Corridor Problem Research Articles

Sampling-Based Global Path Planning Using Convex Polytope Approximation for Narrow Collision-Free Space of Humanoid

In this paper, we propose a computationally fast method of sampling-based global path planning for humanoids under Manifold Constraints such as closed kinematic chains and Volume-Reducing Constraints such as collision avoidance. In multi-contact and whole-body manipulation of humanoids, narrow collision-free space causes path planning to take a long computation time (narrow corridor problem). In previous research of constrained planning, Manifold Constraints are locally approximated by tangent plane, and steering motions along Manifold Constraints are found efficiently by projection or continuation methods. In this paper, we applied constrained planning algorithms to collision avoidance. Since tangent plane cannot approximate Volume-Reducing Constraints, we adopted convex polytope instead of tangent plane. Both Manifold Constraints and Volume-Reducing Constraints are locally approximated by convex polytope with linear equality and inequality constraints, and steering motions inside the convex polytope are found efficiently by the SQP-based prioritized inverse kinematics. We developed CP-KPIECE (Convex Polytope approximation-based KPIECE) with this approach. Benchmarks using the humanoid JAXON proved the effectiveness of our approach for fast path planning in narrow collision-free space of humanoids.

A method for finding a least-cost corridor on an ordinal-scaled raster cost surface

ABSTRACT The least-cost path problem is a widely studied problems in geographic information science. In raster space, the problem is to find a path that accumulates the least amount of cost between two locations based on the assumptions that the path is a one-dimensional object (represented by a string of cells) and that the cost (per unit length) is measured on a quantitative scale. Efficient methods are available for solution of this problem when at least one of these assumptions is upheld. This is not the case when the path has a width and is a two-dimensional object called a corridor (represented by a swath of cells) and the cost (per unit area) is measured on an ordinal scale. In this paper, we propose one additional model that characterizes a least-cost corridor on an ordinal-scaled raster cost surface – or a least ordinal-scaled cost corridor for short – and show that it can be transformed into an instance of a multiobjective optimization problem known as the preferred path problem with a lexicographic preference relation and solved accordingly. The model is tested through computational experiments with artificial landscape data as well as real-world data. Results show that least ordinal-scaled cost corridors are guaranteed to contain smaller areas of higher cost than conventional least-cost corridors at the expense of more elongated and winding forms. The least ordinal-scaled cost corridor problem has computational complexity of O(n 2.5) in the worst case, resulting in a longer computational time than least-cost corridors. However, this difference is smaller in practice.

Kartarpura Corridor: A Step towards Peace

The Kartarpur Corridor's importance and the politics that supported its creation are examined in this essay. This project has sent a message to the world that Pakistan has implemented the corridor, not only granting rights to its own minority but also to the Sikh population across the border. It also calls attention to the symbolic value of the corridor and aims to use religious diplomacy as a method of fostering stronger diplomatic and commercial relations. As a result, religious groups throughout the world and communities in general value this massive initiative. The essay examines the corridor's problems and difficulties as well. Reservations concerning the potential of terrorist infiltration, Pakistan's backing for Sikh separatism, the sorts of permission and regulation regimes to be implemented, the need for Indian consular access to pilgrims in Pakistan, and concerns about these issues are just a few.

A method for finding least-cost corridors with reduced distortion in raster space

ABSTRACT Given a grid of cells, each having a value indicating its cost per unit area, a variant of the least-cost path problem is to find a corridor of a specified width connecting two termini such that its cost-weighted area is minimized. A computationally efficient method exists for finding such corridors, but as is the case with conventional raster-based least-cost paths, their incremental orientations are limited to a fixed number of (typically eight orthogonal and diagonal) directions, and therefore, regardless of the grid resolution, they tend to deviate from those conceivable on the Euclidean plane. In this paper, we propose a method for solving the raster-based least-cost corridor problem with reduced distortion by adapting a distortion reduction technique originally designed for least-cost paths and applying it to an efficient but distortion-prone least-cost corridor algorithm. The proposed method is, in theory, guaranteed to generate no less accurate solutions than the existing one in polynomial time and, in practice, expected to generate more accurate solutions, as demonstrated experimentally using synthetic and real-world data.

