The objective of this work is to generate new fundamental science for computer controlled complex physical systems, a broad class of cyber-physical systems (CPS) and demonstrate this science in aerial vehicles and walking robots. The new science enables autonomous planning and control in the presence of failures and abrupt changes in system variables. A framework for the design of algorithms that exploit awareness of the physical and design constraints to autonomously self-adapt their motion plan and control actions will be generated. The approach exploits elements from geometry, adaptive control, and hybrid control to advance the knowledge on modeling, planning, and design of CPS with constraints, non-smooth, and intertwined continuous and discrete dynamics. Unlike current approaches, which separate the task associated with planning the motion from the design of the algorithm used for control, the algorithms to emerge from this project self-learn and self-adapt in real time to cope with unexpected changes in motion and specification constraints so as to enable autonomous systems to perform robustly and safely, and degrade gracefully under failure conditions. Specifically, the new algorithms will learn and monitor the physical and design constraints in real time and adapt both planner and controller by selecting the appropriate constraints to enforce, with robustness and safety guarantees. The capabilities of the new tools will be demonstrated on multi-legged robots in harsh environments that make them prone to failures, and on aerial vehicles in contested/adversarial environments.