Learning from Demonstrations meets Symbolic Control - A Supervisory Control Architecture for Formal Certification of Learned Motion

Dynamical system (DS)-based learning from demonstration generates flexible robot motions, but existing guarantees rely on certificate generation to obtain formal guarantees of safety and goal convergence. We propose a symbolic supervisory control architecture that automatically generates a fail-safe backup plan, certifying safety, reachability, and actuator feasibility directly from the robot's dynamics, independent of the learned DS. A nominal controller tracks the learned DS, while the supervisory controller monitors safety and target convergence, providing non-conservative intervention when the nominal controller violates necessary constraints. Experimental results include simulations and real robot deployment with various 2D and 3D datasets, including handwriting datasets, validating the effectiveness of our approach in providing formal guarantees with learned motion even in complex, dynamic environments.