Suboptimal Relational Tree Configuration and Robust Control Based on the Leader-follower Model for Self-organizing Systems Without GPS Support

This paper surveys the formation acquisition and maintenance of multi-agent systems, while the communication graph is obtained without human designations. Given that all agents move along unpredictable paths during formation acquisition, the systems adopt the leader-follower model. For better expression of the graph construction, a relational tree is introduced to describe the follower-leader pairs. Then, a distributed method is proposed for suboptimal relational tree configuration. By utilizing particle swarm optimization (PSO), the search for follower-leader pairs is converted to permutation optimization. Based on principal component analysis (PCA), the entire group is divided into several small groups, and the optimization can be implemented in each group, thus releasing the computation burden. To acquire the formation defined by the suboptimal relational tree, a second nonlinear controller subject to the loss of GPS information is established. The controller takes the reference in the local velocity frame as inputs, and proportional and differential components are introduced to provide a soft control. In addition, adaptive parameters are designed for robust control. By tuning the parameters autonomously, self-organized systems can work well in various scenarios even without manual adjustment of parameters. Mathematical and numerical analyses are conducted to prove the feasibility of the proposed strategy.