Lyapunov Vector Field Research Articles

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.

Cascaded Lyapunov Vector Fields for Acceleration-Constrained Spacecraft Path Planning

A variant of Lyapunov vector fields is presented for tracking trajectories within tumbling and accelerating reference frames. This extension is computationally light, and is acceleration constrained rather than velocity constrained, making it suitable for real-time use in spacecraft. A general stability analysis proves globally asymptotic stability given a set of conditions that are analogous to those of standard Lyapunov vector fields. A special case of this novel path-planning law (referred to as a cascaded Lyapunov vector field) is closely studied, and a simple set of conditions guaranteeing bounded acceleration commands for perfect tracking are derived. A design procedure is presented. Finally, a full design example for a spacecraft proximity inspection mission is presented. The simulations demonstrate stable behavior while respecting acceleration and path constraints. Furthermore, all constraints are met by judicious design of the path-planning field, without the need for computationally expensive algorithms running in real-time.

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.

Supergranule aggregation for constant heat flux-driven turbulent convection

Turbulent convection processes in nature are often found to be organized in a hierarchy of plume structures and flow patterns. The gradual aggregation of convection cells or granules to a supergranule which eventually fills the whole horizontal layer is reported and analysed in spectral element direct numerical simulations of three-dimensional turbulent Rayleigh-B\'{e}nard convection at an aspect ratio of $60$. The formation proceeds over a time span of more than $10^4$ convective time units for the largest accessible Rayleigh number and occurs only when the turbulence is driven by a constant heat flux which is imposed at the bottom and top planes enclosing the convection layer. The resulting gradual inverse cascade process is observed for both temperature variance and turbulent kinetic energy. An additional analysis of the leading Lyapunov vector field for the full turbulent flow trajectory in its high-dimensional phase space demonstrates that turbulent flow modes at a certain scale continue to give rise locally to modes with longer wavelength in the turbulent case. As a consequence successively larger convection patterns grow until the horizontal extension of the layer is reached. This instability mechanism, which is known to exist near the onset of constant heat flux-driven convection, is shown here to persist into the fully developed turbulent flow regime thus connecting weakly nonlinear pattern formation with the one in fully developed turbulence. We discuss possible implications of our study for observed, but not yet consistently numerically reproducible, solar supergranulation which could lead to improved simulation models of surface convection in the Sun.

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.

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.

Flight Control for UAV Loitering Over a Ground Target With Unknown Maneuver

This paper proposes a flight controller for an unmanned aerial vehicle (UAV) to loiter over a ground moving target (GMT). We are concerned with the scenario that the stochastically time-varying maneuver of the GMT is unknown to the UAV, which renders it challenging to estimate the GMT's motion state. Assuming that the state of the GMT is available, we first design a discrete-time Lyapunov vector field for the loitering guidance and then design a discrete-time integral sliding mode control (ISMC) to track the guidance commands. By modeling the maneuver process as a finite-state Markov chain, we propose a Rao-Blackwellised particle filter (RBPF), which only requires a few number of particles, to simultaneously estimate the motion state and the maneuver of the GMT with a camera or radar sensor. Then, we apply the principle of certainty equivalence to the ISMC and obtain the flight controller for completing the loitering task. Finally, the effectiveness and advantages of our controller are validated via simulations.

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.

Path-generating regulator following Lyapunov vector field control experiment for four-wheeled vehicles

Path-generating regulator following Lyapunov vector field control experiment for four-wheeled vehicles

Persistent standoff tracking guidance using constrained particle filter for multiple UAVs

This paper presents a new standoff tracking framework of a moving ground target using UAVs with limited sensing capabilities and motion constraints. To maintain persistent track of the target even in case of target loss for a certain period, this study predicts the target existence area using the particle filter and produces control commands that ensure that all predicted particles can stay within the field-of-view of the UAV sensor at all times. To improve target position prediction and estimation accuracy, the road information is incorporated into the constrained particle filter where the road boundaries are modelled as inequality constraints. Both Lyapunov vector field guidance and nonlinear model predictive control-based methods are applied, and the characteristics of them are compared using numerical simulations.

