Guidance Law Research Articles

Modeling, Guidance, and Robust Cooperative Control of Two Quadrotors Carrying a “Y”-Shaped-Cable-Suspended Payload

This paper investigates the problem of cooperative payload delivery by two quadrotors with a novel “Y”-shaped cable that improves payload carrying and dropping efficiency. Compared with the existing “V”-shaped suspension, the proposed suspension method adds another payload swing degree of freedom to the quadrotor–payload system, making the modeling and control of such a system more challenging. In the modeling, the payload swing motion is decomposed into a forward–backward process and a lateral process, and the swing motion is then transmitted to the dynamics of the two quadrotors by converting it into disturbance cable pulling forces. A novel guidance and control framework is proposed, where a guidance law is designed to not only achieve formation transformation but also generate a local reference for the quadrotor, which does not have access to the global reference, based on which a cooperative controller is developed by incorporating an uncertainty and disturbance estimator to actively compensate for payload swing disturbance to achieve the desired formation trajectory tracking performance. A singular perturbation theory-based analysis shows that the proposed parameter mapping method, which unifies the parameter tuning of different control channels, allows us to tune a single parameter, ε, to quantitatively enhance both the formation control performance and system robustness. Simulation results verify the effectiveness of the proposed approach in different scenarios.

Reinforcement learning-based adaptive spiral-diving Manoeuver guidance method for reentry vehicles subject to unknown disturbances

Abstract This paper proposed a reinforcement learning-based adaptive guidance method for a class of spiral-diving manoeuver guidance problems of reentry vehicles subject to unknown disturbances. First, the desired proportional navigation guidance law is designed for the vehicle based on the initial conditions, terminal constraints and the curve involute principle. Then, the first-order multivariable nonlinear guidance command tracking model considering unknown disturbances is established. And the controller design problem caused by the coupling of control variables is overcome by introducing the coordinate transformation technique. Moreover, the actor-critic networks and corresponding adaptive weight update laws are designed to cope with unknown disturbances. With the help of Lyapunov direct method, the stability of the system is proved. Subsequently, the range values of the guidance parameters are analysed. Finally, the validity as well as superiority of the proposed method are verified by numerical simulations.

D Matrix for Keplerian State Error Propagation

The D matrix is an error state transition matrix (STM) for Keplerian motion in cylindrical coordinates employing time as a state variable and reference true or eccentric anomaly as an independent variable. It has been only partially derived in previous articles and applied to different astrodynamics problems such as optimal collision avoidance and Lambert targeting. A rigorous and complete derivation of the full matrix in analytical form is presented. In addition, it is shown that the different terms of the proposed STM can lead to the definition of new variational equations and optimal steering laws applicable to impulsive and low-thrust orbit transfer optimization as well as reachability analysis. Finally, the effectiveness of the proposed STM is evaluated against the well-known Yamanaka–Ankersen STM showing more than one order of magnitude error reduction associated to the semimajor axis and eccentricity of the linearly propagated relative state.

Uncertainty-resilient constrained rendezvous trajectory optimization via stochastic feedback control and unscented transformation

This paper proposes an innovative approach for constrained rendezvous trajectory optimization (CRTO) using stochastic optimal feedback control and unscented transform (UT) uncertainty quantification. The method overcomes limitations of traditional deterministic CRTO solutions that suffer from uncontrolled terminal state error growth and severely deteriorated path constraint satisfaction when initial state uncertainty, dynamics uncertainty, and navigation uncertainty are considered. The approach involves constructing a stochastic optimal feedback control (SOFC) problem with chance constraints and introducing linear feedback control to regulate both the mean and variance of terminal state errors. UT is employed to approximately quantify the state errors and their propagation, transforming the SOFC problem into an unconstrained deterministic optimization (UDO) problem. Differential dynamic programming (DDP) is then used to solve the UDO problem. The obtained stochastic optimal solution provides a robust rendezvous trajectory and a corresponding explicit closed-loop guidance law, improving terminal accuracy and path constraint satisfaction in the presence of various considered uncertainties. The influence of different term weights in the objective function on terminal accuracy and path constraint satisfaction is also studied. The effectiveness of the proposed approach is verified through Monte Carlo simulation, demonstrating the robustness of the closed-loop control strategy. The results highlight the potential of the method in enhancing terminal accuracy and path constraint satisfaction in uncertain rendezvous scenarios.

