Formal verification of quadcopter flight envelop using theorem prover

Quadcopter controllers are in use today and in practice they can often cope well in non adverse weather conditions such as lack of strong sudden gusts of wind around the corner of a building or no frequent demands of travel directions by remote control or a guidance law. Different payloads can alter the boundaries of the stable state space region of a drone, its flight envelop, beyond which its autopilot may not be able to regain stable control of the craft. For fixed gain autopilot controllers, reaching the boundary of the flight envelop can be caused by (1) external disturbance like gusts of wind and turbulence, (2) altered drone mass and its distribution and (3) reduction or misalignment of thrust output in the propulsion system caused ware after multiple uses of the drone. This paper introduces symbolic computation to map out the numerical boundaries of controller tolerances in terms of these three factors that affect the autopilots ability to retain stability of the craft. Proof theoretic methods are developed that can be applied to quadcopter of various nominal parameters.