Formation Tracking of UAV-UGV Systems Over Event-Triggered Communications

Authors: yancheng  yan
tieshan  li
yue  long
hanqing  yang
hongjing  liang
Venue: IEEE_org_ICIST_2024_Conference
Published: 2024-08-12 14:46:19

Abstract: For unmanned aerial vehicle-unmanned ground vehicle (UAV-UGV) systems with disturbances, this paper investigates the formation tracking issue under event-triggered communications. A hierarchical control strategy is proposed, comprising a distributed event-triggered filter and a local controller. The former is responsible for estimating the desired position of the leader, while the latter employs a filter-based robust controller to ensure the formation tracking errors converge to a small residual set. The salient feature lies in the fact that the necessity for continuous communication among neighbors is obviated, and it has wider robustness to disturbances. Finally, simulations are conducted to validate the feasibility of the proposed strategy, showing accurate formation tracking with reduced communication overhead.

Main paper: 
 i. introduction: 
 The distributed coordination control of multi-agent systems has recently attracted significant attention, spurred by the swift development of unmanned equipment and full automation. The goal is to bring all agents to a consensus through local interactions with neighboring agents. Applications include unmanned aerial vehicle formations, mobile robots, and unmanned underwater vehicles [1] - [3] . A typical application is the formation tracking control of unmanned aerial vehicleunmanned ground vehicle (UAV-UGV) systems. For example, consider a combined surveillance-reconnaissance mission which involves two groups of unmanned vehicles (ground and aerial). In such scenario, UAV and UGV are deployed to collaboratively establish a secure passage through hostile territory. The foundation for accomplishing these tasks lies in achieving formation control of the UAV-UGV system. Notably, the UAV-UGV systems possess homogeneous dynamics along with specific heterogeneous dynamics. For the UAV-UGV systems, in recent literature, the formation problem has been effectively addressed [4] - [6] . To mention a few, in [6] , a distributed adaptive formation control approach was developed for human-in-the-loop heterogeneous UAV-UGV systems based on a unified model.Nonetheless, most existing control algorithms are designed with continuous communication among its neighbor nodes, inevitably leading to substantial consumption of communication resources. To mitigate this problem, event-triggered coordination control has become a major and widely researched topic in recent years. In [7] , an event-triggered strategy was employed, and the results indicate that, compared to traditional real-time sampling strategies, the event-triggered strategy can reduce unnecessary communication. Subsequently, there has been significant advancement in the study of event-triggered control. For example, in [8] , the implementation of eventtriggered control alleviates not only the computational load but also controller update frequency. In [9] , the edge-based event-triggered consensus problem was addressed based on the prescribed performance approach. However, the aforementioned control methods are based on event-triggered mechanisms in the controller channel, which inevitably require real-time monitoring using neighbors' information, contrary to the original intention of the event-triggered mechanism. Even though literature [9] extended to self-triggered mechanisms to address this issue, the parameter values for these selftriggered mechanisms were rather conservative. Therefore, it is particularly important to design an event-triggered control strategy that does not rely on neighbors' information for realtime monitoring.Drawing from the aforementioned observations, this paper investigates the formation tracking for UAV-UGV systems over event-triggered communications. The distributed eventtriggered filter for each agent is developed to estimate the state of leader. Based on this filters, the local controller is designed to achieve the leader-follower formation tracking. The contributions are detailed below.1) By employing an derivative operator and its power, an auxiliary observer is designed, along with an eventtriggered mechanism to reduce the high communication demands between agents. Compared to the literature [8] , [9] , this approach eliminates the need for real-time monitoring of neighboring agents' states. Additionally, the order of the observer matches that of the UAV, preventing the issue of the virtual controller being nondifferentiable.2) The leader-follower formation tracking problem for heterogeneous UAV-UGV systems was addressed. Specifically, based on hierarchical control and backstepping techniques, utilizing filters and local controllers, a distributed formation control strategy was proposed, achieving formation tracking of the UAV-UGV system under unknown disturbances and limited communication resources.The l-th UAV model [4] is given asEQUATIONwhere c = cos( ) and s = sin( ); ξ l = [ξ l,x , ξ l,y , ξ l,z ] andν l = [ν l,1 , ν l,2 , ν l,3] represent the position and the attitude angle of l-th UAV; I lx , I ly , and I lz are the body inertia; I lr and m l are the the inertia and the mass; ql represents the residual rotor angular, g is the acceleration of gravity and f l , u l,ν1 , u l,ν2 , and u l,ν3 are the control input generated by four rotors. The UAV's attitude subsystem can be stabilized independently, this study primarily addresses the trajectory tracking problem of UAV-UGV systems. The model for the l-th UAV is expressed as follows:EQUATIONwhereu l = [f l c ν l,1 s ν l,2 c ν l,3 + s ν l,1 s ν l,3 , f l c ν l,1 s ν l,2 s ν l,3 - s ν l,1 s ν l,3 , f l c ν l,1 c ν l,2 -m l g] , ϑ l (t) = [ϑ x l (t), ϑ y l (t), ϑ z l (t)] is the disturbance.The kinematics of l-th UGV [6] is modeled asEQUATIONwhere ξl (t) = [ ξl,x (t), ξl,y (t)] ∈ R 2 , θ l (t), v l (t(t) = [ξ x,l (t), ξ y,l (t)] ∈ R 2 , which is shifted a non-zero distance p l > 0 from ξl (t) along direction θ l (t). The position ξ l (t) is described by ξ l (t) = ξl (t) + p l [c θ l (t) , s θ l (t) ] ,whose dynamics is modeled asEQUATIONwith a non-singular matrixG l = [c θ l , -p l s θ l ; s θ l , p l c θ l ] and input u l = [v l , ω l ] .Consider the disturbance, the l-th UGV model is rewritten as follows:EQUATIONwhere ϑ l (t) = [ϑ v l (t), ϑ ω l (t)] is the disturbance.The following table shows the relevant definitions used in the UAV-UGV system. A = [a l,i ] N ×N : the adjacency matrix with a l,i = 1 if (i, l) ∈ E and a l,i = 0 if (i, l) / ∈ E; N l : = {i ∈ V | (i, l) ∈ E},D = diag( l∈N 1 a 1,l , . . . , l∈N N a N,l ); G 0 = (V 0 , E 0 ): the augmented graph describing one leader and the UAV-UGV system;V 0 = {L, 1, . . . , N } : the node set with L being the leader; E 0 = {(l, i)|i, l ∈ V 0 } :For the UAV-UGV system and the leader, design a control scheme such that(1) all signals in the closed-loop are bounded;(2) the formation tracking error satisfies:EQUATIONwhere ξ 0 is the leader output, ρ > 0 is an arbitrarily adjustable constant,1 N = [1, . . . , 1 N ] , ξ(t) = [ξ l1 (t), l 1 ∈ F 1 , l 2 ∈ F 2 ] ,and o = [o 1 , . . . , o N ] with o l ∈ R 3 being the relative position deviation between the l-th agent's position and the leader's position.The assumptions and lemmas are needed. Assumption 1: The leader's output ξ 0 and its derivatives ξ0 and ξ0 are bounded and continuous.Assumption 2: The disturbances are bounded, i.e., ϑ l (t) ≤ θl , where θl > 0 is a unknown constant. Assumption 3: It is assumed that the graph G contains a spanning tree, and the root node is able to receive information from the leader.Remark 1: Assumptions 1-3 are standard conditions for formation control design.Lemma 1 ( [10]): For a nonsingular M -matrix H ∈ R N ×N , there exists a matrix P > 0 such that Q = PH + H P > 0.In order to implement event-triggered communication between agents, the following filters are designed:EQUATIONwhere vl ∈ R 3 is the filter input, for l ∈ F 1 ∪ F 2 , andEQUATIONfor the leader. Define the formation error and the auxiliary error as e l = v l,1 -ξ 0 -o l and ēl = e l + ėl . Taking its derivative yieldsEQUATIONIn order to alleviate the communication pressure on the UAV-UGV system, the following event-triggered mechanism is establishedEQUATION)if k ∈ V 0 is a neighbour of another agent, where t k,µ+1 and t k,µ represent the next trigger moment and the current trigger moment, where µ = 0, 1, 2, . . ., and t k,0 = 0;ψ k , c v > 0 are designed parameters; hk (t) = h k (t) -h k (t k,µ ) is state measurement error with h k (t) = v k,1 + v k,2 .Then we define the filter input asEQUATIONwhereo l,k = o l -o k .Remark 2: According to equation (10) , it can be observed that h k (t) is only related to its own state and does not utilize information from neighboring agents. This avoids realtime monitoring of neighboring agents, effectively alleviating communication pressure between agents.Lemma 2: As designed in ( 11) and ( 15), the auxiliary filters ensure the boundedness of v l1,1 , v l1,2 , and vl for l 1 ∈ V 0 and l ∈ V, and they compel v l,1 to follow ξ 0 + o l , resulting in the formation error e l = v l,1 -ξ 0 -o l converging to a small residual set. Furthermore, the Zeno behavior is strictly avoided.Proof: Define the error asEQUATIONwhose compact form isEQUATIONwhereε = [ε 1 , . . . , ε N ] , v 1 = [v 1,1 , . . . , v N,1 ] , o = [o 1 , . . . , o N ], and e = [e 1 , . . . , e N ] . Additionally, we defineEQUATIONwhose compact form isEQUATIONwhereEQUATIONAccording to the Assumption 1, there exists a scalar vector φ l > 0 such that k∈N l a lk ψ k + ξ0 + ξ0 ≤ φ l . Thus, it yields ėl ≤ -c v εl + φ l (19)Define the Lyapunov function as V o = 1 2 ε (P ⊗ I 3 ) ε where P > 0 is given in Lemma 1 as the Assumption 3 holds, taking its derivative along with (15) and ( 19) yieldsEQUATIONwhere φ = [φ 1 , . . . , φ N ] . By using the Lemma 1, one hasEQUATIONUsing the Young's inequality, it yieldsEQUATIONHence,EQUATIONBy solving (23), we get (25) Then, from (15) and the definition of ēl , it is deduced that e l ≤ ē ≤ /σ(H), where σ(H) stands for the minimum singular value of H. As a result, it can be concluded that the formation errors e l (l ∈ V) converge to a residual set, which can be made arbitrarily small by increasing c v .EQUATIONNext, we prove that Zeno behavior can be strictly precluded. Define β k (t) = hk (t) 2 . From the boundedness of the boundedness of v l1,1 , v l1,2 and vl (l 1 ∈ V 0 , l ∈ V), it can be checked that hk (t) and ḣk (t) are bounded. As a result, there exists a constant βk > 0 such thatd dt |β k (t)| = |2 h k (t) ḣk (t)| ≤ βk , ∀t ∈ (t k,µ , t k,µ+1). (26) On the other hand, according to (10), we haveEQUATIONwhich together with (26) gives t k,µ+1 -t k,µ ≥ ψ 2 k /(c 2 v βk ). Hence, Zeno behavior is strictly precluded, which completes the proof. The simulation results are presented in TABLE I and Figs. 2 3 4 5 . Fig. 2 shows that displays the inter-event intervals of the leader, UAVs, and UGVs, which presents an aperiodic form. As depicted in Fig. 3 , all the UAVs and UGVs track the trajectory of the leader with formation configuration. In Fig. 4 , the control inputs are bounded. From Fig. 5 it can be seen that the formation tracking errors converge to a small residual set in the presence of event-triggered communication. Thus, the effectiveness of the proposed method is verified.This paper investigates formation tracking for the UAV-UGV systems under event-triggered communications. A hierarchical control strategy is proposed, comprising a distributed event-triggered observer and a local controller, such that the formation tracking errors converge to a small residual set. The salient feature is that continuous communication among neighbors is not required, and the system exhibits wider robustness to disturbances. Finally, simulations validate its feasibility.This work was supported in part by the National Natural Science Foundation of China under Grant 51939001, Grant 62322307, Grant 62273072, and Grant 62203088, in part by the Natural Science Foundation of Sichuan Province under Grant 2022NSFSC0903. (Corresponding author: Yancheng Yan.) 
 
