Formation control and collision avoidance for multi-agent systems based on position estimation

•We develop two formation control algorithm using estimated position.•The control energy is considered in one algorithm based on the Maximum principle.•Another normal consensus algorithm under estimated position is presented.•Relative estimated position is used in extra obstacle avoidance control input.

In this paper, formation control strategies based on position estimation for double-integrator systems are investigated. Firstly, an optimal control formation control strategy is derived based on the estimator. It is proven that the control inputs are able to drive the agents to the predefined formation and the controller is optimal even based on the estimation law if the estimator has converged to stable. Secondly, a consensus law based on the estimator is presented, which enables the agents converge to the formation in a cooperative manner. The stability can be guaranteed by proper parameters. Thirdly, extra control input for inter collision avoidance is added into the derived consensus control strategy, and efficacy analysis are provided in detail. Finally, the effectiveness of the strategies proposed are shown by simulation and experiment results.