25 May 2012 Game theory applied to legged robotics: a variant of the dolichobrachistochrone problem
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Abstract
We model the scenario between a robotic system and its operating environment as a strategic game between two players. The problem will be formulated as a game of timing. We will treat disturbances in a worst case scenario, i.e., as if they were placed by an opponent acting optimally. Game theory is a formal way to analyze the interactions among a group of rational players who behave strategically. We believe that behavior in the presence of disturbances using games of timing will reduce to optimal control when the disturbance is suppressed. In this paper we create a model of phase space similar to the dolichobrachistochrone problem. We discretize phase space to a simple grid where Player P is trying to reach a goal as fast as possible, i.e., with minimum cost. Player E is trying to maximize this cost. To do this, E has a limited number of "chips" to distribute on the grid. How should E distribute his resources and how should P navigate the grid? Rather than treating disturbances as a random occurrence, we seek to treat them as an optimal strategy
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Paul Muench, David Bednarz, "Game theory applied to legged robotics: a variant of the dolichobrachistochrone problem", Proc. SPIE 8387, Unmanned Systems Technology XIV, 838714 (25 May 2012); doi: 10.1117/12.921842; https://doi.org/10.1117/12.921842
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