Guidance Law Research Articles

Partial state-constrained integrated guidance and control for an STT missile with self-adjusting prescribed performance via non-barrier Lyapunov function method

A state-constrained guidance and control law is vital to the flight safety of an aerial interceptor against a maneuvering target. Taking the flight angle limitations, manipulation saturation, and terminal constraints into consideration, a novel integrated guidance and control (IGC) schema with a self-adjusting prescribed performance is proposed. To avoid the feasibility condition via the conventional barrier Lyapunov function-based method, a new state-dependent nonlinear mapping function is designed, based on which the state-constrained IGC system is converted into a constrained-free model. A novel prescribed performance with a self-tuning mechanism is proposed to guarantee satisfied transit and steady guidance performances. The backstepping technique combined with super-twisting integral sliding modes and newly defined predefined-time disturbance observers is implemented to generate state-constrained virtual command signals. All the signals in the closed-loop system are strictly proven to be bounded by Lyapunov stability theory. The simulation results show the effectiveness of the proposed IGC schema.

Exploring and Modeling Directional Effects on Steering Behavior in Virtual Reality.

Steering is a fundamental task in interactive Virtual Reality (VR) systems. Prior work has demonstrated that movement direction can significantly influence user behavior in the steering task, and different interactive environments (VEs) can lead to various behavioral patterns, such as tablets and PCs. However, its impact on VR environments remains unexplored. Given the widespread use of steering tasks in VEs, including menu adjustment and object manipulation, this work seeks to understand and model the directional effect with a focus on barehand interaction, which is typical in VEs. This paper presents the results of two studies. The first study was conducted to collect behavioral data with four categories: movement time, average movement speed, success rate, and reenter times. According to the results, we examined the effect of movement direction and built the SθModel. We then empirically evaluated the model through the data collected from the first study. The results proved that our proposed model achieved the best performance across all the metrics (r2 > 0.95), with more than 15% improvement over the original Steering Law in terms of prediction accuracy. Next, we further validated the SθModel by another study with the change of device and steering direction. Consistent with previous assessments, the model continues to exhibit optimal performance in both predicting movement time and speed. Finally, based on the results, we formulated design recommendations for steering tasks in VEs to enhance user experience and interaction efficiency.

Quaternion-based non-singular nonlinear impact angle guidance for three-dimensional engagements

This paper proposes a three-dimensional impact angle-constrained nonlinear guidance strategy against different types of targets. To avoid the occurrence of singularities, in Euler angle-based approaches, the development of this guidance strategy is solely based on quaternion dynamics. An explicit relationship between the quaternions representing impact orientation and line-of-sight orientation at the time of collision is derived. Based on the obtained relation, a guidance law is derived using a sliding mode control technique to track the desired line-of-sight orientation for target interception. The performance of the proposed guidance strategy is evaluated for constant-speed and different time-varying-speed interceptor models accounting for the effect of varying aerodynamic parameters on interceptor speed. The numerical simulations performed show satisfactory results for all engagements, validating the efficacy and robustness of the proposed guidance law.

Vision-Based Optimal Landing Guidance Law for VTOL UAVs on a Moving Platform

Vision-Based Optimal Landing Guidance Law for VTOL UAVs on a Moving Platform

A Balanced Path-Following Approach to Course Change and Original Course Convergence for Autonomous Vessels

This paper proposes a novel path-following method for autonomous ships that optimizes overall performance by balancing course changes and convergence to the original route. The proposed method extends the line-of-sight (LOS) guidance law by dynamically adjusting key parameters based on the ship’s cross-track error (XTE) and the distance of new course considering maneuvering characteristics. By incorporating these maneuvering characteristics, the method enables more precise adjustments during course changes, improving overall path-following performance. Simulation results showed that the proposed method outperformed three existing methods, including the traditional LOS guidance law, by minimizing overshoot and maintaining reasonable XTE during larger course changes. It achieved the lowest mean absolute cross-track error (MAE) while also significantly reducing the total time required to follow the path, highlighting its superior accuracy and efficiency in path following. These outcomes highlight the method’s potential to enhance significantly the path-following capabilities of autonomous vessels, contributing to greater efficiency and accuracy in pre-determined route navigation.

