Optimal cooperative control of mobile robots based on Pontryagin's Minimum Principle

This work presents the cooperative control with optimization for positioning of mobile robots based on Pontryagin's Minimum Principle. The problem to be solved is the minimum energy related to the control actions of the robots. The objective function is subject to the equations of states of the triangular formation of the 3 mobile robots and is restricted to boundary conditions that include the desired form parameters. The mathematical model of the system is based on the kinematic transformation of the position of the robots towards the parameters of the formation. To solve the differential equations obtained, the shooting method is programmed for two initial value problems. The results show the evolution of the robots' positions and the positioning errors that tend to zero, validating this proposal through simulation. In addition, the control actions allow determining the energy index to compare it with a previous work, achieving a lower value.