• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.577-586
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• 1997

In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

• Journal of Electrical Engineering and Technology
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• v.10 no.2
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• pp.676-687
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• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.1992-2007
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• 1997

A new algorithm for planning a collision-free path is developed based on linear prametric curve. In this paper robot is assumed to a point, and two linear parametric curve is used to construct a path connecting start and goal point, in which single intermediate connection point between start and goal point is considered. The intermediate connection point is set in polar coordinate(${\theta}{\delta}$) , and the interference between path and obstacle is mapped into CPS(connection point space), which is defined a CWS GM(circular work space geometry mapping). GM of all obstacles in workspace creates overlapping images of obstacle in CPS(Connection Point Space). The GM for all obstacles produces overlapping images of obstacle in CPS. The empty area of CPS that is not occupied by obstacle images represents collision-free paths in Euclidian Space. A GM based on connection point in elliptic coordinate(${\theta}{\delta}$) is also developed in that the total length of path is depend only on the variable .delta.. Hence in EWS GM(elliptic work space geometry mapping), increasing .delta. and finding the value of .delta. for collision-free path, the shortest path can be searched without carring out whole GM. The GM of obstacles expersses all possible collision-free path as empty spaces in CPS. If there is no empty space available in CPS, it indicates that path planning is not possible with given number of connection points, i.e. path planning is failed, and it is necessary to increase the number of connection point. A general case collision-free path planning is possible by appling GM to configuration space obstacles. Simulation of GM of obstacles in Euclidian space is carried out to measure performance of algorithm and the resulting obstacle images are reported.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.162-167
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• 2003

In this paper, a novel feasible real-time system was researched for a differential driven wheeled autonomous mobile robot so that the mobile robot can move in a smooth, safe and elegant way. Least Square Minimum Path Planning was well used for the system to generate a smooth executable path for the mobile robot, and the point-to-point tracking algorithm was presented as well as its application in arbitrary path tracking. In order to make sure the robot can run elegantly and safely, trapezoidal speed was integrated into the point-to-point path tracking algorithm. The application to guest following for the autonomous mobile robot shows its wide application of the algorithm. The novel design was successfully proved to be feasible by our experiments on our mobile robot Interactive Robot Usher (IRU) in National University of Singapore.

• Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.132-139
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• 2016

In this paper, a minimum time path planning strategy is proposed for multi points manufacturing problems in drilling/spot welding tasks. By optimizing the travelling schedule of the set points and the detailed transfer path between points, the minimum time manufacturing task is realized under fully utilizing the dynamic performance of robotic manipulator. According to the start-stop movement in drilling/spot welding task, the path planning problem can be converted into a traveling salesman problem (TSP) and a series of point to point minimum time transfer path planning problems. Cubic Hermite interpolation polynomial is used to parameterize the transfer path and then the path parameters are optimized to obtain minimum point to point transfer time. A new TSP with minimum time index is constructed by using point-point transfer time as the TSP parameter. The classical genetic algorithm (GA) is applied to obtain the optimal travelling schedule. Several minimum time drilling tasks of a 3-DOF robotic manipulator are used as examples to demonstrate the effectiveness of the proposed approach.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.8A
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• pp.581-590
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• 2003

This paper proposes the routing path selection mechanism for source routing-based PtMP (Point-to-Multipoint) call in ATM switching system. Especially, it suggests PtMP routing path selection method that can share the maximum resource prior to the optimal path selection, guarantee the reduction of path calculation time and cycle prevention. The searching for the nearest branch point from destination node to make the maximum share of resource is the purpose of this algorithm. Therefore among neighbor nodes from destination node by back-tracking, this algorithm fixes the node crossing first the node on existing path having the same Call ID as branch node, constructs the optimal PtMP routing path. The optimal node to be selected by back-tracking is selected by the use of Dijkstra algorithm. That is to say, PtMP routing path selection performs the step of cross node selection among neighboring nodes by back-tracking and the step of optimal node selection(optimal path calculation) among neighboring nodes by back-tracking. This technique reduces the process of search of routing information table for path selection and path calculation, also solves the cycle prevention easily during path establishment.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2325-2330
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• 2005