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Reviews: review: title: title: This article is very interesting and a good one
main_review: main_review: This paper proposed a hierarchical control strategy, comprising a distributed event-triggered filter and a local controller for UAV-UGVs. The obtained result is valuable and can be accepted if the following problems can be clarified.
(1) In the introduction, the shortages of those relevant studies are suggested to be further summarized. 
(2) In the end of Section 1, the organization of this study is suggested to be summarized.
(3) In the simulation section, more analysis can be added to better explain the main results of this paper, that's not enough. 
(4) The future work is missing in the Conclusion. 
(5) There exist several spelling and grammar errors. Please check carefully and further polish
title: title: accept
main_review: main_review: Comment: This paper proposes a hierarchical control strategy is proposed, comprising a distributed event-triggered filter and a local controller for the formation tracking issue under event-triggered communications. The theory is correct and can be accepted after responding the following comments.
(1) More comprehensive literature review is needed to clarify the research gap and research motivation.
(2) In the simulation section, more analysis can be added to better explain the main results of this paper, that's not enough.
(3) In the end of the conclusions, some research directions are suggested to be added.
title: title: This paper investigates the formation tracking issue under event-triggered communications for unmanned aerial vehicle-unmanned ground vehicle systems with disturbances. A hierarchical control strategy is proposed, comprising a distributed event-triggered filter and a local controller. In my opinion, there are some comments that should be considered during the revision of the manuscript which are listed below.
main_review: main_review: 1. It can be compared with existing articles to make the innovation point clearer.
2. The disadvantages of the proposed method and the direction of the next work should be explained in the conclusion.
3. In the simulation section, the explanatory text for each chart is insufficient, making it challenging to comprehend the author's intended message from the provided images. Please provide more detailed descriptions to enhance the reader's understanding.

Comments: title: This article is very interesting and a good one
comment: This paper proposed a hierarchical control strategy, comprising a distributed event-triggered filter and a local controller for UAV-UGVs. The obtained result is valuable and can be accepted if the following problems can be clarified.
(1)	In the introduction, the shortages of those relevant studies are suggested to be further summarized.
(2)	In the end of Section 1, the organization of this study is suggested to be summarized.
(3)	In the simulation section, more analysis can be added to better explain the main results of this paper, that's not enough.
(4)	The future work is missing in the Conclusion.
(5)	There exist several spelling and grammar errors. Please check carefully and further polish