Tracking Guidance Law Research Articles

PID Controller Based on Improved DDPG for Trajectory Tracking Control of USV

When navigating dynamic ocean environments characterized by significant wave and wind disturbances, USVs encounter time-varying external interferences and underactuated limitations. This results in reduced navigational stability and increased difficulty in trajectory tracking. Controllers based on deterministic models or non-adaptive control parameters often fail to achieve the desired performance. To enhance the adaptability of USV motion controllers, this paper proposes a trajectory tracking control algorithm that calculates PID control parameters using an improved Deep Deterministic Policy Gradient (DDPG) algorithm. Firstly, the maneuvering motion model and parameters for USVs are introduced, along with the guidance law for path tracking and the PID control algorithm. Secondly, a detailed explanation of the proposed method is provided, including the state, action, and reward settings for training the Reinforcement Learning (RL) model. Thirdly, the simulations of various algorithms, including the proposed controller, are presented and analyzed for comparison, demonstrating the superiority of the proposed algorithm. Finally, a maneuvering experiment under wave conditions was conducted in a marine tank using the proposed algorithm, proving its feasibility and effectiveness. This research contributes to the intelligent navigation of USVs in real ocean environments and facilitates the execution of subsequent specific tasks.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

Three-dimensional line-of-sight-angle-constrained leader-following cooperative interception guidance law with prespecified impact time

To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight (LOS) angles in Three-Dimensional (3D) space, this paper proposes a 3D leader-following cooperative interception guidance law. First, in the LOS direction of the leader, an impact time-controlled guidance law is derived based on the fixed-time stability theory, which enables the leader to complete the interception task at a prespecified impact time. Next, in the LOS direction of the followers, by introducing a time consensus tracking error function, a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go. Then, in the direction normal to the LOS, by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control (SMC) theory, an innovative 3D LOS-angle-constrained interception guidance law is developed, which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption. Moreover, it effectively suppresses the chattering phenomenon while avoiding the singularity issue, and compensates for unknown interference caused by target maneuvering online, making it convenient for practical engineering applications. Finally, theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness, superiority, and robustness of the investigated guidance law.

Multiple Leap Maneuver Trajectory Design and Tracking Method Based on Prescribed Performance Control during the Gliding Phase of Vehicles

A novel standard trajectory design and tracking guidance used in the multiple active leap maneuver mode for hypersonic glide vehicles (HGVs) is proposed in this paper. First, the dynamic equation and multiconstraint model are first established in the flight path coordinate system. Second, the reference drag acceleration-normalized energy (D-e) profile of the multiple active leap maneuver mode is quickly determined by the Newton iterative algorithm with a single design parameter. The range to go error is corrected by the drag acceleration profile update algorithm, and the drag acceleration error of the gliding terminal is corrected by the aerodynamic parameter estimation algorithm. Then, the reference drag acceleration tracking guidance law is designed based on the prescribed performance control method. Finally, the CAV-L vehicle model is used for numerical simulation. The results show that the proposed method can satisfy the design requirements of drag acceleration under multiple active leap maneuver modes, and the reference drag acceleration can be tracked precisely. The adaptability and robustness of the proposed method are verified by the Monte Carlo simulations under various combined deviation conditions.

Aerial refueling rendezvous routes for UAVs based on nonlinear guide laws

The route fusion rendezvous strategy is mostly used for air refueling within the safety zone, with fewer restrictions on the rendezvous airspace. There are fewer restrictions on the combined airspace. The refueling aircraft follows a set route, and the UAV gradually converges with the refueling aircraft by adjusting its own course. The UAVs gradually merge with the fueler’s route until they track the fueler to a certain distance behind the fueler and synchronize with the fueler’s status. The subsequent docking process is carried out.The fused route design is analogous to the use of missiles to track and strike moving targets. The unmanned aircraft are treated as pursuers moving at high speed. The fueling aircraft are treated as targets moving in a fixed pattern to be returned. The main objective of the convergent route design is to draw on and select appropriate guidance laws to bring the unmanned aircraft close to the fuel tanker. The main objective of the route fusion design is to use and select a suitable guidance law that allows unmanned aircraft to approach the fueling aircraft and achieve autonomous rendezvous. The traditional navigation laws are Pure Pursuit (PP) and Proportional Navigation (PP). The basic idea is to change the speed vector of a drone by varying its size. The difference is that the pure tracking guidance law requires the speed vector of the drone to coincide with the line of sight. In contrast, the example guidance law starts from the fact that the angular rate of rotation of the drone’s speed vector and the ratio guiding law is to keep the angular rate of rotation of the speed vector of the drone and that of the target in a fixed proportion.