A potential field method for solving the problem of path planning based on global and local information for a mobile robot moving among a set of stationary obstacles is described. The concept of various method used path planning is used design a planning strategy. A real human living area is constructed by many moving and imminence obstacles. Home service mobile robot must avoid many obstacles instantly. A path that safe and attraction towards the goal is chosen. The potential function depends on distance from the goal and heuristic function relies on surrounding environments. Three additional combined methods are proposed to apply to human living area, calibration robots position by measured surrounding environment and adapted home service robots. In this work, we proposed the application of various path planning theory to real area, human living. First, we consider potential field method. Potential field method is attractive method, but that method has great problem called local minimum. So we proposed intermediate point in real area. Intermediate point was set in doorframe and between walls there is connect other room or other area. Intermediate point is very efficiency in computing path. That point is able to smaller area, area divided by intermediate point line. The important idea is intermediate point is permanent point until destruction house or apartment house. Second step is move robot with sensing on front of mobile robot. With sensing, mobile robot recognize obstacle and judge moving obstacle. If mobile robot is reach the intermediate point, robot sensing the surround of point. Mobile robot has data about intermediate point, so mobile robot is able to calibration robots position and direction. Third, we gave uncertainty to robot and obstacles. Because, mobile robot was motion and sensing ability is not enough to control. Robot and obstacle have uncertainty. So, mobile robot planed safe path planning to collision free. Finally, escape local minimum, that has possibility occur robot do not work. Local minimum problem solved by virtual obstacle method. Next is some supposition in real living area.

• Journal of Mechanical Science and Technology
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• v.18 no.1
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• pp.92-105
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• 2004

A new algorithm for planning a collision-free path based on algebraic curve is developed and the concept of collision-free Path Space (PS) is introduced. This paper presents a Geometry Mapping (GM) based on two straight curves in which the intermediate connection point is organized in elliptic locus ($\delta$, $\theta$). The GM produces two-dimensional PS that is used to create the shortest collision-free path. The elliptic locus of intermediate connection point has a special property in that the total distance between the focus points through a point on ellipse is the same regardless of the location of the intermediate connection point on the ellipse. Since the radial distance, a, represents the total length of the path, the collision-free path can be found as the GM proceeds from $\delta$=0 (the direct path) to $\delta$=$\delta$$\_$max/(the longest path) resulting in the minimum time search. The GM of elliptic workspace (EWS) requires calculation of interference in circumferential direction only. The procedure for GM includes categorization of obstacles to .educe necessary calculation. A GM based on rectangular workspace (RWS) using Cartesian coordinate is also considered to show yet another possible GM. The transformations of PS among Circular Workspace Geometry Mapping (CWS GM) , Elliptic Workspace Geometry Mapping (EWS GM) , and Rectangular Workspace Geometry Mapping (RWS GM), are also considered. The simulations for the EWS GM on various computer systems are carried out to measure performance of algorithm and the results are presented.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.24 no.1
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• pp.1-9
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• 2016

In this paper, we integrate three degree of freedom(3DOF) point-mass model for aircraft and three-dimensional path generation algorithms using dubins curve and nonlinear path tracking law. Through this integration, we apply the path generation algorithm to the path planning, and verify tracking performance and feasibility of using the aircraft 3DOF point-mass model for air traffic management. The accuracy of modeling 6DOF aircraft is more accurate than that of 3DOF model, but the complexity of the calculation would be raised, in turn the rate of computation is more likely to be slow due to the increase of degree of freedom. These obstacles make the 6DOF model difficult to be applied to simulation requiring real-time path planning. Therefore, the 3DOF point-mass model is also sufficient for simulation, and real-time path planning is possible because complexity can be reduced, compared to those of the 6DOF. Dubins curve used for generating the optimal path has advantage of being directly available to apply path planning. However, we use the algorithm which extends 2D path to 3D path since dubins curve handles the two dimensional path problems. Control law for the path tracking uses the nonlinear path tracking laws. Then we present these concomitant simulation results.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.413-421
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• 1996

A path g in the plane $R^2$ is the sequence of the points $(t_0, t_1, \ldots, t_n)$, with coordinates in $Z^2$. The point $t_0$ is the starting point and the point $t_n$ is the arriving point. An elementary step of g is a couple $(t_i, t_{i+1}), 0 \leq i \leq n - 1$. We denote the length of the path g by $\mid$g$\mid$ = n.