Improved Stanley guidance law–based adaptive path-following control of underactuated ship with state-constrained and time-varying drift angle

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path.

Double-loop LQR depth tracking control of underactuated AUV: Methodology and comparative experiments

In this paper, a double-loop depth tracking control scheme based on linear quadratic regulator (LQR) is proposed for underactuated autonomous underwater vehicles (AUV). The motivation is to address the problem that the classic single-loop LQR depth controller which is easy to use in practice yet cannot effectively overcome the underactuated AUV features and complex disturbances. First, a double-loop depth control framework is proposed which divides complex disturbances into outer-loop kinematic disturbances and inner-loop dynamic disturbances. Second, the adaptive line-of-sight (ALOS) guidance law is designed in the outer loop to account for the underactuated characteristics. The depth tracking error is converted to the desired pitch and the kinematic disturbance caused by the unknown angle of attack is compensated. Furthermore, based on the linear model in the inner-loop, a concise LQR method is designed to track the desired pitch. Meanwhile, an extended state observer (ESO) is introduced to estimate dynamic disturbances such as model nonlinearity, uncertainty and external environmental disturbances. Finally, the proposed scheme is validated by tank test and compared with the single-loop LQR method. The experiment results show that the proposed double-loop depth tracking method can effectively overcome complex disturbances and the depth tracking accuracy is increased by 83%.

A novel evasion guidance for hypersonic morphing vehicle via intelligent maneuver strategy

This paper presents a novel evasion guidance law for hypersonic morphing vehicles, focusing on determining the optimized wing's unfolded angle to promote maneuverability based on an intelligent algorithm. First, the pursuit-evasion problem is modeled as a Markov decision process. And the agent's action consists of maneuver overload and the unfolded angle of wings, which is different from the conventional evasion guidance designed for fixed-shape vehicles. The reward function is formulated to ensure that the miss distances satisfy the prescribed bounds while minimizing energy consumption. Then, to maximize the expected cumulative reward, a residual learning method is proposed based on proximal policy optimization, which integrates the optimal evasion for linear cases as the baseline and trains to optimize the performance for nonlinear engagement with multiple pursuers. Therefore, offline training guarantees improvement of the constructed evasion guidance law over conventional ones. Ultimately, the guidance law for online implementation includes only analytical calculations. It maps from the confrontation state to the expected angle of attack and the unfolded angle while retaining high computational efficiency. Simulations show that the proposed evasion guidance law can utilize the change of unfolded angle to extend the maximum overload capability. And it surpasses conventional maneuver strategies by ensuring better evasion efficacy and higher energy efficiency.

Integrated entry guidance with no-fly zone constraint using reinforcement learning and predictor-corrector technique

This paper presents an integrated entry guidance law for hypersonic glide vehicles with no-fly zone constraint. Existing methods that employ predictor-corrector technique and lateral guidance logic for both guidance and avoidance, may have limitations in response time and maneuverability when facing sudden threats, because the guidance cycle is limited by computational efficiency and the bank angle magnitude cannot be adjusted according to the urgency of the avoidance. To overcome these challenges, the proposed method divides the entry process into safe flight stages and no-fly zone avoidance stages, and introduces reinforcement learning to develop an intelligent avoidance strategy for the latter. This division reduces the complexity of the learning problem by restricting the state space and increases the applicability in the presence of multiple no-fly zones. The trained avoidance strategy can directly output continuous bank angle command through a single forward calculation, considering both guidance and avoidance requirements. This enables the full utilization of the vehicle’s maneuverability and supports a high command update frequency to effectively handle threats. Additionally, a network trained via supervised learning is employed to generate reference commands, accelerating the training convergence of reinforcement learning. Simulation results demonstrate the effectiveness of the proposed guidance law, highlighting its high computational efficiency, command stability, and robustness. Importantly, the approach offers convenience in extending to multiple no-fly zones and accommodating vast initial state spaces.

