Achieving the science exploration and defense goals of the following decades will require flight systems capable of operations with limited operator contact, system mode changes and retasking based on sensor data, and complex robotic operations. To support these capabilities, increasingly autonomous flight systems are required that can perform dedicated mission functions, e.g. payload targeting and communications, and system-level functions, e.g. planning and goal monitoring. Architecting an autonomous system requires a well-reasoned, self-consistent framework to avoid \textit{ad hoc} design choices that will introduce complexity and risk. The Framework for Robust Execution and Scheduling of Commands On-Board, FRESCO, is the result of lessons learned in developing a software architecture to enable autonomous solar system exploration. FRESCO generalizes this work to offer a modular, software-agnostic approach to developing verifiable architecture for autonomous space systems. FRESCO specifies guiding principles, functions, interfaces, and interactions from which mission-specific autonomous control architectures can be derived. FRESCO is a principled framework relying on explicit, state-based goal definitions, centralized management of state knowledge, clearly separated control boundaries, and hierarchical reasoning. Using components from FRESCO reference architecture, an autonomous decision-making architecture can be designed for spacecraft which can then be mapped to flight software architecture. FRESCO is flexibly defined to enable autonomous control of flight systems built using extensive software and hardware heritage. Finally, FRESCO-derived architectures support a spectrum of operator/spacecraft interactions, ranging from traditional commanding to goal-driven commanding with the ability to change mission goals autonomously. FRESCO has been used in defining the autonomy architectures for the ASTERIA mission and have been demonstrated in laboratory and software simulation for small body rendezvous and in-space servicing missions.