Unmanned Surface Vessel–Unmanned Aerial Vehicle Cooperative Path Following Based on a Predictive Line of Sight Guidance Law

This paper explores the cooperative control of unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs) in maritime rescue and coastal surveillance. The USV-UAV system faces challenges of disturbances and substantial inertia-induced overshooting during path following. A novel position prediction line of sight (LOS) guidance law is proposed to address these issues for USV path following control. Radial basis function-based neural networks (RBF-NNs) are used to estimate disturbances, and a high-order differentiator is used to design a velocity observer for unknown USV velocity. The UAV control system employs proportional–derivative (PD) control with feedforward compensation for quadrotor control design and utilizes a finite-time converging third-order differentiator to differentiate non-continuous functions. The simulation results demonstrate strong robustness in the proposed USV-UAV cooperative control algorithm. It achieves path following control in the presence of wind and wave disturbances and exhibits minimal overshoot.

Automatic Landing Control for Fixed-Wing UAV in Longitudinal Channel Based on Deep Reinforcement Learning

The objective is to address the control problem associated with the landing process of unmanned aerial vehicles (UAVs), with a particular focus on fixed-wing UAVs. The Proportional–Integral–Derivative (PID) controller is a widely used control method, which requires the tuning of its parameters to account for the specific characteristics of the landing environment and the potential for external disturbances. In contrast, neural networks can be modeled to operate under given inputs, allowing for a more precise control strategy. In light of these considerations, a control system based on reinforcement learning is put forth, which is integrated with the conventional PID guidance law to facilitate the autonomous landing of fixed-wing UAVs and the automated tuning of PID parameters through the use of a Deep Q-learning Network (DQN). A traditional PID control system is constructed based on a fixed-wing UAV dynamics model, with the flight state being discretized. The landing problem is transformed into a Markov Decision Process (MDP), and the reward function is designed in accordance with the landing conditions and the UAV’s attitude, respectively. The state vectors are fed into the neural network framework, and the optimized PID parameters are output by the reinforcement learning algorithm. The optimal policy is obtained through the training of the network, which enables the automatic adjustment of parameters and the optimization of the traditional PID control system. Furthermore, the efficacy of the control algorithms in actual scenarios is validated through the simulation of UAV state vector perturbations and ideal gliding curves. The results demonstrate that the controller modified by the DQN network exhibits a markedly superior convergence effect and maneuverability compared to the unmodified traditional controller.

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.

Bounded Containment Maneuvering Protocols for Marine Surface Vehicles With Quantized Communications and Tracking Errors Constrained Guidance: Theory and Experiment.

A new type of containment maneuvering protocols for multiple marine surface vehicles (MSVs) is developed to follow a parameterized path in this work, where the tracking errors are constrained within finite time and the information needed to be transmitted is quantized during coordination. To achieve containment maneuvering of multiple MSVs, a two-objective coordinated control framework is proposed. For the geometric objective, by developing tan-type barrier Lyapunov functions (BLFs) and extended Lyapunov condition-based finite-time guidance laws, the performance of the parameterized line-of-sight guidance framework, including convergence speed and tracking error constraints, is improved. For the dynamic objective, based on quantized control strategy and smooth saturation functions, novel bounded containment maneuvering protocols are proposed to dramatically alleviate the burden of communications among MSVs and ensure more faster dynamic behavior on tracking the path updating speed. Both theoretical analysis and experimental tests with comparative studies illustrate the validity of the proposed containment maneuvering strategy.

Olfactory-based powered descent guidance for Mars methane plume exploration in long-time-average wind environment

This paper investigates an olfactory-based powered descent guidance method that enable a lander to autonomously locate and target the vent source of any methane plume in long-time-average wind environment on Mars. The episodic methane plumes emanating from the Martian surface invite the possibility of direct access to the subsurface methane reservoir to acquire pristine organic materials. Constrained by the insufficient knowledge of the accurate plume vent location, Mars landers must infer the target location — the plume source — autonomously during the powered descent. However, existing powered descent guidance methods require the target location as a terminal constraint, rendering them ineffective in plume exploration missions. We propose an olfactory-based powered descent guidance method that could steer a lander to target the methane vent source by tracking the gradient of methane concentration in long-time-average wind environment, imposing sub-optimal fuel consumption. A novel olfactory navigation method based on tracking the negative logarithmic concentration gradient, and the corresponding gradient measurement method, is proposed. By implementing the negative logarithmic gradient field, gradient-dependent dynamic equations for the powered descending lander are proposed. The gradient-dependent equations provide a way to transform the original optimal guidance problem, which is non-convex and terminal-free, into a convex and terminal-fixed problem. A suboptimal guidance law, similar to E-guidance, is then derived by solving this problem. The proposed guidance could target the vent source of any methane plume in long-time-average wind environment, imposing modest fuel consumption by feeding back the concentration gradient. Numerical simulations illustrate that, in comparison to the terminal-fixed E-guidance and the open-loop fuel-optimal guidance, the lander imposes additional fuel consumption of 2.57% and 12.15% respectively, using the proposed guidance law.

