Line Of Sight Angle Research Articles

Three-Dimensional Approach Angle Guidance Under Varying Velocity and Field-of-View Limit Without Using Line-of-Sight Rate

In this article, a practical three-dimensional (3-D) guidance is designed to achieve trajectory constrained flight, i.e., arriving at the destination with desired approach angles under limited field-of-view (FOV) and varying velocity. For this goal, the nonlinear engagement model is first transformed to a set of new differential equations in terms of the line-of-sight (LOS) angles. Then, the approach angle constraints are handled by constructing two reference range profiles as cubic polynomials of LOS angles. By solving the unknown coefficients involved in the polynomials, a semianalytical 3-D guidance solution is derived from the second-order range dynamics. To meet the FOV limit and avoid the initial guidance saturation, the achievable approach angle set is determined for capturability analysis by introducing the look angle dynamics with respect to the range profiles. The technique does not involve the model linearization, guidance switching logic, constant velocity assumption, and LOS rate information. Notably, only the LOS angle measurement is required during the guidance process once the initial conditions are provided, which makes it preferable for vehicles equipped with passive angles-only sensors. Extensive numerical simulations and Monte Carlo test are conducted to validate effectiveness and robustness of the proposed technique.

Impact angle-based engagement classification and nonlinear guidance against targets with a speed advantage

In this paper, we propose Lyapunov theory-based nonlinear guidance scheme to achieve an angle-constrained interception of a high-speed target (targets with speed advantage). An impact angle based classification between head-on and head-pursuit interception geometries is first proposed to uniquely match a desired impact angle to a corresponding desired line-of-sight (LOS) angle for successful target interception. The proposed guidance scheme comprises two phases, namely orientation and LOS tracking phases. The orientation phase corrects the interceptor's lead angle based on the desired interception geometry whenever required. The LOS tracking phase then enables the tracking of desired LOS angle by enforcing the error is LOS angle to converge onto a manifold with finite-time convergent properties. The applicability of the proposed guidance strategy is validated using numerical simulations for various engagement geometries, in the presence of autopilot, for constant speed as well as time-varying speed interceptors. The performance of the proposed guidance scheme is also compared with existing ones against high-speed targets, and is found to be superior.

Adaptive Line-of-Sight Tracking Control for a Tractor-Trailer Vehicle System With Multiple Constraints

In this paper, for the line-of-sight (LOS) tracking problem of a tractor-trailer vehicle system, we propose a novel adaptive constrained tracking control algorithm for the trailer to track a desired trajectory, while satisfying multiple <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">performance</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasibility</i> constraint requirements during the operation. To deal with these constraint requirements, both a universal barrier function approach and a novel state transformation scheme are incorporated to deal with constraints of different nature. An adaptive control structure is introduced to deal with system parameter uncertainties and external disturbances. We show that for the LOS distance and angle tracking errors, exponential convergence into small neighbourhoods of equilibrium can be guaranteed, with the convergence rate depending on the control input and adaptive gains. In the end, a simulation example and an experimental study further demonstrate the efficacy of the proposed algorithm.

Layout Design of Strapdown Array Seeker and Extraction Method of Guidance Information

This paper proposed a multi-view surface array to enlarge the field-of-view (FOV) from 45° × 45° to 72° × 75° and improve the estimation precision of guidance information. First, based on circular and rectangular FOV sensors, the superposition characteristics of FOV in the +-shaped layout and the X-shaped layout were explored and analyzed. Secondly, normalization processing was applied to obtain the equivalent measurement value of the central sensor and the corresponding error distribution. Based on such measurement value and error distribution, the filtering model could be constructed, which could effectively solve the problem of observation number variation caused by multiple sensors. Thirdly, a multivariate iterated extended Kalman filter (MIEKF) was proposed to make full use of multiple measurements. By iterating multiple unequal observations and making full use of the known error distribution information, the noise of filtered data was found to be effectively reduced and the estimation precision of guidance information was improved. Finally, based on a 6-DOF trajectory simulation, the correctness and effectiveness of the proposed method were verified. Simulation results show that MIEKF can improve the estimation accuracy of the line-of-sight (LOS) angle by at least 30% and the estimation accuracy of the LOS angle rate by nearly 80% compared with EKF.

