ISSN 0005-1179, Automation and Remote Control, 2018, Vol. 79, No. 3, pp. 463–478.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
Yu.V. Morozov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 3, pp. 92–110.
CONTROL IN TECHNICAL SYSTEMS
Emergency Control of a Quadrocopter
in Case of Failure of Two Symmetric Propellers
Yu. V. Morozov
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Received April 3, 2017
Abstract—In this work, we simulate the motion of a quadcopter when two symmetric propellers
fail and the full thrust is gradually decreasing on each of the remaining propellers. Applying
a control obtained in standard mode leads to the ﬂying vehicle falling down. We pose and
solve the problem of synthesizing a bounded control law that lets one land the ﬂying vehicle.
We consider numerical modeling problems that arise in the implementation of the proposed
mathematical model of a quadcopter.
Keywords: quadcopter control, bispinner control, LQR-control, ﬁnite time control
Control of ﬂying vehicles has been the subject of a huge number of works. The invention of
the ﬁrst quadcopters caused a surge of interest in the ﬁeld. The number of works is so large
that at present we can point of several works  that contain a classiﬁcation of control algorithms
for diﬀerent models of a quadcopter with qualitative analysis of these algorithms. However, even
among this ﬂurry of works we can ﬁnd whole directions that have not been worked through or that
appear in the works of diﬀerent authors only on the level of a problem setting. In this work we
consider one such research direction: quadcopter control in emergency situations. The ﬁrst thesis
devoted to this topic was . The author was able to classify emergency situations and propose
methods for solutions, but full failure of an engine was not considered as an emergency situation.
We use the results of  and introduce a new extended classiﬁcation of failures as follows.
1. Propeller thrust reducing but not below a critical value. For practical reasons, we choose
the critical value to be equal to 30% of maximal thrust. This usually happens when the battery
discharges in a non-uniform way.
2. Temporary propeller failure or temporary reduction of thrust below 30% of the maximal
thrust. The time interval over which this happens is rather short, i.e., the time during which we
recognize the failure is smaller than the time needed to compute the control.
3. Full propeller failure or thrust reduction below 30% of the maximal thrust.
4. Full failure of two symmetric propellers.
5. Full failure of two adjacent (neighboring) propellers.
6. Full failure of three propellers.
Using this classiﬁcation, we can ﬁnd only a few works that solve, with varying degree of success,
the problem of control when one or several failures arise. For simplicity of further exposition,
the failure type will correspond to the index in the classiﬁcation above. Thus, the work  pays
most attention to solving the problem with failures nos. 1 and 2 in a quadcopter. The problem
of automatically detecting them during the ﬂight has not been considered. The work  shows a