Design of the dynamic stability properties of the collective behavior of articulated bipeds

The control of the collective behavior of multiple interacting agents is a challenging problem in robotics and autonomous systems design. Such behaviors can be characterized by the dynamic interaction between multiple locomoting bipeds with highly nonlinear articulation dynamics. The analysis and design of the stability properties of such complex multi-component systems is a largely unsolved problem. We discuss a first approach to this problem exploiting concepts from Contraction Theory, a recent framework for the analysis of the stability of complex nonlinear dynamical systems. We demonstrate the application of this framework to groups of humanoid agents interacting collectively in different ways, requiring different types of control rules for their propagation in space and their articulation dynamics. We illustrate the framework based on a learning-based realtime-capable architecture for simulation of the kinematics of propagating bipeds, suitable for the reproduction of natural locomotion trajectories and walking styles. Exploiting central theorems from Contraction Theory and nonlinear control, we derive conditions guaranteeing the global exponential stability of the formation of the coordinated multiagent behavior. In addition, we demonstrate that the same approach permits to derive bounds that guarantee minimum convergence speeds for the formation of ordered states for collective behaviors of multiple humanoid agents.