Three-Dimensional Composite Approach Angle Constrained Guidance Law with Actuator Lag Consideration

Three-Dimensional Composite Approach Angle Constrained Guidance Law with Actuator Lag Consideration

Polynomial shaping based three-dimensional impact angle and field-of-view constrained guidance

This paper proposes a polynomial-based three-dimensional (3D) impact angle-constrained guidance law considering the seeker's field-of-view (FOV) bound. The guidance laws are derived using nonlinear coupled dynamics of the interceptor-target engagement against stationary as well as constant velocity targets. Line-of-sight (LOS) orientations between the interceptor and the target in both pitch and yaw planes are shaped as two cubic polynomial functions of relative range. An explicit expression for the look angle of the interceptor is acquired in terms of the LOS polynomials. This expression facilitates the embodiment of the FOV constraint in the boundary conditions inflicted on the polynomials. A system of equations with the eight unknown coefficients is obtained by employing the appropriate launch and terminal conditions of the interceptor-target engagement. Reference LOS angle and lead angle profiles are generated using the calculated coefficients, complying to which the interceptor achieves a zero miss distance with desired impact angle and FOV constraints. A tracking controller is then designed using a nonlinear control technique that enables the interceptor to follow reference lead angle profiles in mutually orthogonal planes. Unlike the already existing guidance strategies for 3D impact angle and FOV-constrained target interception, the proposed nonlinear guidance strategy is designed without the use of linearization or decoupling. Moreover, no switching logic or multi-phase guidance structures are employed in the proposed guidance strategy, which eliminates possible jumps in the guidance command. The effectiveness of the proposed guidance law is validated using numerical simulations, along with a comparison study with the existing strategy.

Three-dimensional terminal angle constraint guidance law with class [formula omitted] function-based adaptive sliding mode control

This paper investigates the three-dimensional (3-D) interception guidance problem, where the missile is required to intercept the maneuvering target with the desired terminal angles. For the nonlinear relative kinematic model, a class K∞ function-based adaptive sliding mode guidance law is proposed, which ensures that the errors of terminal Line-of-Sight (LOS) angles converge to the small neighborhoods of origin at the time of interception, without relying on information about the target's acceleration. To overcome the challenges of large initial control input and chattering in existing sliding mode guidance laws, two improved control schemes are introduced. The first scheme is to directly impose saturation constraints into the adaptive gain. However, it is important to ensure that the unknown disturbance remains within the prescribed saturation bound. To avoid the limitation, another approach involves introducing auxiliary dynamics to eliminate the reaching phase and slow down the convergence of LOS angles by presetting the convergence time of the sliding mode variables, which helps mitigate excessive initial control inputs. Numerical simulations are conducted using a realistic missile model and considering a 3-DOF point-mass aircraft as the target to evaluate three different guidance laws. The results indicate that the proposed guidance law ensures interception accuracy while substantially reducing the control gain.

Collaborative strategy research of target tracking based on natural intelligence by UAV swarm

Regarding the regional area target collaborative tracking problem widely existing in intelligent scenarios, this paper built a distributed UAV swarm framework inspired by natural intelligence to heighten intricate missions’ efficiency. Also, a standoff collaboratively continuous tracking strategy was proposed based on a lateral guidance law with an improved Reference Point Guidance (RPG) and a longitudinal guidance law with an improved phase collaboration. Under an uncertain environment, this framework used an improved bat algorithm (IBA) to optimize the speed allocation of the UAV swarm’s online control strategy with information consensus estimation. Compared with a case without the designed transformation, statistically, the results demonstrate that the framework operates efficiently and robustly in phase error convergence, swarm flight distance, and fuel consumption, where a dynamic target exists.

