Aerospace and Electronic Systems Magazine September 2016 - 34

An Autonomous Quadrotor Avoiding a Helicopter in Low-Altitude Flights
using the control inputs U2 and U3 defined in (1). The detail implementation is not presented for simplicity.

ITERATIVE ALGORITHM
With control conversion (9), we can apply kinematic control law
(6) at ∂Kh, defined by (7) and (8), to the dynamical system (2) with
control inputs (1). However, the quadrotor will intrude the safety
set Sh due to control delay introduced from RI and aerodynamic
drag in the full dynamic model. To resolve the intrusion, we need
to compute the worst case earlier reaction time (WCERT), or the
time the quadrotor has to react earlier before touching the safety set
Sh, to prevent collision in the worst case scenario.
Algorithm 1: Iterative algorithm to compute WCERT.
Data: dt, wcert
Result: wcert
dt;

% time increment

wcert = 0;

% current WCERT

x(t) = worst_case(wcert);
while mint|x(t)| < rmin do

The hybrid automaton indicating the controller switching mechanism.

mechanism. At the beginning, the quadrotor receives a waypoint
command, and the position controller starts to drive the quadrotor
to the destination. When a helicopter is detected, an avoidance set
calculation is performed using (7). The switching occurs when the
quadrotor intrudes ∂Kh, or
. Once the safety controller is activated, the quadrotor avoids the helicopter by applying amax in the optimal direction . After
, the
optimal controller is deactivated, and the quadrotor switches back
to position control. If another helicopter is passing by, the optimal
control is enabled again.

SIMULATION

wcert = wcert + dt;
x(t) = worst_case(wcert);
end
Algorithm 1 computes WCERT for the horizontal safety controller. The function x(t) = worst_case(wcert) simulates the worst
case avoidance scenario when the kinematic controller reacts wcert
earlier, and return the relative horizontal position x(t) for the whole
simulation period.
We start the simulation from the safety sets (7). If the minimum relative distance mint|xh(t)| is less than rmin, then we increment
wcert and simulate again. In this case, we set dt to be 0.02 s in
the case without drag and 0.05 s with drag, which gives a spacial
resolution of 2 m and 5 m, respectively, when maximum speed is
v = 100 m/s.
Algorithm 1 is applied to a range of amax and v. The result is a
look-up table WCERT(amax,v). With this look-up table, WCMMD
can be recomputed. The generation of WCERT values is time
consuming but performed off line. In real flights, we can just run
the light-weight kinematic safety controller in real-time but react
WCERT(amax,v) earlier. If the dynamic model in the simulation is
close to the real dynamics, then we are safe. To obtain usable results, system identification should be performed to establish conservative quadrotor parameters, which is out of the scope of this
article and not discussed. Interested readers can refer to [37].

THE HYBRID CONTROLLER
The position controller with DSC filters mentioned and the safety
controller together constitute a hybrid controller. The safety controller decides when the safety maneuver starts and terminates.
Figure 2 shows the hybrid automaton of the controller switching
34

Figure 2.

The simulations are divided into two parts. The first part examines
the behavior of the safety controller, and the second part presents
how the hybrid automaton behaves in the scenario defined at the
end of the first section.
Before presenting the results, we should first justify the parameters chosen for the simulations. The parameter values, listed
in (10), are chosen carefully and conservatively to model a realistic quadrotor model (3DR Solo [40]). However, these parameters
vary a lot from different quadrotors, communication systems, and
wind conditions. Therefore, the results are not intended to cover
all possible cases. What we can guarantee is that our safety control
algorithm could give conservative results given conservative parameters for a given quadrotor with a known communication delay
and bounded wind disturbance.

(10)
There are four key parameters which dominate the simulation
results, namely RI I, the translation drag coefficient ct, the communication delay Dtdelay, and the minimum separation distance rmin.
I = diag(Ix, Iy, Iz): We approximate the RI by approximating the
3DR Solo as a solid cylinder of radius 0.1 m and height 0.1 m. The
calculation follows from [38], and the system identification results
in [37] validate our calculation.
ct: Instead of adopting results from [37], which yields an unrealistically large terminal speed, we picked a more conservative
value of 0.5 Ns/m, which yields a terminal horizontal speed of vmax

IEEE A&E SYSTEMS MAGAZINE

SEPTEMBER 2016



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