Three controllers via 2nd-order sliding mode for leader-following formation control of multi-robot systems

Abstract

The multi-robot formation has always been an attractive field for cooperative control of robots. This paper uses the improved second-order sliding mode method to control the leader-following formation system. The traditional second-order sliding mode control is not perfect because the disturbances and uncertainties of the system may cause the compensation control to overestimate. The adaptive gain super-twisting sliding mode control suppresses the output oscillation and speeds up the system response by improving the gain function and adding a differential link. However, this method is generally applied to single-input single-output systems. This paper attempts to apply this method to a multi-input-multi-output leader-following formation system and improve its switching function and compensation control part. We use the estimators, i.e., the extreme learning machine and the nonlinear disturbance observer. These estimators can observe disturbance changes to replace the adaptive gain function to realise disturbance estimation and compensation control. Then combine the extreme learning machine and the nonlinear disturbance observer with the super-twisting sliding mode control to produce two new sliding mode methods. We use the Lyapunov method to prove the system stability as well. Finally, we illustrate the feasibility of the three control methods.