Lyapunov Guidance Vector Field Research Articles

Target encircling control possessing decreased sampling load for quadrotors with experimental verification

This article addresses a target encirclement control with reduced sampling burden for quadrotors using merely bearing measurements without demanding position and velocity of uncooperative target. At the translational level, a target-localization estimator holding the persistent exciting condition is devised assuring an ultimately uniformly bounded estimation via bearing angles only, and a target surrounding guidance law is developed to generate the quadrotor reference velocity, where an orientation vector field capable of steering quadrotors to the circular orbit around the uncooperative target with a pre-specified radius, is constructed based on the relative geometry between estimated target position and quadrotor, eliminating the dependence on relative position and target velocity inherent in existing Lyapunov guidance vector field. At the rotational level, an extended state observer (ESO) is employed to recover system uncertainties, then a robust event-triggered attitude controller is derived following the disturbance estimates and an inverse transformation. The salient merit is that target circumnavigation can be achieved for quadrotors with decreased transmission cost despite of uncertainties, being lack of relative distance measurements and target prior information. Error signals in target encircling system cascaded by guidance and control loops are proved to be bounded using input-to-state stability theorem. Simulations and experiments are provided to validate the property of developed algorithm.

Cooperative Standoff Target Tracking using Multiple Fixed-Wing UAVs with Input Constraints in Unknown Wind

This paper investigates the problem of cooperative standoff tracking using multiple fixed-wing unmanned aerial vehicles (UAVs) with control input constraints. In order to achieve accurate moving target tracking in the presence of unknown background wind, a coordinated standoff target tracking algorithm is proposed. The objective of the research is to steer multiple UAVs to fly a circular orbit around a moving target with prescribed intervehicle angular spacing. To achieve this goal, two control laws are proposed, including relative range regulation and space phase separation. On one hand, a heading rate control law based on a Lyapunov guidance vector field is proposed. The convergence analysis shows that the UAVs can asymptotically converge to a desired circular orbit around the target, regardless of their initial position and heading. Through a rigorous theoretical proof, it is concluded that the command signal of the proposed heading rate controller will not violate the boundary constraint on the heading rate. On the other hand, a temporal phase is introduced to represent the phase separation and avoid discontinuity of the wrapped space phase angle. On this basis, a speed controller is developed to achieve equal phase separation. The proposed airspeed controller meets the requirements of the airspeed constraint. Furthermore, to improve the robustness of the aircraft during target tracking, an estimator is developed to estimate the composition velocity of the unknown wind and target motion. The proposed estimator uses the offset vector between the UAV’s actual flight path and the desired orbit, which is defined by the Lyapunov guidance vector field, to estimate the composition velocity. The stability of the estimator is proved. Simulations are conducted under different scenarios to demonstrate the effectiveness of the proposed cooperative standoff target tracking algorithm. The simulation results indicate that the temporal-phase-based speed controller can achieve a fast convergence speed and small phase separation error. Additionally, the composition velocity estimator exhibits a fast response speed and high estimation accuracy.

Cooperative target search and tracking for multi-UAVs based on control barrier functions

In this paper, a multiple unmanned aerial vehicles (multi-UAVs) cooperative target search and tracking strategy with collision avoidance and flocking constraints are presented applying the control barrier functions (CBFs). First, the constraints of collision avoidance and flocking maintenance are designed based on CBF. Second, the information map and Lyapunov guidance vector field (LGVF) are used to design the corresponding nominal controllers in search mode and tracking mode, respectively. To minimize the difference between the actual controller and the nominal controller, the controller based on quadratic programming (QP) is proposed to achieve the target search and tracking on the premise of security. Finally, the simulation results verify the effectiveness of the proposed method.

