Adaptive bearing rigid formation control for multiple nonholonomic unicycles with nonlinear dead-zone inputs

This paper investigates the bearing rigid formation control problem for nonholonomic systems with unknown nonlinear dead-zone inputs and external disturbances. While most existing research on cooperative formation control has been based on the premise of complete information, the complex dynamics of operational robots inevitably introduce incomplete information, including input nonlinearity, external disturbances, and dynamic coupling within the network, which can significantly impact the performance of the formation system. This study makes two significant contributions. First, it proposes a distributed bearing-based formation control method for nonholonomic systems operating in environments characterised by incomplete information, such as uncertain disturbances and nonlinear dead-zones in actuators. Second, fully distributed adaptive dynamic estimators, which rely on relative bearing measurements, are employed to effectively counteract the adverse impacts of nonlinear dead-zone inputs and external disturbances. Additionally, an input-to-state stable formation control law, relying exclusively on relative bearing measurements of nonholonomic unicycles, is developed to achieve the desired bearing rigid formation without collisions in a multi-robot system. Finally, the global stability of the nonholonomic bearing-rigid formation system is established using the ISS Lemma for cascade systems. The effectiveness of the proposed formation control strategy is demonstrated through both simulation and experimental results.