Objects in Contact: Boundary Collisions as Geometric Wave Propagation
The motivation behind this work is to make the computation of collision-free motions of robots efficiently computable. For translational motions, the boundary of permissible translations of a reference point is obtained from the obstacles and the robot by a kind of dilation, ‘thickening’ the obstacle (see below for details) to produce the forbidden states in the configuration space of translations. The intuitive similarity of this operation to convolution suggests that we might be able to find a kind of Fourier transformation, in the sense that we might separate the shapes into independent ‘spectral components’ and combine those simply; after which the collision boundary would be obtained by the inverse transformation. This would enable the development of a ‘systems theory’ for collisions.
KeywordsWave Propagation Tangent Space Minkowski Space Geometric Algebra Geometric Product
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