Abstract
In this paper we formulate an optimization based approach to determining the maximally inscribed rectangle in a robot’s workspace. The size and location of the maximally inscribed rectangle is an effective index for evaluating the size and quality of a robot’s workspace. Such information is useful for, e. g., optimal worktable placement, and the placement of cooperating robots. For general robot workspaces we show how the problem can be formulated as a constrained nonlinear optimization problem possessing a special structure, to which standard numerical algorithms can be applied. Key to the rapid convergence of these algorithms is the choice of a starting point; in this paper we develop an efficient computational geometric algorithm for rapidly obtaining an approximate solution suitable as an initial starting point. We also develop an improved version of the algorithm of Haug et al. for calculating a robot’s workspace boundary.
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