A general method for C-space evaluation and its application to articulated robots
07 Aug 2002-Vol. 18, Iss: 1, pp 24-31
TL;DR: The proposed method could be seen as a convolution of two functions that describe the robot and the obstacles, respectively, and the computational load can then be reduced drastically if convolution properties are applied.
Abstract: A general method to obtain the obstacle representation in the robot configuration space is presented. The method is based on a solid mathematical formalism that has as a key element a mathematical expression to evaluate the C-obstacle representation. The use of the proposed method and the choice of a suitable coordinate system, in the workspace as well as in the configuration space, lead to the fact that the obstacle representation in the configuration space could be seen as a convolution of two functions that describe the robot and the obstacles, respectively. The computational load can then be reduced drastically if convolution properties are applied. The method is directly applicable to mobile and articulated robots without any kind of adaptation or restriction of the shape of the elements that constitute the robot and the shape of the obstacles. Hence, its utilization is quite suitable to motion planning and control problems.
Citations
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TL;DR: A new method for global, near optimal, motion-planning of a robot (either mobile or redundant manipulator) moving in an environment cluttered with a priori known prohibited areas which have arbitrary shape, size and location is introduced.
49 citations
01 Sep 2010
TL;DR: It is shown that all Minkowski product and quotient operations may be represented implicitly as sublevel sets of the same real-valued convolution function.
Abstract: Group morphology is an extension of mathematical morphology with classical Minkowski sum and difference operations generalized respectively to Minkowski product and quotient operations over arbitrary groups. We show that group morphology is a proper setting for unifying, formulating and solving a number of important problems, including translational and rotational configuration space problems, mechanism workspace computation, and symmetry detection. The proposed computational approach is based on group convolution algebras, which extend classical convolutions and the Fourier transform to non-commutative groups. In particular, we show that all Minkowski product and quotient operations may be represented implicitly as sublevel sets of the same real-valued convolution function.
34 citations
Cites background or methods from "A general method for C-space evalua..."
...The concept of the workspace is used widely in robotics and manufacturing for planning effective device configurations, and techniques for either generating or representing workspaces have been proposed by a number of researchers [22, 1, 6]....
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...Minkowski sum is also long recognized as a convolution of indicator functions [35, 11], which gives the basis for efficient algorithms using Fast Fourier Transform [16, 6]....
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...Minkowski sum is also long recognized as a convolution of indicator functions [35, 11], which gives the basis for e.cient algorithms using Fast Fourier Transform [16, 6]....
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...This problem may be overcome with sampled algorithms [16, 6, 20, 41, 28] that are becoming increasingly popular, but their properties and applicability to other morphological computations remain unclear....
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BMW1
TL;DR: This work gives theoretical and practical insights on how to efficiently check a large number of configurations for collision and cost and presents two efficient algorithms for their calculation: FAMOD, an approximate method based on convolution, which is independent of the size and the shape of the robot mask, and vHGW-360, an exact method based upon the van Herk-Gil-Werman morphological dilation algorithm.
Abstract: Collision checking is the major computational bottleneck for many robot path and motion planning applications, such as for autonomous vehicles, particularly with grid-based environment representations. Apart from collisions, many applications benefit from incorporating costs into planning; cost functions or cost maps are a common tool. Similar to checking a single configuration for collision, evaluating its cost using a grid-based cost map also requires examining every cell under the robot footprint. This work gives theoretical and practical insights on how to efficiently check a large number of configurations for collision and cost. As part of this work, configuration space costs are formulated, which can be seen as generalization of configuration space obstacles allowing a complete configuration check incorporating the robot geometry to be done using a single lookup. Furthermore, this paper presents two efficient algorithms for their calculation: FAMOD, an approximate method based on convolution, which is independent of the size and the shape of the robot mask, and vHGW-360, an exact method based on the van Herk-Gil-Werman morphological dilation algorithm, which can be used if the robot shape is rectangular. Both algorithms were implemented and evaluated on graphics hardware to demonstrate the applicability and benefit to real-time path and motion planning systems.
