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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
Algorithmic Motion Planning
, 1997
"... INTRODUCTION Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the simplest version is as follows. We are given a robot system B, which may consist of several rigid objects attached to each other through various joints, hinges, and links, or moving independen ..."
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Cited by 43 (6 self)
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INTRODUCTION Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the simplest version is as follows. We are given a robot system B, which may consist of several rigid objects attached to each other through various joints, hinges, and links, or moving independently, and a twodimensional or threedimensional environment V cluttered with obstacles. We assume that the shape and location of the obstacles and the shape of B are known to the planning system. Given an initial placement Z 1 and a nal placement Z 2 of B, we wish to determine whether there exists a collisionavoiding motion of B from Z 1 to Z 2 , and, if so, to plan such a motion. In this simpli ed and purely geometric setup, we ignore issues such as incomplete information, nonholonomic constraints, control issues related to inaccuracies in sensing and motion, nonstationary obstacles, optimality of the planned motion, and so on. Since the early 1980's, motion planning has been an intensiv
Planning Paths for Elastic Objects Under Manipulation Constraints
 International Journal of Robotics Research
, 2001
"... This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to ..."
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Cited by 38 (7 self)
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This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to deform in order to achieve a collisionfree path from the initial to the final configuration. Any required deformations are automatically computed by our planner according to the principles of elasticity theory from mechanics. The problem considered in this paper differs significantly from that of planning for a rigid or an articulated object. In the first part of the paper we point out these differences and highlight the reasons that make planning for elastic objects an extremely difficult task. We then present a randomized algorithm for computing collisionfree paths for elastic objects under the abovementioned restrictions of manipulation.
A General Framework for Assembly Planning: The Motion Space Approach
, 1998
"... Assembly planning is the problem of finding a sequence of motions to assemble a product from its parts. We present a general framework for finding assembly motions based on the concept of motion space. Assembly motions are parameterized such that each point in motion space represents a mating motion ..."
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Cited by 27 (5 self)
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Assembly planning is the problem of finding a sequence of motions to assemble a product from its parts. We present a general framework for finding assembly motions based on the concept of motion space. Assembly motions are parameterized such that each point in motion space represents a mating motion that is independent of the moving part set. For each motion we derive blocking relations that explicitly state which parts collide with other parts; each subassembly (rigid subset of parts) that does not collide with the rest of the assembly can easily be derived from the blocking relations. Motion space is partitioned into an arrangement of cells such that the blocking relations are fixed within each cell. In the first part of the paper we give background material, present the motion space approach and describe applications of the approach to assembly motions of several useful types, including onestep translations, multistep translations, and infinitesimal rigid motions. Several efficien...
Assembly Sequencing with Toleranced Parts
, 1995
"... The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geom ..."
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Cited by 23 (4 self)
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The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geometry. Its main contribution is an efficient procedure that decides if a product admits an assembly sequence with infinite translations (i.e., translations that can be extended arbitrarily far along a fixed direction) that is feasible for all possible instances of the components within the specified tolerances. If the product admits one such sequence, the procedure can also generate it. For the cases where there exists no such assembly sequence, another procedure is proposed which generates assembly sequences that are feasible only for some values of the toleranced dimensions. If this procedure produces no such sequence, then no instance of the product is assemblable. These two proced...
Complexity Measures for Assembly Sequences
 In Proc. IEEE Int. Conf. on Robotics and Automation
, 1996
"... Our work examines various complexity measures for twohanded assembly sequences. For many products there exists an exponentially large set of valid sequences, and a natural goal is to use automated systems to select wisely from the choices. Since assembly sequencing is a preprocessing phase for a lo ..."
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Cited by 22 (3 self)
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Our work examines various complexity measures for twohanded assembly sequences. For many products there exists an exponentially large set of valid sequences, and a natural goal is to use automated systems to select wisely from the choices. Since assembly sequencing is a preprocessing phase for a long and expensive manufacturing process, any work towards ndinga\better" assembly sequence isofgreat value when it comes time to assemble the physical product in mass quantities. We take a step in this direction by introducing a formal framework for studying the optimization of several complexity measures. This framework focuses on the combinatorial aspect of the family of valid assembly sequences, while temporarily separating out the speci c geometric assumptions inherent to the problem. With an exponential number of possibilities, nding the true optimal cost solution is nontrivial. In fact in the most general case, our results show that even nding an approximate solution is hard. Furthermore, we can show several hardness results, even in simple geometric settings. Future work is directed towards using this model to study how the original geometric assumptions can be reintroduced toprove stronger approximation results. 1
Separating an Object from its Cast
"... In casting, liquid is poured into a cast that has a cavity with the shape of the object to be manufactured. The liquid then hardens, after which the cast is removed. We consider the case where the cast consists of two parts and address the following problems: (1) Given a cast for an object and a di ..."
