Ensemble Control for Massive-Scale Heterogeneous Robotic Systems under Signal Temporal Logic Specifications

Ensemble control, as a promising area in the mathematical control theory, has emerged as a discipline that involves the guidance of a countless collection of dynamical systems that share a similar structure. By the other hand, task satisfaction by a set of robots can be represented by a specialized semantics that encompasses the task features into a term called robustness degree. This latter measures how well a task is satisfied given a trajectory signal. In this sense, this work presents a combined optimal control framework between ensemble control and Signal Temporal Logic (STL) for task compliance. Initially solved for the system dynamics transformation, a moment-based method is used to establish the one-to-one correspondence between an ensemble system in state space and its equivalent in the moment space. By applying the moment transformation to a task described in terms of STL semantics, an ensemble of trajectories can be generated by rolling out an open loop control in such a way that the specifications of a task are satisfied, i.e., way-points visiting. Experimental validation is performed on a system applied to the unicycle model for an Unmanned Ground Vehicle (UGV).