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During various acts, a robot may unintentionally tip over, rendering it unable to move normally. The ability to self-right and recover in such situations is crucial to mission completion and safe robot recovery. However, nearly all self-righting solutions to date are point solutions, each designed for a specific platform. As a first step toward a generic solution, this paper presents a framework for analyzing the self-righting capabilities of any generic robot on sloped planar surfaces. Based on the planar assumption, interactions with the ground can be modeled entirely using the robotâ€™s convex hull. We begin by analyzing the stability of each robot orientation for all possible joint configurations. From this, we develop a configuration space map, defining stable state sets as nodes and the configurations where discontinuous state changes occur as transitions. Finally, we convert this map into a directed graph and assign costs to the transitions according to changes in potential energy between states. Based upon the ability to traverse this directed graph to the goal state, one can analyze a robotâ€™s ability to self-right. To illustrate each step in our framework, we use a two-dimensional robot with a one degree of freedom arm, and then show a case study of iRobotâ€™s Packbot. Ultimately, we project that this framework will be useful both for designing robots with the ability to self-right and for maximizing autonomous self-righting capabilities of fielded robots.
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