A dynamical systems approach to behavior-based formation control

TLDR

The study uses dynamical systems theory to design a distributed control architecture that enables a team of three autonomous robots to navigate in formation while avoiding obstacles. Behavioral dynamics are modeled over a state‑space of behavioral variables, with task constraints represented as attractors or repellers, and combined into vector fields that govern each robot’s motion. The resulting nonlinear dynamical systems are validated by computer simulations, demonstrating the viability of the proposed architecture.

Abstract

The dynamical systems theory is used here as a theoretical language and tool to design a distributed control architecture that generates navigation in formation, integrated with obstacle avoidance, for a team of three autonomous robots. In this approach the level of modeling is at the level of behaviors. A "dynamics" of behavior is defined over a state-space of behavioral variables. The environment is also modeled in these terms by representing task constraints as attractors (i.e., asymptotically stable states) or repellers (i.e., unstable states) of behavioral dynamics. For each robot attractors and repellers are combined into a vector field that governs the behavior. The resulting dynamical systems that generate the behavior of the robots are nonlinear. Computer simulations support the validity of our dynamic model architectures.