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69
The quadtree and related hierarchical data structures
 ACM Computing Surveys
, 1984
"... A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics ..."
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Cited by 421 (11 self)
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A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data (i.e., twodimensional shapes) and to a lesser extent on point, curvilinear, and threedimensional data. A number of operations in which such data structures find use are examined in greater detail.
A fast procedure for computing the distance between complex objects in three space
 in Proc. IEEE Int. Conf. on Robotics and Automation
, 1987
"... AbstractAn efficient and reliable algorithm for computing the Euclidean distance between a pair of convex sets in Rm is described. Extensive numerical experience with a broad family of polytopes in R3 shows that the computational cost is approximately linear in the total number of vertices specifyi ..."
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Cited by 277 (8 self)
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AbstractAn efficient and reliable algorithm for computing the Euclidean distance between a pair of convex sets in Rm is described. Extensive numerical experience with a broad family of polytopes in R3 shows that the computational cost is approximately linear in the total number of vertices specifying the two polytopes. The algorithm has special features which makes its application in a variety of robotics problems attractive. These are discussed and an example of collision detection is given. I.
The partigame algorithm for variable resolution reinforcement learning in multidimensional statespaces
 Machine Learning
, 1995
"... Abstract. Partigame is a new algorithm for learning feasible trajectories to goal regions in high dimensional continuous statespaces. In high dimensions it is essential that learning does not plan uniformly over a statespace. Partigame maintains a decisiontree partitioning of statespace and ap ..."
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Cited by 224 (8 self)
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Abstract. Partigame is a new algorithm for learning feasible trajectories to goal regions in high dimensional continuous statespaces. In high dimensions it is essential that learning does not plan uniformly over a statespace. Partigame maintains a decisiontree partitioning of statespace and applies techniques from gametheory and computational geometry to e ciently and adaptively concentrate high resolution only on critical areas. The currentversion of the algorithm is designed to nd feasible paths or trajectories to goal regions in high dimensional spaces. Future versions will be designed to nd a solution that optimizes a realvalued criterion. Many simulated problems have been tested, ranging from twodimensional to ninedimensional statespaces, including mazes, path planning, nonlinear dynamics, and planar snake robots in restricted spaces. In all cases, a good solution is found in less than ten trials and a few minutes.
On multiple moving objects
 Algorithmica
, 1987
"... This paper explores the motion planning problem for multiple mov ing objects. The approach taken consists of assigning priorities to the objects, then planning motions one object at a time. For each moving object, the planner constructs a configuration spacetime that represents the timevarying co ..."
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Cited by 171 (0 self)
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This paper explores the motion planning problem for multiple mov ing objects. The approach taken consists of assigning priorities to the objects, then planning motions one object at a time. For each moving object, the planner constructs a configuration spacetime that represents the timevarying constraints im posed on the moving object by the other moving and stationary objects. The planner represents this spacetime approximately, using twodimensional slices. The spacetime is then searched for a collisionfree path. The paper demonstrates this approach in two domains. One domain consists of translating planar objects; the other domain consists of twolink planar articulated arms.
A Search Algorithm for Motion Planning with Six Degrees of Freedom
 ARTIFICIAL INTELLIGENCE
, 1987
"... The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given highlevel specifications of tasks and geometric models of the robot and obstacles. The "Movers'" p ..."
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Cited by 75 (4 self)
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The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given highlevel specifications of tasks and geometric models of the robot and obstacles. The "Movers'" problem is to find a continuous, collisionfree path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the threedimensional Movers' problem: Given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collisionfree path taking P from some initial configuration to a desired goal configuration. This paper describes an implementation of a complete algorithm (at a given resolution)for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a sixdimensional configuration space (called Cspace). The Cspace obstacles, which characterize the physically unachievable configurations, are directly represented by sixdimensional manifolds whose boundaries are fivedimensional Csurfaces. By characterizing these surfaces and their intersections, collisionfree paths may be found by the
Motion planning: A journey of robots, molecules, digital actors, and other artifacts
 International Journal of Robotics Research
, 1999
"... During the last three decades motion planning has emerged as a crucial and productive research area in robotics. In the mid80's the most advanced planners were barely able to compute collisionfree paths for objects crawling in planar workspaces. Today, planners e ciently deal with robots with many ..."
