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Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of t ..."
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Cited by 146 (12 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
A kinematicsbased probabilistic roadmap method for closed chain systems
 In Robotics:New Directions
, 2000
"... In this paper we consider the motion planning problem for arbitrary articulated structures with one or more closed kinematic chains in a workspace with obstacles. This is an important class of problems and there are applications in many areas such as robotics, closed molecular chains, graphical anim ..."
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Cited by 87 (13 self)
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In this paper we consider the motion planning problem for arbitrary articulated structures with one or more closed kinematic chains in a workspace with obstacles. This is an important class of problems and there are applications in many areas such as robotics, closed molecular chains, graphical animation, reconfigurable robots. We use the kinematicsbased probabilistic roadmap (kbprm) strategy proposed in [7] that conceptually partitions the linkage into a set of open chains and applies random generation methods to some of the chains and traditional inverse kinematics methods to the others. The efficiency of the method depends critically on how the linkage is partitioned into open chains, and the original method assumed the partition was provided as input to the problem. In this paper, we propose a fully automated method for partitioning an arbitrary linkage into open chains and for determining which should be positioned using the inverse kinematic solver. Even so, the size (number of links) of the closed loops that can be handled by this method is limited because the inverse solver can only be applied to small chains. To handle high dof closed loops, we show how we can use the Iterative Relaxation of Constraints (IRC) strategy [3] to efficiently handle large loops while still only using inverse kinematics for small chains. Our results in 3dimensional workspace both for planar and spatial linkages show that our framework performs well for general linkage. We also use our planner to simulate an adjustable lamp called Luxo. Using IRC, our planner can handle a single loop of up to 44 links.
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
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Trajectory Generation for the NTrailer Problem Using Goursat Normal Form
, 1995
"... In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the probl ..."
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Cited by 58 (9 self)
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In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the problem of rbxing a mobile robot WMI R trailers. We present an algorithm for finding a family of ~WIS~~~OM whicb will convert the system of rolling constraints on the wheels of the robot with n traiten into the GoaFapt canonical form..nRo of these transformations are studied in detail. The Gomt normal form for exterior diffemtial systems is dual to the socalled chainedform for vector fields that bas been studied previously. Consequently, we are able to give the state feedback law aad change o € e00rdinaW tovert the Ntrai4r system id0 chained form. Tllree metbods for for chainedform systems using shrosoidg and polynomiPls aa inputs are presented. The motion prpnnhag strategy Is therefore to the Ntrailer system into Gonrsat form, use this to lind the cboinedform coordinates, plan a path for the corresponding cimkdform system, and then transform the resalting traje.ctory back into the original coordinates. Simulations and h.ames of mode animations of the Ntnder system for parallel parking and backing into a loading dock using this strategy are included.
Nonholonomic Navigation and Control of Cooperating Mobile Manipulators
 IEEE Transactions on Robotics and Automation
, 2002
"... This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions (DILFs) and a novel extension of the navigation function metho ..."
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Cited by 38 (10 self)
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This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions (DILFs) and a novel extension of the navigation function method to account for nonpoint articulated robots. The Dipolar Inverse Lyapunov Functions introduced are appropriate for nonholonomic control and offer superior performance characteristics compared to existing tools. The new potential field technique uses diffeomorphic transformations and exploits the resulting pointworld topology. The combined approach is applied to the problem of handling deformable material by multiple nonholonomic mobile manipulators in obstacle environment to yield a centralized coordinating control law. Simulation results verify asymptotic convergence of the robots, obstacle avoidance, boundedness of object deformations and singularity avoidance for the manipulators. Index TermsNonholonomic motion planning, cooperative mobile manipulators, potential fields, Inverse Lyapunov Functions.
Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments
 International Journal of Robotics Research
, 1998
"... We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedo ..."
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Cited by 31 (14 self)
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We are interested in using low degreeoffreedom robots to perform complex tasks by nonprehensile manipulation (manipulation without a form or forceclosure grasp). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degreesof freedom of the part. The extra motion freedoms of the part are exhibited as rolling, slipping, and free flight.
A PolynomialTime Algorithm for Computing a Shortest Path of Bounded Curvature amidst Moderate Obstacles
, 1996
"... In this paper, we consider the problem of computing a shortest path of bounded curvature amidst obstacles in the plane. More precisely, given prescribed initial and final congurations (i.e. positions and orientations) and a set of obstacles in the plane, we want to compute a shortest C¹ path jo ..."
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Cited by 29 (4 self)
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In this paper, we consider the problem of computing a shortest path of bounded curvature amidst obstacles in the plane. More precisely, given prescribed initial and final congurations (i.e. positions and orientations) and a set of obstacles in the plane, we want to compute a shortest C¹ path joining those two configurations, avoiding the obstacles, and with the further constraint that, on each C² piece, the radius of curvature is at least 1. In this paper, we consider the case of moderate obstacles (as introduced by Agarwal et al.) and present a polynomialtime exact algorithm to solve this problem.
Nonprehensile Robotic Manipulation: Controllability and Planning
, 1997
"... the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra ..."
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Cited by 23 (5 self)
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the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra actuators; the expectation derived from a good model can minimize sensing requirements. Despite this, most robot systems attempt to dominate or nullify task mechanics, rather than exploit them. There has been little e ort to understand the manipulation capabilities of even the simplest robots under more complete mechanics models. This thesis addresses that knowledge de cit by studying graspless or nonprehensile manipulation. Nonprehensile manipulation exploits task mechanics to achieve a goal state without grasping, allowing simple mechanisms to accomplish complex tasks. With nonprehensile manipulation, a robot can manipulate objects too large or heavy to be grasped and lifted, and a lowdegreeoffreedom robot can control more degreesoffreedom of an object by allowing relative motion between the object and the manipulator. Two key problems are determining controllability of and motion planning for
Control and Coordination of Locomotion and Manipulation of a Wheeled Mobile Manipulator
, 1994
"... In this thesis, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation ..."
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Cited by 22 (1 self)
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In this thesis, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation capability offered by fixedbase manipulators and the mobility offered by mobile platforms. While mobile manipulators offer a tremendous potential for flexible material handling and other tasks, at the same time they bring about a number of challenging issues rather than simply increase the structural complexity. First, combining a manipulator and a platform creates redundancy. Second, a wheeled mobile platform is subject to nonholonomic constraints. Third, there exists dynamic interaction between the manipulator and the mobile platform. Fourth, manipulators and mobile platforms have different bandwidths. Mobile platforms typically have slower dynamic response than manipulators. The objectiv...
Approximation Algorithms for CurvatureConstrained Shortest Paths
, 1996
"... Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let\Omega be a set of polygonal obstacles with n vertices. We study the collisionfree, optimal pathplanning problem for B. Given a parameter ", we present an O((n 2 =" 2 ) log n)time algorithm f ..."
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Cited by 18 (3 self)
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Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let\Omega be a set of polygonal obstacles with n vertices. We study the collisionfree, optimal pathplanning problem for B. Given a parameter ", we present an O((n 2 =" 2 ) log n)time algorithm for computing a collisionfree, curvatureconstrained path between two given positions, whose length is at most (1 + ") times the length of an optimal robust path (a path is robust if it remains collisionfree even if certain positions on the path are perturbed). Our algorithm thus runs significantly faster than the previously best known algorithm by Jacobs and Canny whose running time is O(( n+L " ) 2 + n 2 ( n+L " ) log n), where L is the total edge length of the obstacles. More importantly, the running time of our algorithm does not depend on the size of obstacles. The path returned by this algorithm is not necessarily robust. We present an O((n=") 2:5 log n) time algorithm that...