Bionic fish position control with the desired heading angle of the target position

This paper proposes an underdriven bionic fish position control system with the desired heading angle at the target position. The developed position control system controls the bionic fish to reach the desired target position while maintaining the heading angle at the target position. The system comprises a virtual waypoint-based line-of-sight (VW-LOS) guidance system, an inner-loop control system, and a linear extended state observer (LESO). First, the VW-LOS system generates a virtual waypoint behind the target position, transforming the bionic fish's position control problem into a straight-line path tracking problem. The heading and speed guidance laws are used to generate the desired heading angle and speed required during the tracking process. An inner-loop controller is subsequently used to regulate the controlled reference, including a heading tracking controller, a speed tracking controller, and a fuzzy inference module that converts forces and moments into inputs to the bionic fish's central pattern generator (CPG) network. Moreover, the LESO estimates the unmeasurable speed and sideslip angle and feeds back to the VW-LOS system and the inner-loop controller. Finally, simulation and experimental results verify the effectiveness of the proposed control system.

Three‐dimensional path following control of underactuated autonomous underwater vehicles with nonzero roll dynamics: A novel line‐of‐sight‐guided approach

AbstractMost existing path following control approaches for underactuated Autonomous underwater vehicles (AUVs) assumed that the roll angle can be passively stabilized at zero, and simplified the problem to the 5‐degree‐of‐freedom model. However, in practice, the roll motion suffers from undesirable oscillations induced by environmental disturbances, unbalanced propeller torque, etc. To preserve the stability of the system under nonzero roll dynamics, this paper proposes a novel line‐of‐sight‐ (LOS) guided path following control approach. Firstly, the spatial path following error dynamics model is derived to comprehensively reveal the negative effect of roll dynamics. Secondly, an improved LOS guidance law is designed to compensate for the nonzero roll angle. A salient feature is that the proposed guidance law can be applied to the underwater vehicle no matter it is underactuated in the roll motion or not. Thirdly, by assigning the guidance angles to the desired attitude angles, a robust attitude tracking controller is developed, in which the adaptive estimation technique is employed to handle the lumped uncertainties. The tanh‐based saturation function is incorporated such that the resultant control signals are inherently bounded. The closed‐loop path following and attitude tracking errors are proved to be globally asymptotically stable at the origin. Comparative simulation results are provided to substantiate the effectiveness and superiority of the proposed method.

Optimal sliding mode guidance law against maneuvering target with impact angle constraint

In this paper, an optimal sliding mode guidance law with impact angle constraint is proposed against maneuvering targets. Firstly, the impact angle frame for a static target is extended to a maneuvering target. Then, in this impact angle frame, the optimal reaching law of sliding mode is proposed to design an optimal sliding mode guidance law which is robust to target maneuvers and satisfies an impact angle constraint. The optimal sliding mode guidance law with impact angle constraint is also extended to the three-dimensional case. Numerical simulations in different scenarios with a realistic missile model show that the guidance law can intercept a maneuvering target with a desired impact angle, and the control effort is close to the optimal value, which verifies that the proposed optimal sliding mode guidance law has both robustness and optimality.

Calculate the ignition height of the vertical landing phase online for the reusable rocket

For the vertical landing phase of the reusable rocket, in order to improve the landing accuracy with consideration of multiple uncertainties, a novel strategy to calculate the ignition height online is proposed based on polynomial guidance law (PGL), particle swarm optimization (PSO), and deep reinforcement learning (DRL). Firstly, a deep neural network (DNN) is designed to describe the relationship between the state of the reusable rocket and the ignition height. To accomplish the guidance task of the vertical landing phase, PGL is modified by introducing the estimated aerodynamic acceleration. Through simulation, the output range of the DNN is estimated by the modified PSO. Then, the reward function is shaped and the parameters of the DNN are trained on a training set of simulation scenarios by the DRL algorithm. Finally, to demonstrate the effectiveness of the proposed strategy, the trained DNN is used to calculate the ignition height of 1500 unlearned simulation scenarios online. The numerical simulation results show that the proposed strategy has higher landing accuracy and lower fuel consumption than the offline strategy of fixed ignition height based on the modified PSO.