Trajectory Optimization of Multi-UAVs for Marine Target Tracking during Approaching Stage

This paper focuses on a coordinated tracking planning method of multiple unmanned aerial vehicles (UAVs), which was deployed in the best positions to better fulfill the marine target localization tasks when approaching the target. The optimal planning of multi-UAVs was implemented using an online centralized nonlinear model predictive control (NMPC) based on the target state’s uncertainty criteria. The penalty function is used to solve UAV platform dynamic performance in the model predictive control method to consider the more realistic situation. The coordinated planning problems of multi-UAVs are numerically simulated and compared with the Lyapunov vector field guidance (LVFG) method under classical mission scenarios. Simulation results demonstrate that the algorithm can maintain the optimal observation configuration of multi-UAVs to improve the marine target positioning accuracy, verifying the feasibility and superiority of this method. Furthermore, the simulation results can provide a useful reference for the flight control law design of multi-UAVs with optimal observation configuration.

UAV Standoff Tracking for Narrow-Area Target in Complex Environment

This article studies the path planning for an unmanned aerial vehicle (UAV) standoff tracking a narrow-area target in complex environment. Since the target state estimation considerably influences the target tracking performance, the constrained interacting multiple model, which uses the geographic information of narrow-areas to enhance the estimation accuracy, is proposed. Then, based on the obtained estimation results, the dynamic Lyapunov guidance vector field (DLGVF) is proposed, which can guide UAVs to converge to not only the expected standoff distance in the horizontal plane but also the desired height in the vertical plane. Moreover, the DLGVF renders the UAV trajectories flexible and shortens the convergence time by skillfully introducing adjustment parameters. Finally, to simultaneously complete the missions of target tracking and obstacle avoidance, an integrated method based on the DLGVF and the interfered fluid dynamical system is presented. Simulations are implemented to demonstrate that the proposed framework is effective.

Cooperative trajectory optimization of UAVs in approaching stage using feedback guidance methods

This paper mainly studies the problem of using UAVs to provide accurate remote target indication for hypersonic projectiles. Based on the optimal trajectory trends and feedback guidance methods, a new cooperative control algorithm is proposed to optimize trajectories of multi-UAVs for target tracking in approaching stage. Based on UAV kinematics and sensor performance models, optimal trajectory trends of UAVs are analyzed theoretically. Then, feedback guidance methods are proposed under the optimal observation trends of UAVs in the approaching target stage, producing trajectories with far less computational complexity and performance very close to the best-known trajectories. Next, the sufficient condition for the UAV to form the optimal observation configuration by the feedback guidance method is presented, which guarantees that the proposed method can optimize the observation trajectory of the UAV in approaching stage. Finally, the feedback guidance method is numerically simulated. Simulation results demonstrate that the estimation performance of the feedback guidance method is superior to the Lyapunov guidance vector field (LGVF) method and verify the effectiveness of the proposed method. Additionally, compared with the receding horizon optimization (RHO) method, the proposed method has the same optimization ability as the RHO method and better real-time performance.

Vector field guidance for standoff target tracking

This work presents a guidance algorithm for standoff target tracking by unmanned aerial vehicles using the traditional Lyapunov guidance vector field framework. Unlike the past work, this guidance law is the function of the minimum radius of curvature, and, hence, it can act more flexibly for different maneuverable vehicles. Moreover, normalized even and odd functions are proposed here as circulation and convergence terms to improve performance in terms of optimality. The presence of wind is also considered for real world applications. As the proposed guidance law generates paths of continuous curvature, the designed path is flyable by fixed-wing unmanned vehicles. Simulation results are presented to validate the proposed guidance law.

A learning-based flexible autonomous motion control method for UAV in dynamic unknown environments

This paper presents a deep reinforcement learning (DRL)-based motion control method to provide unmanned aerial vehicles (UAVs) with additional flexibility while flying across dynamic unknown environments autonomously. This method is applicable in both military and civilian fields such as penetration and rescue. The autonomous motion control problem is addressed through motion planning, action interpretation, trajectory tracking, and vehicle movement within the DRL framework. Novel DRL algorithms are presented by combining two difference-amplifying approaches with traditional DRL methods and are used for solving the motion planning problem. An improved Lyapunov guidance vector field (LGVF) method is used to handle the trajectory-tracking problem and provide guidance control commands for the UAV. In contrast to conventional motion-control approaches, the proposed methods directly map the sensorbased detections and measurements into control signals for the inner loop of the UAV, i.e., an end-to-end control. The training experiment results show that the novel DRL algorithms provide more than a 20% performance improvement over the state-of-the-art DRL algorithms. The testing experiment results demonstrate that the controller based on the novel DRL and LGVF, which is only trained once in a static environment, enables the UAV to fly autonomously in various dynamic unknown environments. Thus, the proposed technique provides strong flexibility for the controller.

