Towards optimal path computation in a simplicial complex

2019 ◽  
Vol 38 (8) ◽  
pp. 981-1009
Author(s):  
Subhrajit Bhattacharya
Keyword(s):  
Simplicial Complex ◽  
Metric Space ◽  
Search Algorithm ◽  
Optimal Path ◽  
Shortest Paths ◽  
Reconstruction Algorithm ◽  
Continuous Space ◽  
Rips Complex ◽  
Geodesic Paths ◽  
Configuration Manifold

Computing optimal path in a configuration space is fundamental to solving motion planning problems in robotics and autonomy. Graph-based search algorithms have been widely used to that end, but they suffer from drawbacks. We present an algorithm for computing the shortest path through a metric simplicial complex that can be used to construct a piece-wise linear discrete model of the configuration manifold. In particular, given an undirected metric graph, G, which is constructed as a discrete representation of an underlying configuration manifold (a larger “continuous” space typically of dimension greater than one), we consider the Rips complex, [Formula: see text], associated with it. Such a complex, and hence shortest paths in it, represent the underlying metric space more closely than what the graph does. Our algorithm requires only a local connectivity-based description of an abstract graph, [Formula: see text], and a cost/length function, [Formula: see text], as inputs. No global information such as an embedding or a global coordinate chart is required. The local nature of the proposed algorithm makes it suitable for configuration spaces of arbitrary topology, geometry, and dimension. We not only develop the search algorithm for computing shortest distances, but we also present a path reconstruction algorithm for explicitly computing the shortest paths through the simplicial complex. The complexity of the presented algorithm is comparable with that of Dijkstra’s search, but, as the results presented in this paper demonstrate, the shortest paths obtained using the proposed algorithm represent the geodesic paths in the original metric space significantly more closely.

scholarly journals On Vietoris–Rips complexes of ellipses

2019 ◽  
Vol 11 (03) ◽  
pp. 661-690 ◽  
Author(s):  
Michał Adamaszek ◽  
Henry Adams ◽  
Samadwara Reddy
Keyword(s):  
Simplicial Complex ◽  
Finite Subset ◽  
Metric Space ◽  
Scale Parameter ◽  
Main Tool ◽  
Small Eccentricity ◽  
Scale Parameters ◽  
Homotopy Types ◽  
Rips Complex ◽  
Vertex Set

For [Formula: see text] a metric space and [Formula: see text] a scale parameter, the Vietoris–Rips simplicial complex [Formula: see text] (resp. [Formula: see text]) has [Formula: see text] as its vertex set, and a finite subset [Formula: see text] as a simplex whenever the diameter of [Formula: see text] is less than [Formula: see text] (resp. at most [Formula: see text]). Though Vietoris–Rips complexes have been studied at small choices of scale by Hausmann and Latschev [13,16], they are not well-understood at larger scale parameters. In this paper we investigate the homotopy types of Vietoris–Rips complexes of ellipses [Formula: see text] of small eccentricity, meaning [Formula: see text]. Indeed, we show that there are constants [Formula: see text] such that for all [Formula: see text], we have [Formula: see text] and [Formula: see text], though only one of the two-spheres in [Formula: see text] is persistent. Furthermore, we show that for any scale parameter [Formula: see text], there are arbitrarily dense subsets of the ellipse such that the Vietoris–Rips complex of the subset is not homotopy equivalent to the Vietoris–Rips complex of the entire ellipse. As our main tool we link these homotopy types to the structure of infinite cyclic graphs.

scholarly journals The Effect of Route-choice Strategy on Transit Travel Time Estimates

2019 ◽  
Author(s):  
Nate Wessel ◽  
Steven Farber
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Imperfect Information ◽  
Optimal Path ◽  
Shortest Paths ◽  
Route Choice ◽  
Travel Times ◽  
Selection Strategies ◽  
Time Estimates ◽  
Average Travel Time

Estimates of travel time by public transit often rely on the calculation of a shortest-path between two points for a given departure time. Such shortest-paths are time-dependent and not always stable from one moment to the next. Given that actual transit passengers necessarily have imperfect information about the system, their route selection strategies are heuristic and cannot be expected to achieve optimal travel times for all possible departures. Thus an algorithm that returns optimal travel times at all moments will tend to underestimate real travel times all else being equal. While several researchers have noted this issue none have yet measured the extent of the problem. This study observes and measures this effect by contrasting two alternative heuristic routing strategies to a standard shortest-path calculation. The Toronto Transit Commission is used as a case study and we model actual transit operations for the agency over the course of a normal week with archived AVL data transformed into a retrospective GTFS dataset. Travel times are estimated using two alternative route-choice assumptions: 1) habitual selection of the itinerary with the best average travel time and 2) dynamic choice of the next-departing route in a predefined choice set. It is shown that most trips present passengers with a complex choice among competing itineraries and that the choice of itinerary at any given moment of departure may entail substantial travel time risk relative to the optimal outcome. In the context of accessibility modelling, where travel times are typically considered as a distribution, the optimal path method is observed in aggregate to underestimate travel time by about 3-4 minutes at the median and 6-7 minutes at the \nth{90} percentile for a typical trip.

