In multi-agent systems, robots transmit their planned trajectories to each other or to a central controller, and each receiver plans its own actions by maximizing a measure of mission satisfaction. For missions expressed in temporal logic, the robustness function plays the role of satisfaction measure. It is not clear how the signal representation used to compress and transmit the signal affects the robustness computation error at the receiver, and the efficiency of computing it. An incorrect robustness value, or a delayed computation result, can mean the difference between successful control and a crash. Current practice uses simple Piece-Wise Linear interpolation to reconstruct the transmitted signal, which has little compressive ability. When communication capacity is at a premium, this is a serious bottleneck.
In this talk, we study these questions on two case studies from quadrotor flight and cardiac signal monitoring. We first show that the robustness computation is significantly affected by how the continuous-time signal is reconstructed from the received samples. We show that monitoring spline-based reconstructions yields a smaller robustness error, and that it can be done with the same time complexity as monitoring the simpler piece-wise linear reconstructions. We provide a tight bound on the robustness computation error, and leverage it to design a reconstruction scheme with an even lower computation error than the spline-based schemes. Thus classical signal processing techniques come to the rescue of fragile controller synthesis.