27 citations
TL;DR: The semi-automatic bomb fetching function has greatly improved the operation performance of EOD robot and the model construction of manipulator, bomb and environment, C-space map, path planning and the operation procedure are introduced in detail.
Abstract: An EOD robot system, SUPER-PLUS, which has a novel semi-automatic bomb fetching function is presented in this paper. With limited support of human, SUPER-PLUS scans the cluttered environment with a wrist-mounted laser distance sensor and plans the manipulator a collision free path to fetch the bomb. The model construction of manipulator, bomb and environment, C-space map, path planning and the operation procedure are introduced in detail. The semi-automatic bomb fetching function has greatly improved the operation
19 citations
TL;DR: This new collision test scales with respect to accuracy (in the Hausdorff sense) and can be used as a holonomic unilateral constraint in many applications, such as path planning, rigid body dynamics, nesting or tool placement, replacing the need for more ad-hoc normal/contact-based constraint solvers.
Abstract: We investigate a new approach to narrowphase collision detection for rigid objects based on a Fourier series expansion. This new collision test scales with respect to accuracy (in the Hausdorff sense), which we show rigorously in the case of translational motions. Because our new form of the collision test is also a smooth inequality, it can be used as a holonomic unilateral constraint in many applications, such as path planning, rigid body dynamics, nesting or tool placement, replacing the need for more ad-hoc normal/contact-based constraint solvers. Moreover, we also show how this constraint can be directly differentiated via Fourier multipliers with only a constant factor overhead, which leads to a simple method for constructing a Jacobian for both normal forces and rotational torques.
12 citations
Cites background or result from "A general method for C-space evalua..."
...With the exception of Nelaturi and Shapiro (2009), all of the convolutional methods have so far focused on generating uniformly sampled configuration space obstacles for all configurations simultaneously (Kavraki, 1995; Chirikjian and Kyatkin, 2000; Curto et al., 2002; Lysenko et al., 2010)....
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...In principle, this result also extends to other Fourier obstacle methods such as those of Kavraki (1995), Curto et al. (2002), and Theron et al. (2006)....
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References
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Book•
01 Jan 1990
TL;DR: This chapter discusses the configuration space of a Rigid Object, the challenges of dealing with uncertainty, and potential field methods for solving these problems.
Abstract: 1 Introduction and Overview.- 2 Configuration Space of a Rigid Object.- 3 Obstacles in Configuration Space.- 4 Roadmap Methods.- 5 Exact Cell Decomposition.- 6 Approximate Cell Decomposition.- 7 Potential Field Methods.- 8 Multiple Moving Objects.- 9 Kinematic Constraints.- 10 Dealing with Uncertainty.- 11 Movable Objects.- Prospects.- Appendix A Basic Mathematics.- Appendix B Computational Complexity.- Appendix C Graph Searching.- Appendix D Sweep-Line Algorithm.- References.
6,186 citations
01 Aug 1996
TL;DR: Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).
Abstract: A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).
4,977 citations
"A general method for C-space evalua..." refers background in this paper
...Nevertheless, there are no works where this approach has been applied to articulated robots, not in the sense of a set of mobile robots, as in [ 19 ], but as a whole entity....
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01 Aug 1996
TL;DR: A data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion that can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates are presented.
Abstract: We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates. CR
2,278 citations
"A general method for C-space evalua..." refers methods in this paper
...In fact, there exist some powerful methods [ 25 ] that perform this task in a very efficient way....
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TL;DR: In this article, the authors propose an approach based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object.
Abstract: This paper presents algorithms for computing constraints on the position of an object due to the presence of ther objects. This problem arises in applications that require choosing how to arrange or how to move objects without collisions. The approach presented here is based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object. The configurations forbidden to this object, due to the presence of other objects, can then be characterized as regions in the configuration space, called configuration space obstacles. The paper presents algorithms for computing these configuration space obstacles when the objects are polygons or polyhedra.
1,996 citations
Book•
01 Jul 1990
TL;DR: Algorithms for computing constraints on the position of an object due to the presence of ther objects, which arises in applications that require choosing how to arrange or how to move objects without collisions are presented.
1,641 citations