scholarly journals X-RAY CT Reconstruction by using Spatially Non Homogeneous ICD Optimization

2019 ◽  
Vol 8 (6S3) ◽  
pp. 2043-2046
Keyword(s):  
Search Algorithm ◽  
Computational Cost ◽  
Selection Criterion ◽  
Closed Form Solution ◽  
Helical Ct ◽  
Reconstruction Algorithm ◽  
Form Solution ◽  
Ct Reconstruction ◽  
Practical Applications ◽  
Voxel Selection

Recent applications of conventional iterative coordinate descent (ICD) algorithms to multislice helical CT reconstructions have shown that conventional ICD can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts. However, high computational cost and long reconstruction times remain as a barrier to the use of conventional algorithm in the practical applications. Among the various iterative methods that have been studied for conventional, ICD has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization. The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed. The NH-ICD algorithm has a mechanism that adaptively selects voxels for update. First, a voxel selection criterion VSC determines the voxels in greatest need of update. Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence. In order to speed up each voxel update, we also propose a fast 3-D optimization algorithm that uses a quadratic substitute function to upper bound the local 3-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm. The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries.

scholarly journals Resilient Capacity-Aware Routing

2021 ◽  
pp. 411-429
Author(s):  
Stefan Schmid ◽  
Nicolas Schnepf ◽  
Jiří Srba
Keyword(s):  
Communication Networks ◽  
Search Algorithm ◽  
Shortest Paths ◽  
Capacity Constraints ◽  
High Availability ◽  
Worst Case ◽  
Shortest Path Routing ◽  
Link Failures ◽  
Algorithmic Question ◽  
Improved Performance

AbstractTo ensure a high availability, communication networks provide resilient routing mechanisms that quickly change routes upon failures. However, a fundamental algorithmic question underlying such mechanisms is hardly understood: how to verify whether a given network reroutes flows along feasible paths, without violating capacity constraints, for up to k link failures? We chart the algorithmic complexity landscape of resilient routing under link failures, considering shortest path routing based on link weights as e.g. deployed in the ECMP protocol. We study two models: a pessimistic model where flows interfere in a worst-case manner along equal-cost shortest paths, and an optimistic model where flows are routed in a best-case manner, and we present a complete picture of the algorithmic complexities. We further propose a strategic search algorithm that checks only the critical failure scenarios while still providing correctness guarantees. Our experimental evaluation on a benchmark of Internet and datacenter topologies confirms an improved performance of our strategic search by several orders of magnitude.

Obstacle avoidance and path planning of humanoid robot using fuzzy logic controller aided owl search algorithm in complicated workspaces

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abhishek Kumar Kashyap ◽  
Dayal R. Parhi
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Logic Controller ◽  
Fuzzy Controller ◽  
Search Algorithm ◽  
Optimal Path ◽  
Humanoid Robots ◽  
Steering Angle ◽  
Content Type ◽  
Hybrid Controller ◽  
Humanoid Nao

Purpose This paper aims to outline and implement a novel hybrid controller in humanoid robots to map an optimal path. The hybrid controller is designed using the Owl search algorithm (OSA) and Fuzzy logic. Design/methodology/approach The optimum steering angle (OS) is used to deal with the obstacle located in the workspace, which is the output of the hybrid OSA Fuzzy controller. It is obtained by feeding OSA's output, i.e. intermediate steering angle (IS), in fuzzy logic. It is obtained by supplying the distance of obstacles from all directions and target distance from the robot's present location. Findings The present research is based on the navigation of humanoid NAO in complicated workspaces. Therefore, various simulations are performed in a 3D simulator in different complicated workspaces. The validation of their outcomes is done using the various experiments in similar workspaces using the proposed controller. The comparison between their outcomes demonstrates an acceptable correlation. Ultimately, evaluating the proposed controller with another existing navigation approach indicates a significant improvement in performance. Originality/value A new framework is developed to guide humanoid NAO in complicated workspaces, which is hardly seen in the available literature. Inspection in simulation and experimental workspaces verifies the robustness of the designed navigational controller. Considering minimum error ranges and near collaboration, the findings from both frameworks are evaluated against each other in respect of specified navigational variables. Finally, concerning other present approaches, the designed controller is also examined, and major modifications in efficiency have been reported.