A uniform semiglobal exponential stable adaptive line-of-sight (ALOS) guidance law for 3-D path following

This paper presents a 3-D adaptive line-of-sight (ALOS) path-following algorithm for autonomous vehicles, marine craft, and aircraft. The origins of the cross- and vertical-track errors are proven to be uniform semiglobal exponential stable (USGES). The stability proof is based on a kinematic amplitude-phase representation of the North-East-Down (NED) positional rates instead of the classical Euler angle rotation matrix representation. Parameter adaption is used to obtain integral action such that the vehicle converges to the path in the presence of winds, waves, and ocean currents. Typical applications are guidance and path-following control systems for autonomous vehicles, marine craft, and aircraft, where the horizontal- and vertical-plane motions are strongly coupled.

Segmented guidance method for multi-UAVs cooperative attack with spatio-temporal constraints

This paper presents a segmented guidance method for multi-UAVs (unmanned aerial vehicles) cooperative attack with spatio-temporal constraints, and successfully implemented in the flight tests. First, the uniform distribution of UAVs around the target is completed through cooperative path planning and tracking in the mid-course phase. The path planning method for cooperative arrival is proposed based on Dubins curve, and the guidance strategy for circular formation flight enables the UAVs to accurately track the reference points which are evenly distributed on the circle. Second, the terminal guidance law in 3D space with impact time cooperation is proposed during the cooperative attack stage, which would further eliminate the accumulated deviation. Finally, simulations and field flight tests for coordinated attack are carried out, which show the effectiveness of the proposed method.

Impact time guidance law for arbitrary lead angle using sliding mode control

PurposeThis paper aims to investigate a novel impact time control guidance (ITCG) law based on the sliding mode control (SMC) for a nonmaneuvering target using the predicted interception point (PIP).Design/methodology/approachTo intercept the target with the minimal miss distance and desired impact time, an estimation of time-to-go is introduced. This estimation results in a precise impact time for multimissiles salvo attack the target at the same time. Even for a large lead angle, the desired impact time is achieved by using the sliding mode and Lyapunov stability theory. The singularity issue of the proposed impact time guidance laws is also analyzed to achieve an arbitrary lead angle with the desired impact time.FindingsNumerical scenarios with desired impact time are presented to illustrate the performance of the proposed ITCG law. Comparison with the state-of-art impact time guidance laws proves that the guidance law in this paper can enable the missile to intercept the target with minimal miss distance and final impact time error. This method enables multiple missiles to attack the target simultaneously with different distances and arbitrary lead angles.Originality/valueAn ITCG law based on sliding mode and Lyapunov stability theory is proposed, and the switching surface is designed based on a novel estimation time-to-go for the missile to intercept the target with minimal miss distance. To intercept the target with initial arbitrary lead angles and desired impact time, the authors analysis the singular issue in SMC to ensure that the missile can intercept the target with arbitrary lead angle. The proposed approach for a nonmaneuvering target using the PIP has simple forms, and therefore, they have the superiority of being implemented easily.

Fixed Time Cooperative Scheme Design for Missiles Salvo Attack

This paper proposes a fixed-time cooperative control strategy for multiple missiles with impact angle constraints to accomplish the salvo attack guidance scenario on maneuvering targets. A fixed-time extended state observer (ESO) is proposed to estimate the target accelerations. In order to execute the salvo attack, along the line of sight (LOS) direction guidance law and the LOS normal direction guidance law are the two components of the proposed fixed time guidance scheme. The efficiency of the designed method is demonstrated through simulation results.