using nonlinear inner–outer factorization

A control scheme for flexible‐link manipulators is advanced which is based on the notion of nonlinear inner–outer factorization. It is well known that the inverse of the forward dynamics map from joint torques to manipulator tip motion is noncausal and cannot be implemented in conjunction with real‐time path planning. The methods used here determine causal approximations for the inverse dynamics using the inverse of the outer (stable and minimum phase) factor and a static approximation for the inverse of the inner (lossless but nonminimum phase) factor. The Hamilton–Jacobi equation that arises is approximated by a state‐dependent Riccati equation at each time step. The factorization procedure yields the corresponding joint trajectories which can serve as reference trajectories for closing joint‐based feedback loops. Experimental results from a planar three‐link manipulator with two flexible links demonstrate the efficacy of the procedure. © 2001 John Wiley & Sons, Inc.     

Hybrid ant colony algorithms for path planning in sparse graphs

The general problem of path planning can be modeled as a traveling salesman problem which assumes that a graph is fully connected. Such a scenario of full connectivity is however not always realistic. One such motivating example for us is the application of path planning for unmanned reconnaissance aerial vehicles (URAVs). URAVs are widely deployed for photography or imagery gathering missions of sites of interest. These sites can be targets in a combat zone to be investigated or sites inaccessible by ground transportation, such as those hit by forest fires, earthquake or other forms of natural disasters. The navigation environment is one where the overall configuration of the problem is a sparse graph. Unlike graphs that are fully connected, sparse graphs are not always Hamiltonian. In this paper, we describe hybrid ant colony algorithms (HACAs) proposed for path planning in sparse graphs since existing ant colony solvers designed for solving TSP do not apply to the present context directly. HACAs represent ant inspired algorithms incorporated with a local search procedure and some heuristic techniques for uncovering feasible route(s) or path(s) in a sparse graph within tractable time. Empirical results conducted on a set of generated sparse graphs demonstrate the excellent convergence property and robustness of HACAs in uncovering low risk and Hamiltonian visitation paths. Further, the obtained results also indicate that HACAs converge to secondary closed paths in situations where a Hamiltonian cycle does not exist theoretically or is not attainable within the bounded computational time window.     

Real-time path planning in dynamic virtual environments using multiagent navigation graphs

We present a novel approach for efficient path planning and navigation of multiple virtual agents in complex dynamic scenes. We introduce a new data structure, Multi-agent Navigation Graph (MaNG), which is constructed using first- and second-order Voronoi diagrams. The MaNG is used to perform route planning and proximity computations for each agent in real time. Moreover, we use the path information and proximity relationships for local dynamics computation of each agent by extending a social force model [Helbing05]. We compute the MaNG using graphics hardware and present culling techniques to accelerate the computation. We also address undersampling issues and present techniques to improve the accuracy of our algorithm. Our algorithm is used for real-time multi-agent planning in pursuit-evasion, terrain exploration and crowd simulation scenarios consisting of hundreds of moving agents, each with a distinct goal.     

Rapidly exploring random graphs: motion planning of multiple mobile robots

Rapidly exploring random trees (RRT) and probabilistic roadmaps (PRM) are sampling-based techniques being extensively used for robot path planning. In this paper, the tree structure of the RRT is generalized to a graph structure which enables a greater exploration. Exploration takes place simultaneously from multiple points in the map, all explorations fusing at multiple points producing well-connected graph architecture. Initially, in a typical RRT manner, the search algorithm attempts to reach the goal by expansions, and thereafter furtherer areas are explored. With some additional computation cost, as compared to RRT with a single robot, the results can be significantly improved. The so-formed graph is similar to roadmap produced by PRM. However as compared to PRM, the proposed algorithm has a more judicious search strategy and is adaptable to the number of nodes as a parameter. Experimental results are shown with multiple robots planned using prioritization scheme. Results show the betterment of the proposed algorithm as compared to RRT and PRM techniques.     

Motion planning of multiple mobile robots by a combination of learned visibility graphs and virtual impedance

A motion planning algorithm for multiple mobile robots is proposed in this paper. A hierarchical architecture with two layers 'learned visibility graph layer (upper layer)' and 'virtual impedance layer (lower layer)' (one of the potential field planning method) is presented. This system has the following characteristics: (1) is applicable to unknown dynamic environments, (2) is applicable to distributed multiple robot systems and (3) is capable of adequate path generation and motion. At the upper layer, efficient exploration of environments makes it possible to generate sub-shortest paths that avoid static obstacles. At the lower layer, on-line avoidance can be made with virtual impedance against moving obstacles such as other robots. Simulation results show the validity of the proposed method.     

Disassembly sequence structure graphs: An optimal approach for multiple-target selective disassembly sequence planning

Modern green products must be easy to disassemble. Specific target components must be accessed and removed for repair, reuse, recycling, or remanufacturing. Prior studies describe various methods for removing selective targets from a product. However, solution quality, model complexity, and searching time have not been considered thoroughly. The goal of this study is to improve solution quality, minimize model complexity, and reduce searching time. To achieve the goal, this study introduces a new ‘disassembly sequence structure graph’ (DSSG) model for multiple-target selective disassembly sequence planning, an approach for creating DSSGs, and methods for searching DSSGs. The DSSG model contains a minimum set of parts that must be removed to remove selected targets, with an order and direction for removing each part. The approach uses expert rules to choose parts, part order, and part disassembly directions, based upon physical constraints. The searching methods use rules to remove all parts, in order, from the DSSG. The DSSG approach is an optimal approach. The approach creates a high quality minimum-size model, in minimum time. The approach finds high quality, practical, realistic, physically feasible solutions, in minimum time. The solutions are optimized for number of removed parts, part order, part disassembly directions, and reorientations. The solutions remove parts in practical order. The solutions remove parts in realistic directions. The solutions consider contact, motion, and fastener constraints. The study also presents eight new design rules. The study results can be used to improve the product design process, increase product life-cycle quality, and reduce product environmental impact.     

Causal invertibility

It is well known that in a given resolution space structure the inverse of a memoryless operator, when it exists, is also memoryless. Given a Hilbert resolution space, we define new resolution structures which preserve causality. We show that every causal, causally invertible operator can be viewed as a memoryless operator between resolution spaces. The characterization is both necessary and sufficient. We also identify causal operators which can be considered as memoryless in a suitable resolution space.     

Rediscover flowers structurally

Existing methods for flower classification are usually focused on segmentation of the foreground, followed by extraction of features. After extracting the features from the foreground, global pooling is performed for final classification. Although this pipeline can be applied to many recognition tasks, however, these approaches have not explored structural cues of the flowers due to the large variation in their appearances. In this paper, we argue that structural cues are essential for flower recognition. We present a novel approach that explores structural cues to extract features. The proposed method encodes the structure of flowers into the final feature vectors for classification by operating on salient regions, which is robust to appearance variations. In our framework, we first segment the flower accurately by refining the existing segmentation method, and then we generate local features using our approach. We combine our local feature with global-pooled features for classification. Evaluations on the Oxford Flower dataset shows that by introducing the structural cues and locally pooling of some off-the-shelf features, our method outperforms the state-of-the-arts which employ specific designed features and metric learning.