Adaptive Super-Twisting Sliding Mode Forward Tracking Guidance Law Considering Missile Body Characteristics

Aiming at the problem of forward tracking guidance munitions with missile body characteristics intercepting maneuvering targets, and to improve the hit accuracy of forward tracking guidance system, this paper proposes an adaptive super-twisting sliding mode forward tracking guidance algorithm considering the impact of first-order overload characteristics of missile body and input saturation limitation. Firstly, the nonlinear model of the guidance system is made by the kinematic relation for projectile-target, the principle for the forward tracking interception, the overload characteristic of the missile body, and the input saturation limitation. Secondly, a finite time interference observer (FTIO) is adopted to accurately estimate the nonlinear interference in the guidance system, furthermore, an adaptive super-twisting algorithm for slide mode control is used to design the forward tracking guidance algorithm considering the characteristics of the projectile body. Finally, the results by simulation indicate the adaptive super-twisting slide mode for forward tracking guidance algorithm considering characteristics of the projectile body designed in this paper has better-hit accuracy.

Distributed observer-based finite-time control of moving target tracking for UAV formation

This paper disseminated two formation control strategies for multiple unmanned aerial vehicles (multi-UAV) system of moving target tracking in a windy environment. The communication among UAVs is modeled by a directed graph. The first control strategy proposes a distributed dynamic error observer and a guidance law to make the system global uniform asymptotic stability when the wind disturbance is a known constant. The second control strategy employs a distributed fixed-time observer and a finite-time stable guidance law to make the system globally finite-time stable with unknown wind disturbances. The stability of both formation control strategies is rigorous demonstrated mathematically. Finally, the excellent performance and reliability of the proposed guidance law for target tracking in a windy environment are verified through several simulation examples.

Propellant-Optimal Powered Descent Guidance Revisited

This paper presents new and significant advances in propellant-optimal powered descent guidance based on the indirect method. The paper starts by reviewing and improving a recent indirect method relying on analytical equations and pointing out certain numerical perils of the approach. By taking a fully numerical approach, the developments in this paper take relatively simple and concise software to implement, producing a fully automated algorithm capable of rapidly and reliably generating the complete optimal powered descent trajectory subject to imposed constraints, including on the thrust pointing direction, without the need for any empirical assumptions or hard-to-make user-supplied guesses. Furthermore, a “solution degradation” phenomenon not recognized before is brought to attention in the closed-loop solution of the propellant-optimal powered descent problem with a fully constrained final state that can pose a potential safety risk. This risk is mitigated in the proposed guidance approach, where guidance in the later half of the powered descent tracks an onboard generated optimal reference trajectory with a globally convergent tracking guidance law.

Nonsingular Fixed-Time Tracking Guidance for Mars Aerocapture With Neural Compensation

Mars aerocapture is one of the most concerned technologies for future Mars sample-return and manned exploration missions. This article investigates the challenging problem of the reference trajectory tracking guidance for Mars aerocapture under uncertainties. Based on an integral sliding surface, a fixed-time neural adaptive tracking guidance law is synthesized by incorporating the neural network (NN) approximation into the fixed-time integral sliding mode control approach. Benefiting from the integral sliding surface design, the proposed tracking guidance law has no singularity problem inherently existing in terminal sliding mode control. By adopting the NN approximation to compensate for the lumped uncertain term in the feedforward loop, the proposed tracking guidance law is strongly robust against aerodynamic coefficient uncertainties and atmospheric density uncertainty. Stability analysis shows that the radial distance tracking error and its time derivative can stabilize to the small neighborhoods around the origin in fixed time under the proposed tracking guidance law. Finally, the effectiveness and advantages of the proposed tracking guidance law are illustrated through simulations and comparisons.

A Fuzzy-PLOS Guidance Law for Precise Trajectory Tracking of a UAV in the Presence of Wind

A Fuzzy-PLOS Guidance Law for Precise Trajectory Tracking of a UAV in the Presence of Wind

Task coupling based layered cooperative guidance: Theories and applications

Task coupling based layered cooperative guidance design and analysis issues for multiple missiles system are investigated. First, to deal with cooperative guidance problems with multiple task requirements, a task coupling based layered cooperative guidance structure is constructed by the leader layer and the follower layer. Then, for the leader missile layer, the cooperative detection guidance law is designed to achieve the coordination of the detection field of view (FOV) and cooperative interception, while providing the reference trajectories. Third, for the follower missile layer, the time-varying line of sight (LOS) angle formation tracking guidance law is proposed based on the leader missiles’ LOS angle trajectories convex combination. In addition, the design process and stability analysis of the closed-loop system are given. Finally, an equivalent experiment platform based on multiple mobile robots is introduced, which consists of two leaders, three followers, and a target is constructed. The theoretical results are verified by numerical simulation examples, and experimental results are presented on the platform.