Priority-based speed control strategy for automated guided vehicle path planning in automated container terminals

2020 ◽  
Vol 42 (16) ◽  
pp. 3079-3090 ◽  
Author(s):  
Meisu Zhong ◽  
Yongsheng Yang ◽  
Shu Sun ◽  
Yamin Zhou ◽  
Octavian Postolache ◽  
...  
Keyword(s):  
Path Planning ◽  
Control Strategy ◽  
Search Algorithm ◽  
Waiting Times ◽  
Optimal Path ◽  
Speed Control ◽  
Container Terminals ◽  
Automated Guided Vehicles ◽  
Operating Efficiency ◽  
Continuous Increase

With the continuous increase in labour costs and the demands of the supply chain, improving the efficiency of automated container terminals has been a key factor in the development of ports. Automated guided vehicles (AGVs) are the main means of horizontal transport in such terminals, and problems in relation to their use such as vehicle conflict, congestion and waiting times have become very serious, greatly reducing the operating efficiency of the terminals. In this article, we model the minimum driving distance of AGVs that transport containers between quay cranes (QCs) and yard cranes (YCs). AGVs are able to choose the optimal path from pre-planned paths by testing the overlap rate and the conflict time. To achieve conflict-free AGV path planning, a priority-based speed control strategy is used in conjunction with the Dijkstra depth-first search algorithm to solve the model. The simulation experiments show that this model can effectively reduce the probability of AGVs coming into conflict, reduce the time QCs and YCs have to wait for their next task and improve the operational efficiency of AGV horizontal transportation in automated container terminals.

scholarly journals A Method for Obtaining Optimal Path in Angle and Avoiding Collision for Robotic Belt Grinding

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Tie Zhang ◽  
Xiaohong Liang ◽  
Ye Yu ◽  
Bin Zhang
Keyword(s):  
Coordinate System ◽  
Search Algorithm ◽  
Optimal Path ◽  
Recursive Method ◽  
Coordinate Plane ◽  
Angular Variation ◽  
Belt Grinding ◽  
Robotic Grinding ◽  
Path Search ◽  
Robotic Belt Grinding

The angular variation of the joints may be large, and collision between workpieces and tools may occur in robotic grinding. Therefore, this paper proposes an optimal robotic grinding path search algorithm based on the recursive method. The algorithm is optimized by changing the position of the tool coordinate system on the belt wheel; thus, the pose of the robot during grinding is adjusted. First, the position adjustment formula of the tool coordinate system is proposed, and a coordinate plane is established to describe the grinding path of the robot based on the position adjustment formula. Second, the ordinate value of this coordinate plane is dispersed to obtain the search field of the optimal robotic grinding path search algorithm. Third, an optimal robotic grinding path search algorithm is proposed based on the recursive method and single-step search process. Finally, the algorithm is implemented on the V-REP platform. Robotic grinding paths for V-shaped workpieces and S-shaped workpieces are generated using this algorithm, and a grinding experiment is performed. The experimental results show that the robotic grinding paths generated by this algorithm can smoothly complete grinding operations and feature a smaller angular variation of the joint than other methods and no collision.

scholarly journals Picking Path Optimization of Agaricus bisporus Picking Robot

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Xiaomei Hu ◽  
Zhaoren Pan ◽  
Shunke Lv
Keyword(s):  
Field Experiments ◽  
Search Algorithm ◽  
Optimal Path ◽  
Temperature Drop ◽  
Optimization Method ◽  
Labor Cost ◽  
Path Optimization ◽  
Parallel Optimization ◽  
Storage Location ◽  
Short Time

The design and application of the mushroom picking robot will greatly reduce the labor cost, and it has become one of the research hotspots in the world. Therefore, we independently developed an A. bisporus (a kind of mushroom) picking robot and introduced its functional principle in this paper. At the same time, in order to improve the picking efficiency of the picking robot, a picking path optimization algorithm based on TSP model is proposed. Firstly, based on the TSP model, a picking route model for A. bisporus was established to determine the storage location of each A. bisporus. Then, an improved simulated annealing (I-SA) search algorithm is proposed to find the optimal path sequence. By improving the path initialization module, path generation module, and temperature drop module, the I-SA search algorithm can optimize the picking path in a short time. Finally, in order to improve the stability and reduce the running time of the I-SA search algorithm, a parallel optimization method for global search (“rough exploration”) and local search (“precision exploration”) is proposed. Through simulation experiments, the I-SA search algorithm can search stable and excellent path solution in a relatively short time. Through field experiments on mushroom base, the efficiency of picking A. bisporus can be improved by 14% to 18%, which verifies the effectiveness of the I-SA search algorithm.

Optimal Path Planning of Redundant Cooperative Robots Under Equality and Inequality Constraints

2003 ◽  
Author(s):  
Ali Hosseini ◽  
Mehdi Keshmiri
Keyword(s):  
Path Planning ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Minimum Principle ◽  
Optimal Path ◽  
Inequality Constraints ◽  
Optimal Path Planning ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Cooperative Manipulators

Using kinematic resolution, the optimal path planning for two redundant cooperative manipulators carrying a solid object on a desired trajectory is studied. The optimization problem is first solved with no constraint. Consequently, the nonlinear inequality constraints, which model obstacles, are added to the problem. The formulation has been derived using Pontryagin Minimum Principle and results in a Two Point Boundary Value Problem (TPBVP). The problem is solved for a cooperative manipulator system consisting of two 3-DOF serial robots jointly carrying an object and the results are compared with those obtained from a search algorithm. Defining the obstacles in workspace as functions of joint space coordinates, the inequality constrained optimization problem is solved for the cooperative manipulators.

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