Safe affine formation using terminal sliding mode control with input constraints

Formation control is a fundamental task in the realm of autonomous multiagent systems. To drive a group of agents to maneuver continuously with the desired formation, this paper studies the finite-time affine formation control problem with disturbances, input constraints and safety guarantee. A non-singular terminal sliding mode control (NTSMC) is implemented to achieve finite-time convergence of all followers to their desired positions. Additionally, an auxiliary system is deployed to address input constraints resulting from the physical properties of the affine formation system. To mitigate the impact of lumped disturbances, a finite-time disturbance observer (FTDO) is employed to estimate the disturbances and compensate for their effects. Based on FTDO, the auxiliary system and the above NTSMC, a finite-time robust controller is developed as the nominal controller. By modifying the nominal controllers to comply with safety constraints, control barrier functions are employed to ensure the safety of the formation system in obstacle-filled environment. Finally, the effectiveness and feasibility of this method are validated through simulations and real-world experiments.