Motion Planning and Tracking MPC for Multiagent Systems: A Dynamic Affine Formation Approach

In complex and variable terrains, affine formation control, with its flexible formation adjustment ability, can achieve various formation shapes to adapt well to the environment. Notably, the existing affine formation research based on stress matrices require the variation parameters for translation, rotation, scaling, and shearing of formations to be predesigned offline. To address this, we propose a novel method for online affine parameter adjustment that enables self-reconfiguration of formations in multiobstacle environments. By adopting APF environment excitation, the proposed motion planning algorithm can dynamically adjust the affine transformation parameters online, and realize the self-reconfiguration of formation shape to avoid collision. Then, a distributed model predictive controller is proposed for multiagent systems, which actively utilizes historical control input information to flexibly adjust controller performance while avoiding algebraic loops between neighboring agent controllers. The algorithm separates stability and performance optimization within the nonlinear model predictive control framework, ensuring both the feasibility and stability of the underlying optimization. Finally, the simulation results confirm the effectiveness of the proposed controller.