Reentry vehicle fixed-time terminal guidance and attitude control with impact angle constraints

The motivation of this paper is to handle the terminal guidance and attitude control problem for the unpowered reentry vehicle in the diving phase, which is crucial for interception to the target. The most important objectives of this study are to intercept the maneuvering target with the miss distance and impact angle error as small as possible. First, the second-order derivatives of the aerodynamic angles are derived with the fin deflections as control input, which is objective to avoid the tracking of reentry vehicle body angle rate command in the traditional methods. Second, a novel fixed-time time-varying parameter nonsingular terminal sliding mode guidance law is proposed to improve the convergence speed of line-of-sight angle rate, which can avoid control input singularity without switching to the polynomial form when the error approaches the origin. Thirdly, a new global time-varying sliding mode is developed to design the attitude controller, with the predefined fixed convergence time and analytical solution. The system states are proved to be fixed-time convergence based on the Lyapunov stability theory. Six-degree-of-freedom flight simulations are conducted to validate the superiority of the proposed algorithm in terms of miss distance, impact angle error, intercepting time and control input energy.

Practical three-dimensional path following and control for unmanned combat aerial vehicles based on expansion of L1+ guidance logic and disturbance rejection

An effective virtual-target-based three-dimensional path-following algorithm is proposed for unmanned combat aerial vehicles, which extends from the planar [Formula: see text] guidance. The separated implementation of the planar guidance law in two perpendicular planes provides the longitudinally-laterally decoupled acceleration commands. In order to obtain a non-unique virtual-target-point, a numerical iterative method using auxiliary path-related variables is proposed. Moreover, two protection improvements are discussed for real-word implementation: one involves the modification of adaptive [Formula: see text] length for vehicle position far away from the desired path; the other involves a switching strategy for multi-segment paths. The improved algorithm eliminates complex coordinate transformation and easily connects different types of path segments. For the control loop, technology enhanced with the active disturbance rejection control was used to facilitate the design of a bank-to-turn autopilot. For the pitch and roll channels, a rate-damping augmentation loop was used first to transform the original system into a generalized plant. Then the second-order active disturbance rejection control was structured to estimate the total disturbance, including time-varying dynamics, model mismatch, and coupling of channels, making the system an ideal integral-series type. The non-smooth optimization technique in the H-infinity methodology was used to facilitate tuning of the fixed-structure active disturbance rejection control.

PCLOS based fractional-order sliding mode stochastic path following control for underactuated marine vehicles with multiple disturbances and constraints

This paper investigates the stochastic path following control of underactuated marine vehicles (UMVs) subject to multiple disturbances and constraints. Firstly, the complex marine environment in which UMVs navigate typically contains stochastic components, thus the multiple disturbances are categorized as slow-varying deterministic disturbances and stochastic disturbances. Secondly, a position-constrained line-of-sight (PCLOS) based fractional-order sliding mode stochastic (FSMS) control strategy is established to achieve path following control of UMVs. A PCLOS guidance law based on universal barrier Lyapunov function is proposed to ensure that the position errors remain within the constraint ranges, which is versatile for systems with symmetric constraints or without constraints. An FSMS controller based on fractional-order theory and sliding mode control is designed to improve the dynamic response speed of the system and effectively attenuate chattering phenomenon. A stochastic disturbance observer is developed to estimate the slow-varying deterministic disturbances in the stochastic system, and auxiliary dynamic compensators are used to mitigate the impact of input constraints. Lastly, theoretical analysis indicates that the closed-loop system is stable and the position constraint requirements are satisfied. Comparative simulations illustrate the effectiveness of the proposed control strategy.

Optimal strategies design of active target defense differential game

In this paper, the optimal strategies are investigated for the differential game of active target defense. Specifically, we describe a pursuitevasion game with three agents (namely, an attacker, a target and a defender). For the three agents engagement scenario, two different differential game guidance laws–pure pursuit (PP) and proportional navigation (PN)–are presented for defender. Firstly, the relative motion kinematic models of the three agents are established. We subsequently derive the coupled Hamilton-Jacobi (HJ) equations to design the optimal control strategies for the three agents. Through the construction of actor-critic neural networks, optimal solutions are obtained. Then, the stability of the three-agent system is ensured, and the convergence to the Nash equilibrium equations is demonstrated. Finally, we simulate the optimal strategies employed by the attacker and the defender-target team, thereby highlighting the contrasting outcomes and superiority of different defensive approaches.