Coordinated Standoff Target Tracking Guidance Method for UAVs

We need a coordinated control method to continuously track a moving target using a group of UAVs. In this paper, we study the predicted reference point guidance method, where the target is considered to move with a constant velocity in a very short time window and the trajectories of the UAVs are designed as several tiny arcs around the target. The control law of the UAV is divided into roll angle control and velocity control. Simulations are used to verify that the proposed control laws have smaller standoff distances and phase angle control errors than the Lyapunov vector field guidance and model-based predictive control, and the wind is considered in the simulation, too. Therefore, we show that our proposed method has higher steady state accuracy among existing techniques.

Ground Target Tracking and Collision Avoidance for UAV Based Guidance Vector Field

This paper focuses on ground-moving target tracking of an unmanned aerial vehicle (UAV) in the presence of static obstacles and moving threat sources. Due to a UAV is restricted by airspace restrictions and measurement limitations during flight, we derive a dynamic path planning strategy by generating guidance vector filed combined Lyapunov vector field with collision avoidance potential function to track target in standoff distance loitering pattern, and resolved collision avoidance, simultaneously. This method relies only on the current information of the UAV and target, and generates a single-step route plan in realtime. Its performance is simple, efficient, and fast and have low computational complexity. The results of numerical simulation verify the effectiveness of the tracking and collision avoidance process of the UAV.

UAV Path Planning with Tangent-plus-Lyapunov Vector Field Guidance and Obstacle Avoidance

A dynamic path-planning algorithm is proposed for routing unmanned air vehicles (UAVs) in order to track ground targets under path constraints, wind effects, and obstacle avoidance requirements. We first present the tangent vector field guidance (TVFG) and the Lyapunov vector field guidance (LVFG) algorithms. We demonstrate that the TVFG outperforms the LVFG as long as a tangent line is available between the UAV's turning circle and an objective circle, which is a desired orbit pattern over a target. Based on a hybrid version of the TVFG and LVFG, we then derive a theoretically shortest path algorithm with UAV operational constraints given a target position and the current UAV dynamic state. This algorithm has the efficiency of the TVFG when UAV is outside the standoff circle and the ability to follow the path via the LVFG when inside the standoff circle. In addition we adopt point-mass approximation of the target state probability density function (pdf) for target motion prediction by exploiting road network information and target dynamics as well as obstacle avoidance strategies. Overall, the proposed technical approach is practical and competitive, supported by solid theoretical analysis on several aspects of the algorithm performance. With extensive simulations we show that the tangent-plus-Lyapunov vector field guidance (T+LVFG) algorithm provides effective and robust tracking performance in various scenarios, including a target moving according to waypoints or a random kinematics model in an environment that may include obstacles and/or winds.

Nonlinear Model Predictive Coordinated Standoff Tracking of a Moving Ground Vehicle

This paper proposes a nonlinear model-predictive control framework for coordinated standoff tracking by a pair of unmanned aerial vehicles. The benefit of this approach is to get optimal performance compared with using a decoupled controller structure: heading control for standoff-distance keeping and speed control for phase keeping. The overall controller structure is fully decentralized as each unmanned aerial vehicle optimizes its controller based solely on the future propagation of the pair vehicle states and the target estimates received via communication. This paper uses an acceleration model for sophisticated and realistic target dynamics, which can consider a more reasonable system noise covariance matrix reflecting the target’s motion characteristics. To simplify optimization formulation and decrease computation burden, a new manipulation using the inner product of position vectors of the unmanned aerial vehicles with respect to the target position is proposed for antipodal tracking instead of using the relative phase-angle difference. To consider a more realistic situation, inequality constraints are considered for collision avoidance between unmanned aerial vehicles and control input saturations using penalty functions in the model-predictive control scheme. Simulations with a pair of unmanned aerial vehicles are done using realistic car trajectory data in an urban environment in the United Kingdom to verify the feasibility and benefit of the proposed approach with comparing to a Lyapunov vector field guidance.

UAV Guidance Law for Target Tracking along constrained Bow-Shaped Trajectory based on Lyapunov Vector Field

AbstractThis paper describes a 2D target loitering problem addressed to UAV applications. While target tracking and loitering problems have been studied for long time in literature, here a new and particular type of loitering trajectory around the target (fix o moving) is considered: a Lemniscate-type trajectory. The proposed way to track this particular curve derives from the Lyapunov Vector Field theory, a recently developed methodology that has been used and tested for simpler cases before, such as circles or basin-like trajectory tracking. A stability analysis and preliminary simulation results are given in this paper.