Hybrid Trajectory Optimization Method and Tracking Guidance for Variable-Sweep Missiles

In this paper, an offline hybrid trajectory optimization approach is proposed for variable-sweep missiles to explore the superiority in the diving phase. Aiming at the maximal terminal velocity with the impact angle constraint, the trajectory optimization model is formulated under multiple constraints, and the aerodynamic analysis in different sweep angles is discussed. Unlike only the attack angle used for the optimization process traditionally, the two-variable optimization scheme on both the attack angle and sweep angle is investigated for variable-sweep missiles. Then, the trajectory optimization problem is transformed into the nonlinear programming problem via a hybrid optimization strategy combining the Gauss pseudospectral method and direct shooting method to obtain the high precision and fast convergence solution. Finally, to verify the feasibility of the optimal trajectory under uncertainties, the tracking guidance law is designed on basis of the gain scheduled linear quadratic regulator control. Numerical simulation results reveal not only of the proposed hybrid optimization strategy but also of the superiority of variable-sweep missiles compared with traditional missiles.

A Cooperative Guidance Law for UAVs Target Tracking

The problem of automatic tracking of ground targets is one of the important issues that UAVs need to face in task applications. The main concern of cooperative tracking is how to track a ground target and maintain the UAV formation simultaneously. In this paper, a new leader-follower formation is constructed to track a ground target. Firstly, a new leader UAV guidance law is proposed to track the ground target in the standoff mode, the stability is proved using a Lyapunov function. Secondly, new guidance laws for standoff tracking of the leader UAV and controlling of the inter-UAV angle of the circle formation are designed for follower UAVs, respectively, stabilities are also proved using two Lyapunov functions. Numerical simulation experiments show that the new leader-follower formation can track the static and moving targets well and its performance is better than the classic LVFG algorithm

Adaptive Integral Terminal Sliding Mode Control for an Unmanned Surface Vehicle Against External Disturbances

Abstract This paper addresses a robust controller for an unmanned surface vehicle subject to external disturbances. An adaptive integral terminal sliding mode technique is designed to control the surge speed and yaw dynamics of the vehicle. Such controller is robust against bounded disturbances, allows finite-time convergence of the tracking error variable, and attenuates the chattering effect common to sliding mode approaches by adapting its control gain. Furthermore, a trajectory tracking guidance law is designed to provide speed and heading references. Simulation results illustrate and compare the advantages and feasibility of the proposed approach in the presence of wind, waves, and currents disturbances.

Neural network-based adaptive trajectory tracking control of underactuated AUVs with unknown asymmetrical actuator saturation and unknown dynamics

In this paper neural-network (NN) based adaptive trajectory tracking control scheme has been designed for underactuated Autonomous Underwater Vehicles (AUVs) which are subjected to unknown asymmetrical actuator saturation and unknown dynamics. First, some control preliminaries and assumptions along with AUV kinematic & kinetic models and trajectory tracking problems are elaborated. Secondly, the tracking error model and tracking guidance law are derived based on the theory of relative motion and the principle of approach angle respectively. Then the kinematic controller is designed by using the backstepping technique and Lyapunov theory. Similarly, AUV kinetic controller is designed by using the NN compensation and adaptive estimation techniques which is termed as NN-based adaptive controller (NNAC). Pertinently, a novel bounded saturation function has been developed to describe the unknown asymmetrical actuator saturation. The NN is adopted to approximate the complex AUV hydrodynamics and differential of desired tracking velocities. The bound of the generalized disturbance, which is composed of NN approximation error and ocean disturbances, are approximated based on the adaptive estimation technique. To analyze the stability of the developed NNAC, Lyapunov theory and backstepping technique are utilized by considering the control actions on different saturation sections. Finally, effectiveness and superiority of the proposed NNAC are validated through two sets of comparative simulation studies.

