Abstract

In this paper we show that the workspace of a highly articulated manipulator can be found by solving a partial differential equation. This diffusion-type equation describes the evolution of the workspace density function depending on manipulator length and kinematic properties. The support of the workspace density function is the workspace of the manipulator. The PDE governing workspace density evolution is solvable in closed form using the Fourier transform on the group of rigid-body motions. We present numerical results that use this technique.

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