Target tracking based on the extended line of sight guidance law and information fusion

The extended line of sight (LOS) guidance law is designed to track toward a target in a three-dimensional space, and this method presents a family of guidance laws resulting in a rich behaviour for different parameters. First, polar kinematics models for the pursuer and target are established by taking the observer as a reference point. Second, the extended LOS guidance law was deduced through polar kinematics models. Third, information fusion weighted by matrices was applied to target tracking, providing a good estimate for extended LOS guidance. This combination can enrich the application range of guidance laws and information fusion. Finally, the simulations were implemented in MATLAB. The simulation results confirm the availability of this guidance law.

Design and Analysis of Terminal Guidance Law for Kinetic Interceptors based on Pulse Engine

A new terminal guidance law is proposed based on a solid propellant pulse engine and an improved proportional navigation method to address the terminal guidance issue for kinetic interceptors. On this basis, the start-stop curve of the pulse motor during the terminal guidance process is designed, along with its start-up logic. The effectiveness of the proposed guidance strategy is verified through simulation.

Three-dimensional cooperative guidance with impact angle constraints via value-policy decomposed multi-agent reinforcement learning

For a three-dimensional impact angle-constrained time-coordination guidance problem, a value-policy decomposed multi-agent twin delayed deep deterministic (VPD-MATD3) policy gradient algorithm is proposed in this paper, and a temporal-spatial cooperative guidance law is designed consequently. The derived cooperative engagement kinematics is formulated as a value-policy decomposed partially observable Markov decision process. Value decomposition and policy decomposition are correspondingly proposed to address the two bottlenecks of reward coupling and policy coupling in 3D guidance, thus improving the training process. The training environment with multiple uncertainties, such as observation noise, maneuverability perturbation, autopilot time lag, switching communication topology, and random initialization, is subsequently constructed. Time-energy type reward functions are designed, incorporating energy consumption as a direct optimization indicator via a penalty term. A long short-term memory network layer is inserted inside the policy networks to suppress the negative effect of observation noise. The policy training curves verify the significant effect of the proposed algorithm in improving training convergence. The policy testing results illustrate the robustness and generalization of the VPD-MATD3 cooperative guidance law and its ability to cope with randomly switched communication topologies. Moreover, the comparative testing further reveals its time-energy suboptimal property.

A Climb-and-dive Guidance Law with the Altitude Constraint

A Climb-and-dive Guidance Law with the Altitude Constraint

Terminal Phase Guidance Law Against Maneuvering Targets: Adaptive State-Dependent Differential Riccati Equation Approach

This paper provides a methodology to address the terminal guidance issue for a highly maneuverable target by formulating the problem as a nonlinear autonomous system with matched term uncertainty. This method involves the utilization of the State-Dependent Differential Riccati Equation (SDDRE) technique to develop an optimal adaptive strategy. Since the SDDRE is vulnerable to variations in the model, the adaptive framework has been devised to address the issue of system uncertainty. The utilization of Laguerre Functions (LFs) is employed to characterize the target acceleration due to its arbitrary shape, while the adaptation law computes the coefficients associated with this representation. The effectiveness of the proposed guidance law has been demonstrated in numerical simulation for various target maneuvers. In addition, the effect of the type and number of basis functions on the estimation had been studied. Ultimately, a sensitivity analysis of design parameters is presented and a comparison is provided between the effectiveness of the proposed guidance law and some of the methods that have been proposed in the literature.

Differential Game-Based Cooperative Interception Guidance Law with Collision Avoidance

To deal with the offense-defense confrontation problem of multi-missile cooperative intercepting a high-speed and large-maneuvering target, a differential game-based cooperative interception guidance law with collision avoidance is proposed, in which the offense-defense parties are the incoming target and the interceptors, respectively. Given that both offense-defense parties have uniformly decreasing speeds and first-order biproper dynamics, the relative motion models among the offense-defense parties are established, and the performance indices of the target and the interceptors are proposed. After that, the cooperative interception guidance law with collision avoidance is derived based on a differential game. The guidance law considers the effects of speed variations and rudder layouts on the motions of both offense-defense parties, ensuring excellent algorithmic real-time property and interception accuracy while introducing inter-missile collision avoidance constraints. In addition, the parameters of the target performance index are set according to the target acceleration information estimated by the interceptors. The simulation results verify the effectiveness of the guidance law designed in this paper, under various three-to-one scenarios, the interceptors could achieve collision-free interceptions with the interception accuracy of less than 5 m and the interception time difference of less than 0.1 s.