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This work investigates the position centroid rendezvous problem of multiple unicycle agents for the first time.By constructing a new output, the unicycle model is converted to canonical normal form via feedback linearization approach.Then, the centroid rendezvous control law is proposed, guaranteeing that all the agents globally meet at the common initial centroid location.The proposed control law is distributed, smooth and time-varying, ensuring the internal orientation states and the velocity inputs convergent to some fixed values and zero respectively.The result is proved under the communication scenarios of fixed directed balanced graph with a spanning tree.Simulation result verifies the effectiveness of the proposed control scheme.