Minimum cost open chain reconfiguration

An open chain or nn-link is a sequence of nn links with fixed lengths that are joined together at their endpoints and can turn about their endpoints, which act as joints. Positions of the joints of a chain define a configuration of the chain in the space. In one-dimensional space, we define a binary configuration as a sequence of direction of links. Open chain reconfiguration is a sequence of predefined transformation operations which can be used to convert a given binary configuration to another given binary configuration. Each transformation operation is assigned a cost. For two given binary configurations, there may be many reconfigurations whose costs are different. We formalize the problem, and we propose a dynamic programming approach to find a reconfiguration whose cost is minimum for the conversion of two given binary configurations of an open chain in the one-dimensional space. Our algorithm takes O(n2)O(n2) time using O(n)O(n) space.

► We introduce a formalizing method for the configuration of a robot arm.
► We find a dynamic programming approach for the minimum cost reconfiguration method for snake robots.
► We introduce some methods for realizing folding algorithms for snake robots.