This paper presents periodic solutions for a quadrocopter maintaining a height around a position in space despite having lost a single, two opposing, or three propellers. In each case the control strategy consists of the quadrocopter spinning about a primary axis, fixed with respect to the vehicle, and tilting this axis for translational control. A linear, time- invariant description of deviations from the attitude equilibrium is derived, allowing for a convenient cascaded control design. The results for the cases of losing one and two propellers are validated in experiment, while the case of losing three propellers is validated in a nonlinear simulation. These results have application in multicopter fault-tolerant control design, and also point to possible design directions for novel flying vehicles.

/pdf/stability-and-control-of-a-quadrocopter-despite-the-complete-26zvur815f.pdf

Stability and control of a quadrocopter despite the complete loss of one, two, or three propellers

This paper provides nonlinear tracking control systems for a quadrotor unmanned aerial vehicle (UAV) that are robust to bounded uncertainties. A mathematical model of a quadrotor UAV is defined on the special Euclidean group, and nonlinear output-tracking controllers are developed to follow (i) an attitude command, and (ii) a position command for the vehicle center of mass. The controlled system has the desirable properties that the tracking errors are uniformly ultimately bounded, and the size of the ultimate bound can be reduced arbitrarily by control system parameters. Numerical examples illustrating complex maneuvers are provided.

/pdf/nonlinear-robust-tracking-control-of-a-quadrotor-uav-on-se-3-tma8fklcw3.pdf

Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3)

This brief describes robust adaptive tracking control systems for the attitude dynamics of a rigid body. Both the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and ambiguities associated with other attitude representations, such as Euler angles or quaternions. By designing an adaptive law for the inertia matrix of a rigid body, the proposed control system can asymptotically follow an attitude command without the knowledge of the inertia matrix, and it is extended to guarantee boundedness of tracking errors in the presence of unstructured disturbances. These are illustrated by the experimental results of the attitude dynamics of a quadrotor unmanned aerial vehicle.

Robust Adaptive Attitude Tracking on ${\rm SO}(3)$ With an Application to a Quadrotor UAV

Exponential stability of an attitude tracking control system on SO(3) for large-angle rotational maneuvers☆

http://flyingmachinearena.org/wp-content/publications/2014/lupashin2014platform.pdf

A platform for aerial robotics research and demonstration: The Flying Machine Arena

Rigid-body attitude control is motivated by aerospace applications that involve attitude maneuvers or attitude stabilization The set of attitudes of a rigid body is the set of 3 X 3 orthogonal matrices whose determinant is one This set is the configuration space of rigid-body attitude motion; however, this configuration space is not Euclidean Since the set of attitudes is not a Euclidean space, attitude control is typically studied using various attitude parameterizations Motivated by the desire to represent attitude both globally and uniquely in the analysis of rigid-body rotational motion, this article uses orthogonal matrices exclusively to represent attitude and to develop results on rigid-body attitude control An advantage of using orthogonal matrices is that these control results, which include open-loop attitude control maneuvers and stabilization using continuous feedback control, do not require reinterpretation on the set of attitudes viewed as orthogonal matrices The main objec tive of this article is to demonstrate how to characterize properties of attitude control systems for arbitrary attitude maneuvers without using attitude parameterizations

N A Chaturvedi

Papers

Rigid-Body Attitude Control