Adaptive guidance and control of uncertain lunar landers in terminal landing phases

A novel double-loop guidance and control strategy for under-actuated lunar landers in terminal landing phases is developed by using adaptive nonlinear control approach in this study. To derive the main thrust input and inner-loop desired attitude trajectory, the outer-loop position tracking guidance law is firstly developed based on the hyperbolic tangent functions to guarantee the constrained thrust and singularity avoidance of the desired attitudes. Then, to avoid the complicated analytic-derivative computing of the desired attitude trajectory, a stable second-order filter is employed to generate the command attitude trajectory for the inner-loop attitude motion. Finally, an adaptive attitude tracking controller is designed by combining the barrier Lyapunove function and the backstepping technique to get rid of the singularities of the Euler angles-based attitude kinematic Jacobian matrix. In addition, tuning rules for designing parameters in guidance law and attitude controller are derived based on the Lyapunov analysis, and the pose tracking errors in the closed-loop system ultimately converge to the small neighborhoods of the origin. An example is simulated to verify the effectiveness of the proposed control design approach.

Research on Maneuvering Trajectory Tracking Accuracy of Target Missile Based on Feedback Linearization

Aiming at the trajectory tracking accuracy of missile target, a trajectory tracking guidance law is designed based on feedback linearization theory and linear quadratic optimal control theory, and the tracking accuracy of the designed trajectory tracking guidance law under different maneuvering trajectories is tested. The motion equations of missiles are typical non-linear motion models, so feedback linearization is introduced as an exact linearization method, and the definition and necessary and sufficient conditions of feedback linearization theory are listed. Firstly, the non-linear equations of the longitudinal motion of target missile are established, and the feedback linearization method is used to linearize the non-linear model accurately. Then, the linearized model is designed by using the linear quadratic optimal control theory, and a target trajectory tracking guidance law is obtained. Finally, given gust disturbance and different maneuvering trajectories, the designed trajectory tracking guidance law is simulated, and the tracking accuracy of the guidance law is studied by changing the control coefficient. The results show that the trajectory tracking guidance law based on feedback linearization has excellent trajectory tracking ability, good tracking accuracy and strong anti-jamming ability under different maneuvering trajectories.

Standoff Tracking of a Moving Target for Quadrotor Using Lyapunov Potential Function

This paper presents a control scheme for standoff tracking of a ground moving target by a quadrotor unmanned aerial vehicle (UAV). The control system is decoupled into outer loop for position control and inner loop for attitude regulation. In the outer loop design, the standoff motion of the vehicle is described in a cylindrical coordinate system attached to the target. After that, the standoff tracking guidance law is designed based on a Lyapunov potential function which can guarantee the stability of the movement. The acceleration signals are produced from the proposed guidance law, and converted to Euler angle commands for the inner control system. A integral backstepping controller is developed to stabilize the attitude of the quadrotor. In particular, the disturbance observer technique is used to deal with the correction terms that account for a non-uniform moving target and constant wind. Numerical simulations are performed to verify the feasibility and performance of the proposed control scheme.

Theory of Fractional-Polynomial Powered Descent Guidance

The notion and the theory of constructing planetary powered descent guidance laws based on fractional polynomials are introduced. Along the way a new perspective to the classical Apollo powered descent guidance designs is gained. As a foundation of this work, a theory is first developed on how to derive an explicit powered descent guidance law by selecting the feedback gains in a unique way in an implicit tracking guidance law. Then by employing a particular profile of the reference thrust acceleration in the tracking law with a special set of gains, a large family of powered descent guidance laws is obtained that offer the flexibility in trajectory shaping and thrust characteristics by two adjustable parameters. An equivalence theory is established to show that each in this family of guidance laws is actually the explicit guidance law from a fractional-polynomial thrust acceleration profile. This insight provides a perfect explanation to the predictable behavior and good targeting performance of these guidance laws. The well-known Apollo lunar descent guidance and E-guidance laws are revealed to be two members of this much broader class of fractional-polynomial powered descent guidance laws.

A new guidance law for trajectory tracking of an underactuated unmanned surface vehicle with parameter perturbations

This paper proposes a novel trajectory tracking controller for an underactuated unmanned surface vessel (USV) with multiple uncertainties and input constraints. Unlike previous dynamic surface control (DSC) methods that utilize a first-order filter to obtain derivatives and avoid “explosion of complexity”, we introduce nonlinear tracking differentiators (NTDs) that achieve satisfactory differential performance and fast tracking response and control the vessel to converge to the pseudo-yaw angle and surge. First, a new guidance law for yaw angle and surge is constructed. Second, inner and outer disturbances caused by uncertainties can be observed by reduced-order extended state observers. With the new guidance law, the design process of the controller is simplified and easy to implement. The simulation results show the trajectory tracking error can be stabilized to a certain extent under the parameter perturbations and other uncertainties, which verified the effectiveness of the proposed algorithm.