Neural network-based prescribed performance adaptive finite-time formation control of multiple underactuated surface vessels with collision avoidance

In this paper, a leader-follower formation control scheme of multiple underactuated surface vessels (USVs) is proposed for trajectory tracking, which not only solves the line of sight (LOS) and angle tracking errors within the prescribed performance, but also avoids collisions and maintains the communication connection distance. To achieve the prescribed performance and converge the tracking errors in finite time, a tan-type barrier Lyapunov function (TBLF) is introduced into the designed control strategy. In the process of formation control design, the measured values of the LOS range and angle are available, and the velocity of the leader is estimated using a high-gain observer. Next, a novel self-structuring neural network (SNN) is proposed to estimate the uncertain dynamics induced by the model uncertainties and environmental disturbances, and the computation amount is reduced by optimizing the number of neurons. Combining coordinate transformation and dynamic surface control (DSC), an adaptive NN controller with prescribed performance is proposed. The Lyapunov analysis shows that, although uncertain dynamics exist, the tracking errors can converge to a small region in finite time while achieving the prescribed performance, avoiding collisions, and maintaining the communication distance. In the closed-loop system, all signals are practical finite-time stable (PFS). Finally, the effectiveness of the proposed scheme is illustrated through a numerical simulation.

Guidance law based on deep Q network algorithm

In this paper, an intelligent guidance law based on Deep Q Network (DQN) algorithm is proposed, for enabling the missile to intercept different maneuvering targets following the idea of the parallel-approach method. In specific, we propose the inverse ratio of the absolute value of line-of-sight (LOS) angle rate as the shaping reward function which guarantees the successful finding of the control strategy and the speeding up of the training process of the reinforcement learning (RL) model. Furthermore, to avoid rapid chattering caused by directly choosing missile acceleration as an action, we introduce the change rate of the acceleration as the action in the DQN algorithm and integrate it to obtain the acceleration command. Therefore, in our algorithm only LOS angle, LOS angle rate, and missile overload information are used in the established RL model to generate the guidance command, which is easy to implement. The simulation results and comparative experiments demonstrate that the proposed RL based guidance method achieves better guidance accuracy and higher success rate. The great performance of the proposed method suggests that the RL based guidance method is promising for the maneuvering target, and deserve further investigations in future.

Gravity-compensated guidance for impact-angle interception of a moving target

This paper proposes an impact-angle control guidance (IACG) law for anti-ship and anti-tank missiles in which the command converges to zero at the point of interception, even in a gravity field. The desired line-of-sight (LoS) angle that satisfies the terminal impact-angle and acceleration constraints is first defined. The guidance command is then derived as a solution that realizes the convergence of the actual LoS angle to the desired LoS angle during the terminal stage of homing in on a target. Gravity is considered when designing the guidance law such that the desired terminal constraints are accurately satisfied, even under realistic pitch-axis engagement. We also investigated whether the proposed law is optimal for minimizing the total expense of maneuvering while performing IACG in a gravity field. The results of the numerical simulations included in this study demonstrate that the proposed guidance law achieves accurate impact-angle interception with the command converging to zero at the end of homing.

Fixed-Time Terminal Angle-Constrained Cooperative Guidance Law Against Maneuvering Target

In this article, fixed-time cooperative guidance laws are designed for multiple missiles to simultaneously attack a maneuvering target at desired terminal angles. The 3-D guidance commands consist of tangential acceleration along line-of-sight (LOS) direction to achieve a salvo attack and normal acceleration perpendicular to the LOS direction to realize a terminal angle-constrained interception. First, the tangential acceleration is derived from a distributed cooperative protocol to guarantee the fixed-time consensus of impact times for multiple missiles. Second, based on the integral sliding manifold and fixed-time reaching law, the normal acceleration is developed for each missile to converge the LOS angle to the desired value within a fixed time. In particular, the unknown target acceleration components are estimated by fixed-time observers and compensated in the guidance commands. The fixed-time stability of the proposed cooperative guidance law is rigorously proved and the explicit estimate for the convergence time is theoretically provided. Then, the proposed methods are utilized to realize the cooperative mission in the planar guidance scenario. Finally, the effectiveness and advantages of the proposed cooperative guidance laws are demonstrated through numerical simulations with comparative studies.

A trajectory shaping guidance law with field-of-view angle constraint and terminal limits

In this paper, a trajectory shaping guidance law, which considers constraints of field-of-view (FOV) angle, impact angle, and terminal lateral acceleration, is proposed for a constant speed missile against a stationary target. First, to decouple constraints of the FOV angle and the terminal lateral acceleration, the third-order polynomial with respect to the line-of-sight (LOS) angle is introduced. Based on an analysis of the relationship between the looking angle and the guidance coefficient, the boundary of the coefficient that satisfies the FOV constraint is obtained. The terminal guidance law coefficient is used to guarantee the convergence of the terminal conditions. Furthermore, the proposed law can be implemented under bearings-only information, as the guidance command does not involve the relative range and the LOS angle rate. Finally, numerical simulations are performed based on a kinematic vehicle model to verify the effectiveness of the guidance law. Overall, the work offers an easily implementable guidance law with closed-form guidance gains, which is suitable for engineering applications.

