An Optimization-Based Hierarchical Framework for Affine Formation Control of Nonholonomic Mobile Robots

This paper proposes a hierarchical framework for achieving the affine formation of multiple nonholonomic mobile robots in undirected graphs with moving leaders. The proposed framework consists of three layers, each serving a specific function: First, through the communication between robots, a distributed optimization-based algorithm is applied in the top layer to generate the affine formation position-velocity trajectories for the followers. Then, the middle layer reconstructs the aforementioned trajectories into equivalent reference linear- and angular-velocity signals in virtual nonholonomic mobile robots. Meanwhile, to address inaccessibility of angular velocity signals in reference nonholonomic mobile robots, a linear extended state observer is designed to provide bounded estimation. Finally, based on the reference nonholonomic mobile robots, a tracking algorithm is employed in the bottom layer to enable the follower robots to track the desired position in affine formation, along with a robustness analysis of tracking performance concerning reconstruction errors in reference nonholonomic mobile robots. The effectiveness of the proposed framework are verified by simulation results.