Standoff tracking control of underwater glider to moving target

The standoff tracking control of underwater glider to moving targets has non-negligible potentials in oceanic observations. To perform such operations, this study presents an integrated standoff tracking method that focuses on dealing with the coupled motions and under-actuated characteristics of the gliders as well as offsetting the dilemma caused by lacking of navigation system. The proposed approach contains guidance algorithm, basic controller, and reinforcement learning optimizer to improve the tracking accuracy. The verified simulation model for the OUC-III glider is utilized to develop the algorithm and evaluate the effectiveness of tracking. The adaptive navigation law called Lyapunov guidance vector field method generates the desired heading in this framework. The guidance only requires positioning information that is accessible through dead-reckoning. For the deficiency that the glider’s state controlled by the proportional integral differential controller can not immediately reach the required state, the reinforcement learning optimizer is introduced. The gliding status constitutes optimizer input while the compensating rotation signals are outputted to actuate the movable mass. The reward function of the optimizer is designed for maintaining the glider position error within 1 m with respect to the standoff circle. On this basis, the objective is set to maximize the rewards and consequently to guarantee the best accuracy. Three reinforcement learning algorithms are adopted and tested in our proposed framework. In the training phase, the training speeds of composite methods and pure reinforcement learning algorithms are compared. To test the stability, we design different types of moving targets, standoff radium and disturbance in the validation simulation, which have not appeared in the training. This study can provide patterns and solutions for the standoff tracking applications of underwater gliders. Also, it enlarges the glider’s scope of deployment based on the existing hardware.

Coordinated target tracking of two UAVs based on game theory approach and Lyapunov guidance vector fields

Considering the problems of the lack of tracking the intelligent target, which is “smart” enough to escape from the detection by maximizing the estimation error in the current tracking methods by multi-UAVs, a cooperative control method for tracking intelligent target by two UAVs is proposed based on Lyapunov guidance vector field. The mathematical model of an intelligent target is established. According to the multi-UAV distributed intelligent target state fusion estimation method, the target state information is obtained to control two UAVs to circle the target through the Lyapunov guidance vector method. The simulation results demonstrated that the method enables two UAVs to track the intelligent target stably and improve the intelligent target’s positioning accuracy effectively

Design of Standoff Cooperative Target-Tracking Guidance Laws for Autonomous Unmanned Aerial Vehicles

This paper investigates two guidance laws of standoff cooperative tracking static and moving of multiple autonomous unmanned aerial vehicles for targets from the perspective of the control system design. In the scheme of the proposed guidance laws, one vehicle is chosen as leader and others as followers. The leader only needs the measurement of the target, and the followers only measure the leader and its neighbors in the communication topology network. By using the proposed guidance laws, it is guaranteed that all vehicles can track a static or moving target with an evenly spaced formation of circle. Considering the coupling of tracking and cooperation, the stability analysis is performed by constructing two relatively independent subsystems based on Lyapunov theory, and the corresponding rigorous proofs of stability are given. By comparing with the Lyapunov vector field guidance law, the simulation results verify the effectiveness and superiority of the proposed guidance laws.

Multi-UAV surveillance implementation under hierarchical dynamic task scheduling architecture

In this paper, we consider a multi-UAV surveillance scenario where a team of unmanned aerial vehicles (UAVs) synchronously covers an area for monitoring the ground conditions. In this scenario, we adopt the leader-follower control mode and propose a modified Lyapunov guidance vector field (LGVF) approach for improving the precision of surveillance trajectory tracking. Then, in order to adopt to poor communication conditions, we propose a prediction-based synchronization method for keeping the formation consistently. Moreover, in order to adapt the multi-UAV system to dynamic and uncertain environment, this paper proposes a hierarchical dynamic task scheduling architecture. In this architecture, we firstly classify all the algorithms that perform tasks according to their functions, and then modularize the algorithms based on plugin technology. Afterwards, integrating the behavior model and plugin technique, this paper designs a three-layer control flow, which can efficiently achieve dynamic task scheduling. In order to verify the effectiveness of our architecture, we consider a multi-UAV traffic monitoring scenario and design several cases to demonstrate the online adjustment from three levels, respectively.