Analysis of trip cost allowing late arrival in a traffic corridor with one entry and one exit under car-following model

In this paper, a generalized car-following model is proposed to investigate the trip cost of each commuter in a traffic corridor with one entry and one exit at equilibrium state. Trip cost consists of the travel time cost and the penalty cost of arriving at destination early or late. At equilibrium, all commuters experience identical trip cost regardless of their departure time. We use the full velocity difference (FVD) model to compute the trip cost of a commuter who leaves home at specific time, find a function to fit each commuter’s time headway at the equilibrium state, and verify the fitted function from different perspectives. Finally, we utilize the fitted function of time headway to explore some extension cases (e.g., the number of commuters or the first commuter’s departure time is changed). The paper has revealed some properties of the traffic corridor and proposed some methods to research the traffic corridor in deep from microscopic perspective, which can be easily extended to investigate complex traffic corridor problems and policy making.

The corridor problem with discrete multiple bottlenecks

This paper presents a transparent approach to the analysis of dynamic user equilibrium and clarifies the properties of a departure-time choice equilibrium of a corridor problem where discrete multiple bottlenecks exist along a freeway. The basis of our approach is the transformation of the formulation of equilibrium conditions in a conventional “Eulerian coordinate system” into one in a “Lagrangian-like coordinate system.” This enables us to evaluate dynamic travel times easily, and to achieve a deep understanding of the mathematical structure of the problem, in particular, about the properties of the demand and supply (queuing) sub-models, relations with dynamic system optimal assignment, and differences between the morning and evening rush problems. Building on these foundations, we establish rigorous results on the existence and uniqueness of equilibria.

The Corridor Problem with Discrete Multiple Bottlenecks

This paper presents a transparent approach to the analysis of dynamic user equilibrium and clarifies the properties of a departure- time choice equilibrium of a corridor problem where discrete multiple bottlenecks exist along a freeway. The basis of our approach is the transformation of the formulation of equilibrium conditions in a conventional “Eulerian coordinate system” into one in a “Lagrangian-like coordinate system.” This enables us to evaluate dynamic travel times easily, and to achieve a deep understanding of the mathematical structure of the problem, in particular, about the properties of the demand and supply (queuing) sub-models, relations with dynamic system optimal assignment, and differences between the morning and evening rush problems. Building on these foundations, we establish rigorous results on the existence and uniqueness of equilibria.

Path Planning Under Kinematic Constraints by Rapidly Exploring Manifolds

The situation arising in path planning under kinematic constraints, where the valid configurations define a manifold embedded in the joint ambient space, can be seen as a limit case of the well-known narrow corridor problem. With kinematic constraints, the probability of obtaining a valid configuration by sampling in the joint ambient space is not low but null, which complicates the direct application of sampling-based path planners. This paper presents the AtlasRRT algorithm, which is a planner especially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize a manifold and to coordinate the charts, forming an atlas that fully covers it. AtlasRRT simultaneously builds an atlas and a bidirectional rapidly exploring random tree (RRT), using the atlas to sample configurations and to grow the branches of the RRTs, and the RRTs to devise directions of expansion for the atlas. The efficiency of AtlasRRT is evaluated in several benchmarks involving high-dimensional manifolds embedded in large ambient spaces. The results show that the combined use of the atlas and the RRTs produces a more rapid exploration of the configuration space manifolds than existing approaches.

Reliable Traffic Sensor Deployment Under Probabilistic Disruptions and Generalized Surveillance Effectiveness Measures

Sensor systems as critical components of a transportation network provide a variety of real-time traffic surveillance information for traffic management and control. The deployment of sensors significantly affects their overall surveillance effectiveness. This paper proposes a reliable sensor location model to optimize surveillance effectiveness when sensors are subject to site-dependent probabilistic failures, and a general effectiveness measure is proposed to encompass most existing measures needed for engineering practice (e.g., flow volume coverage, vehicle-mile coverage, and squared error reduction). The problem is first formulated into a compact mixed-integer program, and we develop a variety of solution algorithms (including a custom-designed Lagrangian relaxation algorithm) and analyze their properties. We also propose alternative formulations including a continuum approximation model for single corridor problems and reliable fixed-charge sensor location models. Numerical case studies are conducted to test the performance of the proposed algorithms and draw managerial insights on how different parameter settings (e.g., failure probability and spatial heterogeneity) affect overall surveillance effectiveness and the optimal sensor deployment.

