Online safety verification of trajectories for unmanned flight with offline computed robust invariant sets

We address the problem of verifying motion plans for aerial robots in uncertain and partially-known environments. Thereby, the initial state of the robot is uncertain due to errors from the state estimation and the motion is uncertain due to wind disturbances and control errors caused by sensor noise. Since the environment is perceived at runtime, the verification of partial motion plans must be performed online (i.e. during operation) to ensure safety within the planning horizon and beyond. This is achieved by efficiently generating robust control invariant sets based on so-called loiter circles, where the position of the aerial robot follows a circular pattern. Verification of aerial robots is challenging due to the nonlinearity of their dynamics, the high dimensionality of their state space, and their potentially high velocities. We use novel techniques from reachability analysis to overcome those challenges. In order to ensure that the robot never finds itself in a situation for which no safe maneuver exists, we provide a technique that ensures safety of aerial robots beyond the planning horizon. Our method is applicable to all kinds of robotic systems that follow reference trajectories, such as bipedal robotic walking, robotic manipulators, automated vehicles, and the like. We evaluate our method by simulations of high speed helicopter flights.