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The results show that these strategies can significantly reduce the processing time of C-space construction from hours to less than 10 min.
The main function of the C-space is to capture all of the feasible geometry of the layout design so that a genetic algorithm (GA) can be used to explore the design space.
For examples of a C-space, see [4, 10].
This paper reports a further extension of the C-space method in two respects.
Many of the path planning algorithms, based on cell decomposition or potential field, fail due to the high dimensionality and complex nature of the C-space.
By capturing useful information generated during the computation of the C-space, the new method enables the GA to explore both the geometry and the topology of the design during the evolutionary process.
If a robot is thought of a finite collection of rigid links organized in a kinematic hierarchy, and has n degrees of freedom, this leads to an n-dimensional manifold C, called configuration space (or C-space) of the robot.
The completion of the space C c ∞ with respect to the norm ∥ ⋅ ∥ W α 1 is denoted by W α, 0 1 , where C c ∞ is the space of smooth functions on Ω with compact support.
Let X μ r ( M ) denote the space of C r divergence-free vector fields, and we consider the usual C r Whitney topology on this space.
Let X μ 1 ( M ) denote the space of C r divergence-free vector fields, and we consider the usual C 1 Whitney topology on this space.
where ( C b, 1 ( H ) ) ∗ is the topological dual space of C b, 1 ( H ) ; see Theorem 4.3.
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