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Cited by 56 (3 self)
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During the last three decades motion planning has emerged as a crucial and productive research area in robotics. In the mid80's the most advanced planners were barely able to compute collisionfree paths for objects crawling in planar workspaces. Today, planners e ciently deal with robots with many degrees of freedom in complex environments. Techniques also exist to generate quasioptimal trajectories, coordinate multiple robots, deal with dynamic and kinematic constraints, and handle dynamic environments. This paper describes some of these achievements, presents new problems that have recently emerged, discusses applications likely to motivate future research, and nally gives expectations for the coming years. It stresses the fact that nonrobotics applications (e.g., graphic animation, surgical planning, computational biology) are growing in importance and are likely to shape future motion planning research more than robotics itself. 1
A Study of the Clash Detection Problem in Robotics
 In Int. Conf. Robotics & Automation
, 1985
"... To solve the clash detection problem we must decide whether a collision will occur between any pair of objects from a set of objects with known shapes and motions. We have considered three methods for performing clash detection: in the first we sample the motion at a finite number of times and perfo ..."
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Cited by 38 (6 self)
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To solve the clash detection problem we must decide whether a collision will occur between any pair of objects from a set of objects with known shapes and motions. We have considered three methods for performing clash detection: in the first we sample the motion at a finite number of times and perform interference detection at each time; in the second we create models of the shapes and their motions in spacetime, and look for intersections between these fourdimensional entities; and in the third we create models of the volumes swept out by the objects. This paper is a brief, comparative study of these three methods, and includes some details of our experiments with the first two methods as implemented in a geometric modelling system. This paper originally appeared in Int. Conf. Robotics & Automation, St. Louis, March 1985, pages 488493. c flIEEE 1985. It was reformatted using L a T E X in September 1996. Contact address: Oxford University Computing Laboratory, Wolfson Building, Par...
Stereo Vision Based Mapping and Navigation for Mobile Robots
, 1997
"... This paper describes a visually guided robot that can plan paths, construct maps and explore an indoor environment. The robot uses a trinocular stereo vision system to produce highly accurate depth images at 2 Hz allowing it to safely travel through the environment at 0.5 m/s. The algorithm integrat ..."
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Cited by 28 (1 self)
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This paper describes a visually guided robot that can plan paths, construct maps and explore an indoor environment. The robot uses a trinocular stereo vision system to produce highly accurate depth images at 2 Hz allowing it to safely travel through the environment at 0.5 m/s. The algorithm integrates stereo vision, occupancy grid mapping, and potential field path planning techniques to form a robust and cohesive robotic system for mapping and navigation. Stereo vision is shown to be a viable alternative to active sensing devices such as sonar and laser range finders.
InterferenceFree Insertion of a Solid Body into a Cavity: An Algorithm and a Medical Application
, 1994
"... This paper presents a novel algorithm for efficiently computing an interferencefree insertion path of a body into a cavity and shows its practical use in the insertability analysis of custom orthopaedic hip implants. The algorithm is designed to handle tightly fit, very complex threedimensional ..."
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Cited by 27 (8 self)
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This paper presents a novel algorithm for efficiently computing an interferencefree insertion path of a body into a cavity and shows its practical use in the insertability analysis of custom orthopaedic hip implants. The algorithm is designed to handle tightly fit, very complex threedimensional bodies requiring fine, complex, coupled sixdegree of freedom motions in a preferred direction. It provides a practical method for efficiently handling the geometric complexity of tight fit insertions. The algorithm computes an insertion path consisting of small interferencefree body motion steps. It formulates local, linearized configuration space constraints derived from the shapes and computes successive motion steps by solving a series of linear optimization problems whose solution corresponds to the maximum allowed displacement in a preferred direction satisfying the constraints. It either finds a successful insertion path or a stuck configuration. We demonstrate the algorithm ...