A Wind Estimation Based on Unscented Kalman Filter for Standoff Target Tracking Using a Fixed-Wing UAV

To address standoff target tracking using a fixed-wing UAV in unknown background wind, a wind estimation based on Unscented Kalman Filter (UKF) is proposed. In the paper, UAV dynamic model and target state estimation are constructed, and Lyapunov vector field guidance (LVFG) framework is introduced to achieve standoff target tracking. The unknown target state and wind dynamic model have seldom been discussed for standoff tracking in the previous research. Therefore, two typical wind dynamic models with Dryden and Davenport spectrums are constructed for the target in the high altitude or near the ground. Then, the unscented transformation is adopted to estimate the position of UAV under guidance command generated by LVFG and saturation constraint. A wind state estimation method based on UKF is proposed to improve performance of standoff tracking. Simulated and realistic ground vehicle trajectories are used to demonstrate the availability and effectiveness of the proposed method for different wind dynamic models.

Cooperative Standoff Tracking of Moving Targets Using Modified Lyapunov Vector Field Guidance

Cooperative standoff tracking of moving targets is an important application of fixed-wing unmanned aerial vehicles (UAVs). To cope with the problem of long convergence time and unstable tracking in cooperative target tracking, traditional Lyapunov vector field guidance (LVFG) is modified. The guidance parameter c is discussed, and the gradient descent method is utilized to develop the optimal guidance parameter search algorithm. As for tracking moving targets, an interacting multiple model-based unscented Kalman filter (IMM-UKF) estimator is built for predicting the target state, and the result is used for correcting the guidance law. Meanwhile, a speed-based controller is developed for faster convergence to the desired intervehicle phase, and the stability of the controller is proved using the Lyapunov stability theory. Numerical simulation results indicate the proposed guidance converges faster to the standoff circle without intersecting the orbit. The state estimator reduces the estimate error and the intervehicle phase converges faster to the desired phase than the traditional control method. Furthermore, extensive hardware-in-the-loop simulations are carried out to verify the feasibility of the algorithm.

Nonlinear Disturbance Observer-Based Standoff Target Tracking for Small Fixed-Wing UAVs

Small fixed-wing UAVs have attracted significant attention thanks to its pragmatic features such as small size, light weight, and low cost. Although many researchers have extensively studied small fixed-wing UAVs, there still remains a room for improvement. One of the improvements is to deal with external disturbances such as wind as small fixed-wing UAVs are susceptible to such external forces. This makes it difficult for UAVs to follow desired paths or moving targets, which may lead to a mission failure. In this paper, we present nonlinear disturbance observer-based standoff tracking guidance for multiple small fixed-wing UAVs in the presence of wind. The nonlinear disturbance observer is used to estimate the wind disturbance and the Lyapunov guidance vector field technique is used to compensate the effect of the wind and follow a ground target. The numerical simulations are carried out and outdoor flight experiments are performed to demonstrate the performance of the proposed approach in a real-world environment.

A method of simulated motion tracking control based on lyapunov vector field

For the problem of irregular formation in aircraft cluster planning, this paper proposes a simulated motion tracking control of cluster planning. The simulated motion is the expected motion trajectory for one aircraft provided by the planning system. Using Lyapunov vector field guidance and omnidirectional speed control method, this paper realizes the tracking control of the simulated motion for the aircraft. The simulation results demonstrate that the proposed method can realize the tracking control of the simulated motion and achieve the expected effect, which lays a foundation for the cluster planning.

