Formation Control with Mismatched Orientation in Multi-Agent Systems

In formation control problems, the orientation information of an autonomous agent may suffer from measurement errors among sensors, e.g., gyroscopes drifts, calibrate data errors and communication link failures. These measurement errors may lead to some changes of the positions of agents such that the specified formation of all agents cannot be achieved. This paper investigates the formation control problem of multi-agent systems, where each agent has orientation measurement errors when moving forward in a three-dimensional space. Such orientation measurement errors can be considered as rotation behaviors of agents, and we call this phenomenon mismatched orientation. To analyze the formation control problem with mismatched orientation, the position and velocity information of multi-agent systems is tackled by utilizing the Hajnal inequality and several mathematical techniques. The derived results reveal that the actual final formation of multi-agent systems is distorted from the desired position and can asymptotically approach to some local spheres. Based on the derived results, a distributed compensation control strategy is then applied to dealing with the formation control problem under mismatched orientation to achieve the specified shape. Subsequently, an example validates the effectiveness of our results.