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Cited by 22 (10 self)
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In casting, liquid is poured into a cast that has a cavity with the shape of the object to be manufactured. The liquid then hardens, after which the cast is removed. We consider the case where the cast consists of two parts and address the following problems: (1) Given a cast for an object and a direction ~d, can the cast be partitioned into two parts such that the parts can be removed in directions ~d and \Gamma ~d, respectively, without colliding with the object or the other cast part? (2) How can one find a direction ~d such that the above cast partitioning can be done? We give necessary and sufficient conditions for both problems, as well as algorithms to decide them for polyhedral objects. We also give some evidence that the case where the cast parts need not be removed in opposite directions is considerably harder.
Path planning for deformable linear objects
 IEEE Transactions on Robotics
"... Abstract—We present a new approach to path planning for deformable linear (onedimensional) objects such as flexible wires. We introduce a method for efficiently computing stable configurations of a wire subject to manipulation constraints. These configurations correspond to minimalenergy curves. B ..."
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Cited by 21 (0 self)
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Abstract—We present a new approach to path planning for deformable linear (onedimensional) objects such as flexible wires. We introduce a method for efficiently computing stable configurations of a wire subject to manipulation constraints. These configurations correspond to minimalenergy curves. By restricting the planner to minimalenergy curves, the execution of a path becomes easier. Our curve representation is adaptive in the sense that the number of parameters automatically varies with the complexity of the underlying curve. We introduce a planner that computes paths from one minimalenergy curve to another such that all intermediate curves are also minimalenergy curves. This planner can be used as a powerful local planner in a samplingbased roadmap method. This makes it possible to compute a roadmap of the entire “shape space, ” which is not possible with previous approaches. Using a simplified model for obstacles, we can find minimalenergy curves of fixed length that pass through specified tangents at given control points. Our work has applications in cable routing, and motion planning for surgical suturing and snakelike robots. Index Terms—Deformation, differential geometry, flexible manipulation, flexible object representation, minimalenergy curves, modeling, motion planning, path planning. I.
Folding Cartons with Fixtures: A Motion Planning Approach
, 2000
"... Packaging products such as telephones and twoway radios after assembly is a common manufacturing task. Carton folding is a packaging operation typically performed by human operators or with fixed automation. We present a flexible method to fold cardboard cartons using fixtures; a carton blank is fo ..."
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Cited by 18 (1 self)
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Packaging products such as telephones and twoway radios after assembly is a common manufacturing task. Carton folding is a packaging operation typically performed by human operators or with fixed automation. We present a flexible method to fold cardboard cartons using fixtures; a carton blank is folded by moving it through a fixture with a robot. This method uses interchangeable fixtures to enable rapid changeovers between product models. We outline an approach to design a fixture given a carton and a folding sequence. We present an implemented motion planning algorithm that generates all folding sequences for a carton by modeling it kinematically as a many degreeoffreedom robot manipulator with revolute joints and branching links. Folding fixtures constrain the carton motion to paths consisting of line segments in its configuration space. We characterize the set of valid paths for these carton robots and generate them using the motion planner. To illustrate the method, we selected a folding sequence for an example carton, designed a fixture, and demonstrated folding of the carton from blanks with an industrial robot.
Path Planning for Elastic Plates Under Manipulation Constraints
 In Int. Conf. on Robotics and Automation
, 1999
"... This paper addresses the problem of path planning for a thin elastic metal plate under fairly general manipulation constraints. The underlying geometric model for the plate is provided by a B'ezier representation. The geometric model is augmented by a realistic mechanical model. We assume that the p ..."
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Cited by 17 (2 self)
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This paper addresses the problem of path planning for a thin elastic metal plate under fairly general manipulation constraints. The underlying geometric model for the plate is provided by a B'ezier representation. The geometric model is augmented by a realistic mechanical model. We assume that the plate is manipulated in accordance with a set of userdefined grasping constraints that specify the position and orientation of two opposite edges. Our mechanical model permits the computation of the shape of the plate with respect to the grasping constraints by minimizing the energy function of the deformation of the plate. Paths are computed by a planner that is based on the principle of probabilistic roadmaps. The planner builds a roadmap in the configuration space. The nodes of the roadmap are equilibrium configurations of the plate under the grasping constraints, while its edges correspond to quasistatic equilibrium paths. Paths are found by searching the roadmap. Several experimental r...