Cooperative Dynamic Fuzzy Perimeter Surveillance: Modeling and Fluid-Based Framework

In this article, considering the performance limitations of the sensors used in real missions, the cooperative dynamic fuzzy perimeter surveillance (CDFPS) problem and its fluid-based solution framework are proposed for the first time. First, the two-dimensional concentration diffusion distribution function is used to imitate an irregular dynamic perimeter. Then, according to the onboard sensor resolution ratio, a fuzzification process is applied for the perimeter area. On this basis, the detected fuzzy perimeter area is modeled with virtual obstacles (VOs). Considering an obstacle set composed of VOs, fixed obstacles and agents, we transform the CDFPS problem into a unified obstacle avoidance problem for the first time and a fluid-based path planning method is designed based on restrained interfered fluid dynamical system and Lyapunov guidance vector field. To quantify the surveillance effect, two indexes for the CDFPS problem are proposed: the perimeter neutrality index and the phase angle uniformity index. Around these proposed indexes, the attractive/repulsive effects and the multiagent cooperative mechanism are constructed. Finally, the receding horizon control is introduced to further improve the surveillance effect. Simulations show that the proposed framework can drive agents to persistently track the perimeter and establish relatively stable phase angle offsets between adjacent agents.

Comprehensive Optimization of Energy Storage and Standoff Tracking for Solar-Powered UAV

Compared with traditional unmanned aerial vehicle (UAV), the solar-powered UAV (SUAV) has longer endurance by converting solar energy into electric energy. This article focuses on the comprehensive optimization of energy storage and standoff tracking performance for SUAV with application to the target tracking task. First, an adjustable Lyapunov guidance vector field (ALGVF) is proposed and combined with the interfered fluid dynamical system (IFDS) method to achieve the standoff target tracking mission in obstacle environment, making it possible to adjust the tracking trajectory flexibly. Then, the adjustment factor of ALGVF and the obstacle reaction coefficients of IFDS are optimized simultaneously to generate the optimal trajectory of SUAV, aiming to maximize the solar energy storage while minimize the tracking error. Finally, the simulation results verify the feasibility of our method and give the influence of different solar irradiance on SUAV trajectory optimization.

Hierarchical Collaboration Approach for Tracking of Flying Target by UAVs

This paper investigates a hierarchical target tracking method based on the collaboration of unmanned aerial vehicles (UAVs) at different altitudes. To enhance the target tracking range, the high-altitude UAVs monitor the wide area, and transmit their surveillance information to low-altitude UAVs which directly detect and collect information about the target's movements. The contributions of this paper are threefold: First, to track the flying target in a dynamic environment, a modified Lyapunov guidance vector field (LGVF) method is used to plan velocities for UAVs, where a time-varying vertical component is incorporated into the traditional LGVF function to satisfy the constraints of cluster communication. Secondly, a three-dimensional local collision-free guidance vector field (TLCGVF) method is proposed for UAVs to plan collision-free paths on line. To simultaneously track the target and avoid obstacles, the vector field by LGVF is used as the original vector field of TLCGVF. Thirdly, the rolling optimization strategy is used to adjust the reactive parameters of TLCGVF to enhance the path quality. The simulation results confirm the feasibility of the above approach.

Fast Lyapunov Vector Field Guidance for Standoff Target Tracking Based on Offline Search

To address the problem of the long convergence time of traditional Lyapunov Vector Field Guidance (LVFG), a fast convergent LVFG designed with guidance function is proposed. The necessary criteria of a fast convergent vector field are first illustrated through an analysis of the contraction and circulation components. Then, two types of guidance functions of the distance between aircraft and target are constructed to replace the original guidance parameter. Considering the saturation constraints from the aircraft performance, the optimal parameter in guidance functions based on offline search is estimated to achieve the best convergence. Meanwhile, standoff tracking for a moving target is solved with analysis of motion correction. Simulation results indicate the proposed vector field guidance converges faster to the standoff circle without traversing the orbit regardless of whether the aircraft’s initial position is inside or outside the circle, even for a moving target. In addition, selection of parameter in the guidance function is proved to make convergence speed approach the limit.