Abstract
This paper develops a Bearing-Ratio-of-Distance (B-RoD) rigidity theory to study when a framework can be uniquely determined by a set of B-RoD constraints up to directly similar transformation (translation, positive scaling). In particular, a framework is specified by a set of B-RoD constraints, i.e., mixed bearing and RoD measurements (the ratio of distances of a pair of edges joining a common vertex), instead of distance, bearing and angle constraints assumed in existing literature. The proposed B-RoD rigidity theory is further applied to the B-RoD-based directly similar formation stabilization problem where the desired formation shape is expressed as a set of B-RoD constraints. Finally, numerical simulations are presented to illustrate the effectiveness of the theoretical results.
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