Practical time-varying formation tracking for multiple non-holonomic mobile robot systems based on the distributed extended state observers

Practical time-varying formation tracking analysis and design problems for multiple non-holonomic mobile robot systems with directed interaction topologies are investigated by using the distributed extended state observers, where the practical time-varying formation tracking error is controlled within an arbitrary small bound. Different from the previous work, the dynamics of each robot is non-holonomic and the followers are required to form the practical time-varying formation with respect to the leader of unknown control inputs. Besides, the disturbances and the uncertainties are considered in the dynamic model of the follower. Distributed extended state observers are constructed by using only the neighbouring relative information to estimate both the state and the unknown control inputs of the leader simultaneously. A practical time-varying formation tracking protocol is presented based on the distributed extended state observers. The gain matrices of the observers in the practical time-varying formation tracking protocol can be obtained by solving three linear matrix inequalities. Moreover, the stability of the multiple non-holonomic mobile robot system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, two numerical simulation examples are given to illustrate the effectiveness of the obtained theoretical results.