Ensuring safety in autonomous systems is essential as they become more integrated with modern society. One way to accomplish this is to identify and maintain a safe operating space. To this end, much effort has been devoted in the field of reachability analysis to obtaining control-invariant sets which ensure that a system inside of these sets can remain in these sets, and are thus essential for guaranteeing a system's safety. However, control invariance does not imply that a system can move from any state in the control-invariant set to any other state in the control-invariant set, within a given time horizon. In this paper, we develop an algorithm to obtain a control-invariant set that allows a given system to move from any state in the set to any other state in the set within a given time horizon without having to leave the set. We call this the 'maneuver set', M. We substantiate the algorithm's efficacy through mathematical proof, affirming that the maneuver set obtained through the algorithm is indeed control-invariant. Furthermore, we prove that the system is indeed able to move from any state within this set to any other state in the set. To illustrate the use of our algorithm, we provide the numerical example of a Dubins car, utilising Hamilton-Jacobi-Bellman reachability analysis along with the proposed algorithm in order to obtain M.

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Unmanned aerial vehicles (UAVs) are becoming an integral part of both industry and society. In particular, the quadrotor is now invaluable across a plethora of fields and recent developments, such as the inclusion of aerial manipulators, only extends their versatility. As UAVs become more widespread, preventing loss-of-control (LOC) is an ever growing concern. Unfortunately, LOC is not clearly defined for quadrotors, or indeed, many other autonomous systems. Moreover, any existing definitions are often incomplete and restrictive. A novel metric, based on actuator capabilities, is introduced to detect LOC in quadrotors. The potential of this metric for LOC detection is demonstrated through both simulated and real quadrotor flight data. It is able to detect LOC induced by actuator faults without explicit knowledge of the occurrence and nature of the failure. The proposed metric is also sensitive enough to detect LOC in more nuanced cases, where the quadrotor remains undamaged but nevertheless losses control through an aggressive yawing manoeuvre. As the metric depends only on system and actuator models, it is sufficiently general to be applied to other systems.

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Quadcopters are becoming increasingly popular across diverse sectors. Since rotor damages occur frequently, it is essential to improve the attitude estimation and thus ultimately the ability to control a damaged quadcopter. This research is based on a state-of-the-art method that makes it possible to control the quadcopter despite the total failure of a single rotor, where the attitude and position of the quadcopter are provided by an external system. In the present research, a novel attitude estimator called Adaptive Fuzzy Complementary Kalman Filter (AFCKF) has been developed and validated that works independently of any external systems. It is able to estimate the attitude of a quadcopter with one fully damaged rotor while only relying on the on-board MARG (Magnetometer, Accelerometer, Rate Gyroscope) sensors. The AFCKF provides significantly better attitude estimates for flights with a damaged rotor than mainstream filters, estimating the roll and pitch of the quadcopter with an RMS error of less than 1.7 degrees and a variance of less than 2 degrees. The proposed filter also provides accurate yaw estimates despite the fast spinning motion of the damaged quadcopter, and thus outperforms existing methods at the cost of only a small increase in computation.@en