Modified adaptive discrete-time incremental nonlinear dynamic inversion control for quad-rotors in the presence of motor faults

Abstract

Unmanned air vehicles are intrinsically non-linear, unstable, uncertain, and prone to a variety of faults, most commonly the motor faults. The main objective of this paper is to develop a fault-tolerant control algorithm for the quadrotors with the motor faults. Accordingly, a novel adaptive modified incremental nonlinear dynamic inversion (MINDI) control is proposed to stabilize and control the quad-rotor with partial motor faults. The controller consists of a MINDI controller augmented with a discrete-time nonlinear adaptive algorithm. Since the incremental nonlinear dynamic inversion (INDI) algorithm is essentially based on the sensor measurements, it necessitates the angular rates differentiation and therefore amplifies the high-frequency noises produced by the gyroscopes. The application of derivative filters causes unavoidable internal state delays in the INDI structure. Henceforth, the performance of the controller developed for the unstable and uncertain quadrotors degrades considerably. To address this drawback, this paper proposes the MINDI controller which basically derives the angular accelerations from the angular moment estimations. Furthermore, to increase the robustness of the MINDI against motor faults, a discrete-time adaptive controller has been incorporated. The performance of the proposed controllers is verified both through the nonlinear simulations and testbed experiments. The results are compared with a recent efficient algorithm, which had been implemented on a quad-rotor model.

Introduction

Multi-rotor Unmanned Aerial Vehicles (UAVs) have rapidly attracted the interest of researchers since they are being implemented in a variety of real-life areas including surveillance, reconnaissance, agriculture, rescue, and mining. One of the outstanding research challenges in multi-rotor design is the requirement of a sophisticated control algorithm that can cope with unexpected casualties like actuator (motor) failures [1], [2]. As faults and failures are inevitable in complex systems like aircraft, the researchers focus on the development of fault-tolerant control strategies for impaired UAVs [3], [4], [5]. Various fault-tolerant control (FTC) techniques have been proposed in a number of researches aiming to recover the faulty aircraft [6], [7], [8], [9], [10], [11], [12], [13]. Nonlinear L₁ adaptive control [6], robust adaptive control [7], adaptive sliding mode control [8], Linear Parametric Variable (LPV) sliding mode control [9], optimal adaptive control [10], Model Reference Adaptive Control (MRAC) [11], and Incremental Nonlinear Dynamic Inversion (INDI) controller [12], are the recent fault-tolerant control algorithms. In addition to the direct methods, a variety of fault detection and identification algorithms are also incorporated with the fault-tolerant controllers [14]. Timely detection of the actuator failures and estimation of their severity plays an important role in avoiding crashes and also leading to fast recovery for a safe landing. Fault detection algorithms [15], [16], [17] can be categorized as model-based, signal-based, knowledge-based, and active diagnosis techniques [15].

Several researchers concentrate on the control and recovery of multi-rotor UAVs in case of motor faults or failures. The FTC basically can be classified into two groups; partial actuator faults and complete loss of actuator effectiveness (actuator failure). Some researchers investigate the effects of the partial faults on the rotor and propose fault-tolerant strategies while other researches have examined the effects of motor failures and designed appropriate FTC algorithms. According to the literature, some have applied fault detection algorithms as a part of the FTC strategy, while others apply direct FTC algorithms to control multi-rotor UAVs. The partial fault of the motor results in controller effectiveness reduction which has been extensively investigated. Ref. [18] introduced an FTC to control a quad-rotor in case of a time-varying motor fault. The proposed fault-tolerant strategy includes fault detection and an identification algorithm based on the controller outputs where the angular rates are estimated with a discrete extended Kalman filter and stabilized with a discrete nonlinear adaptive tracking controller. In terms of the control of the quad-rotor in presence of the partial faults [2], a sliding mode control technique has been applied in Ref. [19] as a passive FTC to control the quad-rotor’s attitude with the partial rotor fault. An adaptive fuzzy controller is used as a compensator to alleviate the estimation error of the nonlinear functions. Ref. [20] applies a sliding mode disturbance observer incorporated with the fault-tolerant sliding mode controller to manipulate the quad-rotor with partial actuator faults as desired.

