Hierarchical control of cooperative nonlinear dynamical systems

Cooperative control methods that are scalable with low computational cost are crucial for networked dynamical systems to respond quickly in unknown or cluttered environments. In an attempt to make the problem tractable, many existing cooperative controls are designed with oversimplified assumptions and/or without the capabilities of rapidly handling different environmental and dynamical constraints. In this article, proposed is a two-level hierarchical, cooperative control framework using a divide-and-conquer strategy so that challenges can be separately handled at different levels. It is scalable and has low computational cost. Based on a simplified homogeneous double-integrator dynamic model, the top-level planner first computes cooperative trajectories satisfying obstacle avoidance requirements. Then at the lower level, state and control constraints, nonlinear dynamics and self-collision/obstacle avoidance as related to the real system are addressed through a bio-inspired fast trajectory planning algorithm. The stability of the overall hierarchical structure is proven. Two examples, a differential-drive ground vehicle formation control and an unmanned aerial vehicle formation flight, are used to illustrate the advantages of the proposed hierarchical framework.