On synchronization and collision avoidance for mechanical systems

The current interest in coordinating nonlinear dynamical systems with safety guarantees is driven by emerging practical applications. One of the primary objectives in coordination of multiple mechanical systems (agents) is velocity synchronization with guarantees for collision avoidance among the agents. However, previous results in this direction assume point models for the agent, allow only linear dynamics and neglect delays in communication between the agents. In this paper we demonstrate that velocity synchronization and collision avoidance are simultaneously achievable in non-point, nonlinear mechanical systems in the presence of communication delays and switching interconnection topologies. A numerical example is presented to justify the proposed results.