Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

Abstract

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.

Introduction

Heterogeneous formation systems of unmanned ground vehicle (UGV) and unmanned aerial vehicle (UAV) combine the advantages of rapid reconnaissance over a wide area of UAV and precise positioning of ground targets of UGV. It has obtained increasingly attentions in academic and application fields [1], [2], [3], [4], [5], [6]. Agents from different dynamic characteristics can overcome individual limitations, and complete the more complicated and multivariant missions, which increases the probability for more tough applications. In particular, the complementary group of UAV and UGV combines their advantages, such as satisfactory payload and task configuration capabilities, and localization capabilities, which provides the better performance. However, the air-ground cooperative formation confronts many challenges. For example, the external environment and task switching have strong randomness, and the practical system is inevitably subject to model uncertainties, disturbances and actuator faults. Moreover, with the increasing complexity of the heterogeneous systems and formation tasks, centralized control approaches are no longer applicable. Therefore, alternative and effective schemes should be further developed [7], [9].

Currently, the formation controller design is mainly based on consensus theory [22], leader-follower [13], virtual structure [9] and behavior-based method. Nevertheless, the existing consensus strategy mainly aims at homogeneous multi-agent systems, and is difficult to be applied to heterogeneous unmanned systems. Heterogeneous collaborative formation is an emerging research orientation. Collaboration means that the goal of all agents is to improve the overall performance of the whole system [9]. Few approaches have been reported in the past decades [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. In [8], [13], [16], authors designed formation controllers based on the centralized method for a UGV-UAV system to achieve linear or nonlinear formation tasks. However, a centralized controller is overly dependent on the perfect interactive networks and prone to fail when connection fails or fault occurs in the controller [9], [15]. To overcome this problem, decentralized and distributed formation strategies have received increasing attentions. In [2], [3], [6], [11], based on a decentralized method, tracking controller and formation controller were established for UGV and UAV respectively. Backstepping-based decentralized formation controllers were designed in [9], [18] to solve the leader-follower formation problem. A decentralized controller was designed in [15] by employing LMI (Linear Matrix Inequalities) approach for a collaboration of UAVs and UGVs with some constrains on the velocity. In [19], based on a specific communication protocol, a decentralized controller was designed to maintain cohesion and separation behavior of two heterogeneous groups. With the widespread applications of distributed theory, researchers attempt to introduce it to the field of heterogeneous formation. However the using of distributed methods need to meet the condition of consistent state dimension of all agents. In [7], a distributed rigid formation controller was established for the movement of UAVs-UGVs system only in the XY plane. A distributed formation control algorithm was designed for a heterogeneous unmanned system in [10] to drive multiple UGVs to achieve the desired formation relying only on the visual information obtained by a camera mounted on the UAV. It should be pointed out that the robustness is not considered in [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [13], [15], [16], [17], [18], [19], [20], [21] and all depend upon the model parameters. Taking robustness into consideration, robust controllers of UGVs were designed in [12], [14] during the processing of heterogeneous cooperative formation. Nevertheless, the robustness of UAV is not discussed in these papers. As we all know, UAV is an under-actuated system with dynamic instability, parameter uncertainty, strong coupling and sensitive to external disturbances. On the other hand, practical UAV systems are inevitably subject to actuator faults [23], [24] due to component degradation or damage to the motors, propellers, and so on. The existence of actuator faults will lead to undesirable effects on the formation performance. Therefore in order to enhance the safety and reliability, it is improtant to establish a fault-tolerant controller for UAV to ensure the completion of the formation missions.

In the past few years, researchers have proposed various fault-tolerant control algorithms for UAV systems, such as neuroadaptive control [23], sliding mode control [24], adaptive control [25], disturbance observer-based control [26], type-2 fuzzy backstepping control [27], nonlinear robust control [28], just to mention a few. Those methods in [23], [24], [25], [26], [27], [28] guarantee the asymptotic stability, which means that the system state trajectories converge to equilibrium as time tends to infinity. However, the UGV-UAV real-time task systems need to form a predefined formation quickly with high precision, so the convergence speed may be insufficient.

In addition to faster convergence, the finite-time control shows satisfactory performance, such as high-precise tracking, faster convergence speed, better robustness to uncertainties [29]. With these advantages, finite-time control methods have been successfully used on many application devices [29], [30], [31], [32], [33]. As for UAV system, there are also several designed algorithms [34], [35], [36], [37], [38], [39], [40]. For example, an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) algorithm was proposed in [34] to solve the trajectory tracking problem of UAV subject to modeling uncertainties and unknown external disturbances. Fixed-time fault-tolerant controller in [35] was developed to address the problem of attitude stabilization of UAV with external disturbances and actuator faults. In [38], a neural network-based fault estimation observer was developed and an attitude stabilization fault-tolerant control approach was established with combining the non-singular fast terminal sliding mode control (NFTSMC) technology. A finite-time backstepping control strategy combined with a finite-time auxiliary system was proposed in [39] for the UAV outer loop system. To the best of the author’s knowledge, robust finite-time cooperative formation control problems for UGV-UAV systems are still open.

Inspired by the above-mentioned facts, this paper investigates the problem of finite-time cooperative formation control based on leader-follower strategy for two types of heterogeneous robots, consisting of an UGV and an UAV. It is assumed in this paper that UAV is affected by a bounded lumped uncertainty composed of actuator faults, model uncertainties, and external disturbances, which is not considered in existing results [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [13], [15], [16], [17], [18], [19], [20], [21]. The major contributions of this paper are stated as follows.

• Motivated by the distributed formation method [22], this paper utilizes the local interaction information of follower UAV to design formation controller and achieve cooperative formation, which is independent of a central controller and provides reliability and safety in uncertain environment. Furthermore, the performances of robustness and fault tolerance are also considered, so this paper has more application value comparing to the existing works [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [13], [15], [16], [17], [18], [19], [20], [21].

• Compared with the existing results [13], [16], [18], where the formation controller is established for the follower-UAV, but the trajectory tracking problem of the leader UGV is not considered. Here, a nonlinear tracking controller based on backstepping method is developed for the leader UGV.

• Based on the formation error, a non-singular fast terminal sliding mode surface is constructed for UAV, which solves the singular value problems. Then, under the condition that the upper bound of the lumped uncertainty is known previously, the robust nonsingular fast terminal sliding mode formation controller (RNFTSMFC) is designed without fault estimation [41], [42] to achieve the finite-time fault-tolerant formation control, ensuring the performance of strong robustness and fault tolerance.

• Inspired by Song et al. [23], combining RBFNN with an adaptive virtual parameter to deal with the lumped uncertainty, a novel NN-based adaptive nonsingular fast terminal sliding mode formation controller (NN-ANFTSMFC) is designed for UAV, where the norm of the lumped uncertainty is only assumed to be bound. Therefore, the proposed NN-ANFTSMFC not only realizes the finite-time formation control, but also removes the restriction on the upper bound of the lumped uncertainty.

• By utilizing the virtual parameter, the number of parameters adjusted adaptively online are largely reduced compared with [32], [33], [34], [35], [36], [37], [38], which provides a more convenient uncertainty estimation method.

The remaining parts of this paper are arranged as follows: the kinematic models of UGV and UAV are presented in Section 2. Section 3 is dedicated to controllers with a stability analysis. Section 4 presents experimental simulation to validate the developed scheme of UGV-UAV formation control. Section 5 concludes the paper.