The corridor problem: Preliminary results on the no-toll equilibrium

Consider a traffic corridor that connects a continuum of residential locations to a point central business district, and that is subject to flow congestion. The population density function along the corridor is exogenous, and except for location vehicles are identical. All vehicles travel along the corridor from home to work in the morning rush hour, and have the same work start-time but may arrive early. The two components of costs are travel time costs and schedule delay (time early) costs. Determining equilibrium and optimum traffic flow patterns for this continuous model, and possible extensions, is termed “The Corridor Problem”. Equilibria must satisfy the trip-timing condition, that at each location no vehicle can experience a lower trip price by departing at a different time. This paper investigates the no-toll equilibrium of the basic Corridor Problem.

Approximating corridors and tours via restriction and relaxation techniques

Given a rectangular boundary partitioned into rectangles, the Minimum-Length Corridor (MLC-R) problem consists of finding a corridor of least total length. A corridor is a set of connected line segments, each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectangles, and must include at least one point from the boundary of every rectangle and from the rectangular boundary. The MLC-R problem is known to be NP-hard. We present the first polynomial-time constant ratio approximation algorithm for the MLC-R and MLC k problems. The MLC k problem is a generalization of the MLC-R problem where the rectangles are rectilinear c -gons, for c ≤ k and k is a constant. We also present the first polynomial-time constant ratio approximation algorithm for the Group Traveling Salesperson Problem (GTSP) for a rectangular boundary partitioned into rectilinear c -gons as in the MLC k problem. Our algorithms are based on the restriction and relaxation approximation techniques.

CONSTRAINED DISJOINT PATHS IN GEOMETRIC NETWORKS

We address the problem of constructing a pair of node-disjoint paths connecting two given nodes in a geometric network. We propose a simple algorithm for constructing such a path that does not use any complicated data structure which can be easily implemented. We also consider two variations of disjoint path pair problems which we call narrow corridor problem and width-bounded corridor problem and present efficient algorithms for solving them.

Complexity of the minimum-length corridor problem

We study the Minimum-Length Corridor (MLC) problem. Given a rectangular boundary partitioned into rectilinear polygons, the objective is to find a corridor of least total length. A corridor is a set of line segments each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectilinear polygons. The corridor is a tree, and must include at least one point from the rectangular boundary and at least one point from the boundary of each of the rectilinear polygons. We establish the NP-completeness of the decision version of the MLC problem even when it is restricted to a rectangular boundary partitioned into rectangles.

The widest k-dense corridor problems

The widest k-dense corridor problems

AN OPTIMAL ALGORITHM FOR COMPUTING (≤K)-LEVELS, WITH APPLICATIONS

This paper gives an optimal O(n log n+nk) time algorithm for constructing the levels 1,…, k in an arrangement of n lines in the plane. This algorithm is extended to compute these levels in an arrangement of n unbounded x-monotone polygonal convex chains, of which each pair intersects at most a constant number of times. We then show how these results can be used to solve several geometric optimization problems including the weak separation problem for sets of red and blue points or polygons, the maximum line transversal problem for sets of line segments, the densest hemisphere problem for sets of points on a sphere and the optimal corridor problem for sets of points in the plane. All of the algorithms are quality-sensitive; they run faster if the optimal solution is a good one.

The K-dense corridor problems

A corridor through a planar set of n points S is a closed/open region bounded by two parallel straight lines intersecting the convex hull of S; it is K-dense if it contains K points of S. In this paper we propose simple algorithms to find a narrowest/widest K-dense corridor (N KDC/W KDC) in O( n 2) space. The algorithm employs a vertical plane sweep technique in the dual of S. We also suggest an improved algorithm for N KDC which runs in O( n 2) time and O( n) space. We conclude with various other related corridor problems.

Poland Corridor Problems in View of the Political Geography

Poland Corridor Problems in View of the Political Geography