Concerning the controllability of the multi-rotors in the presence of rotor faults or failures, different configurations including the quad-rotor, hexa-rotor, and octa-rotors have been investigated to determine the level of controllability [19], [20]. Among the aforementioned multi-rotors, the quad-rotors suffer more from rotor faults due to a lack of actuator redundancy. Respecting the controllability of the quad-rotors, it is well known that the failure of one rotor might result in an uncontrollable system. Therefore, full attitude control of the quad-rotor can be achieved for a worst-case magnitude of the partial fault and is not achievable in the presence of complete one rotor failure [22]. In case of one rotor failure of the quad-rotors, controllability of the yaw state is sacrificed and the controller aims at controlling the roll and pitch angles of the quad-rotor [23]. Various control methodologies have been developed in the literature for the complete loss of one or two rotors of the quad-rotor [24], [25], [26]. A backstepping approach is adopted in [24] to stabilize the roll and pitch angles around the desired operating points. A nonlinear sensor-based fault-tolerant controller is developed in Refs. [25], [26] for the quad-rotor with failure of two opposing rotors under the high-speed flight condition. Ref [27] proposes a complete FTC design approach with fault detection and diagnosis (FDD) of a quad-rotor in the presence of a partial fault. Hexa-rotor seems to be more robust with respect to motor failure due to the existence of redundant actuators. Despite the larger number of motors in the hexa-rotor configuration, the researchers demonstrated that the standard hexa-rotors are not fully controllable in case of one motor failure, in which the yaw control is lost [28]. It is difficult to develop a controller that can cope with motor failures in the standard configurations, and the majority of the proposed controller algorithms in the literature are confined to reduced attitude control [29].

In the standard configuration of the hexa-rotor (PNPNPN: P stands for rotation in the positive direction and N stands for rotation in the negative direction), all the neighboring motors rotate in opposite directions. Non-standard configurations (PPNNPN) can maintain full controllability in the presence of one motor failure. Accordingly, Ref. [30] applies the composition of a Tau-observer and a disturbance-based sliding mode controller on a non-standard configuration of the hexa-rotor and investigates the fault detection and control of a hexa-rotor in the presence of one and two motor failures. The control targets are to stabilize the attitudes including the heading and to keep the flight hovering before landing. It is revealed that the non-standard configurations of the hexa-rotor are fully controllable in 33 % of up to two random motor failures [21]. A reconfiguration technique based on control allocation has been proposed to transform a quad-rotor into a tri-copter in Ref. [31]. The proposed approach can tolerate complete failure but requires an extra weight mounted on the opposite motor. In a similar strategy, Ref. [24] applied a backstepping control algorithm and transformed the quad-rotor into a bi-rotor for an emergency landing in the presence of one motor failure. In fact, investigation of the full controllability of the quad-rotor (roll, pitch, and yaw) is not possible for the complete loss of one motor effectiveness or motor failure.

Fault-tolerant control is a key subsystem in multi-rotor’s safe landing architecture in the presence of motor faults [32], [33]. Motivated by the above discussion and the existing gap in the literature, the paper’s contributions are summarized as follows; 1) presents a Modified Incremental Nonlinear Dynamic Inversion (MINDI) control algorithm, which removes the drawbacks of the traditional INDI algorithm, 2) augments a discrete-time nonlinear robust adaptive algorithm with the MINDI controller, 3) develops an appropriate testbed for the purpose of application in multi-rotor fault-tolerant control, 4) verify the proposed fault-tolerant controller through nonlinear simulations and real-time testbed experiments. Based on the simulation and testbed results, the proposed controller has satisfactory performance when compared to other algorithms. Accordingly, to the best of the authors' knowledge, the proposed algorithm and its successful implementation on a multi-rotor as a fault-tolerant control algorithm are novel aspects of the paper respecting the literature.

The remainder of the paper is organized as follows. The quad-rotor’s nonlinear dynamic equation of motion is derived in Section II. The controller architecture including the INDI algorithm, robust adaptive controller approach, and PID controller is presented in Section III. Numerical results, controller performance, and the comparison are examined in Section IV, and finally, the conclusion section briefly discusses the key results of the paper.