Fail-Safe Controller Architectures for Quadcopter with Motor Failures

Abstract

A fail-safe algorithm in case of motor failure was developed, simulated, and tested. For practical fail-safe flight, the quadcopter may fly with only three or two opposing propellers. Altitude for two-propeller architecture was maintained by a PID controller that is independent from the inner and outer controllers. A PID controller on propeller force deviations from equilibrium was augmented to the inner controller of the threepropeller architecture. Both architectures used LQR for the inner attitude controller and a damped second order outer controller that zeroes the error along the horizontal coordinates. The restrictiveness, stability, robustness, and symmetry of these architectures were investigated with respect to their output limits, initial conditions, and controller frequencies. Although the three-propeller architecture allows for distribution of propeller forces, the two-propeller architecture is more efficient, robust, and stable. The two-propeller architecture is also robust to model uncertainties. It was shown that higher yaw rate leads to greater stability when operating in fail-safe mode.

Modeling and Implementation of Quadcopter Autonomous Flight Based on Alternative Methods to Determine Propeller Parameters

“…Under basic flight conditions, a state space that completely specifies the six degrees of freedom of a quadcopter and may be used for dynamic computations is (ϕ, θ, ψ, p, q, r, x, y, z, x, y, z). [1] x inertial position along x $ i in C i y inertial position along y $ i in C i z altitude along ẑi in C i u body frame velocity along x $ b in C b v body frame velocity along y $ b in C b w body frame velocity along ẑb in C b ϕ roll angle in C v2 θ pitch angle in C v1 ψ yaw angle in C v p roll angular velocity about x $ b in C b q pitch angular velocity about y $ b in C b r yaw angular velocity about ẑb in C b…”

“…where B is the base weight which is set to Mg or one-fourth the total weight of the quadcopter; this is to ensure equal sharing of load among the four motors at hover. u z , before being used in Equation (25), is first rescaled by dividing it by ẑb •ẑi=cos(ϕ)cos(θ) or the directional cosine between the quadcopter's body frame z-axis and the direction pointing opposite to gravity in order to take into account the quadcopter tilt which reduces the lift force [1].…”

“…Notice that the model for the drag is more accurate at higher angular velocities. This property proved useful in fail-safe mode [1] where the quadcopter's yaw rate would exceed normal operation values. Figure 10 shows the breakdown of the basic flight controller to various sub-algorithms with their execution times.…”

“…The exponential smoothing of p, q, r were done first before performing the sensor fusion technique [1]. The α EMA for each gyroscope reading was tuned while the quadcopter was being held mid-air.…”

“…This paper is an extension of work originally presented in the 6th International Conference on Control, Automation and Robotics [1].…”