Three-dimensional prescribed performance cooperative guidance law with spatial constraint for intercepting manoeuvring targets

This paper proposes three-dimensional cooperative guidance laws with prescribed performance. To avoid degradation in performance due to error in the estimation of the time-to-go, the relative distance between the missiles and the target is chosen as a coordination variable, and a fixed-time cooperative guidance law along the direction of the line-of-sight (LOS) is proposed. The guidance laws with prescribed performance for the elevation and direction of the azimuth of the LOS are then developed by combining the LOS angle tracking error with a performance constraint function to formulate a transformed error function. The problem of prescribed performance control is transformed into that of the boundedness of the transformed error function. A fixed-time convergence disturbance observer is designed to discuss the problem whereby information on aggregate uncertainty, including on the target, is unavailable. The results of simulations show that the proposed guidance laws are effective.

Finite-Time Distributed Leaderless Cooperative Guidance Law for Maneuvering Targets under Directed Topology without Numerical Singularities

A new distributed leaderless cooperative guidance algorithm is suggested for multi-directional saturation strikes against maneuvering targets. First, the finite-time disturbance observer (FDO) is used to estimate the target’s unknown maneuvers. After that, the guidance laws along the line-of-sight (LOS) direction and the LOS normal direction are designed separately based on the finite-time consensus theory. The proposed guidance law could satisfy both impact time and LOS angle constraints. Numerical singularities due to feedback linearization are avoided by nonlinear stability analysis. Finally, the effectiveness of the proposed cooperative guidance law is proved by numerical simulation arithmetic.

Prescribed-time cooperative guidance law against maneuvering target based on leader-following strategy

This paper proposes a prescribed-time cooperative guidance law (PTCGL) against maneuvering target with variable line-of-sight (LOS) angle constraint for leader-following missiles, where the convergence times of the state errors can be arbitrarily set. The leader missile against the maneuvering target is provided as the modified proportional navigation (MPN) guidance law. The proposed PTCGL for follower missiles consist of two parts, in LOS direction, the range-to-go (Rgo) is selected as a co-variable, avoiding the estimation of time-to-go (Tgo), and a novel second-order nonlinear consensus protocol is developed to design the PTCGL; in normal LOS direction, considering the variable LOS angle constraint, the cooperative guidance law is designed with the proposed prescribed-time sliding model control (PTSMC) method. Besides, the prescribed-time convergence of Rgo and LOS errors are proved. Finally, the effectiveness and superiority of the proposed PTCGL with leader-following strategy is illustrated by numerical simulation results.

Finite Time Convergent Cooperative Guidance Law for Multiple Flight Vehicles Considering Detection Efficiency

Aiming at the problem of cooperative interception of maneuvering target, a cooperative guidance of multiple flight vehicles considering detection efficiency was designed based on the multi-agent finite time consensus theory. Considering the first-order dynamic of the flight vehicle, the guidance law was designed according to the relative motion equations and the model of cooperative detection, which can improve the estimation accuracy of the relative distance using the terminal LOS (Line-of-sight) angle and guarantee simultaneously strike the target in a finite time. Numerical simulation results show that in the case of different maneuvers of an evader, each flight vehicle can hit the target at the same time with a designed terminal LOS angle, and the detection accuracy of the relative distance was continuously improved during the terminal guidance.

Prescribed-time cooperative guidance law against manoeuvring target with input saturation

This paper proposes a novel prescribed-time cooperative guidance law (PTCGL) for multiple missiles cooperatively attacking a manoeuvring target. Guidance models in two directions are used and the acceleration saturations are also considered in both two directions. In line-of-sight (LOS) direction, by applying prescribed-time multi-agent consensus theory, the problem of the times-to-go () of multiple missiles converging to a same value is transformed into a stabilisation problem. Then the cooperative guidance law in LOS direction is designed based on the prescribed time integral sliding mode surface (PTISMS) and a new variable coefficient exponential reaching law, and a first-order auxiliary system is introduced to deal with the input saturation problem; based on a prescribed time linear sliding surface (PTLSMS), the cooperative guidance law in normal LOS direction is designed to ensure the LOS angle and LOS angle rate convergence within a prescribed time, and a second-order auxiliary system is designed to deal with the input saturation problem. Furthermore, the prescribed time convergence of the PTCGL is proved with the Lyapunov stability theory. Finally, numerical simulations demonstrate the effectiveness and advantages of the proposed PTCGL.

Impact time and angle constrained guidance via range‐based line‐of‐sight shaping

AbstractIn this article, impact time and angle constrained guidance law is proposed using a range‐based line‐of‐sight (LOS) shaping strategy. The relative motion of missile and target is described in a polar coordinate, where the LOS angle can be shaped as a polynomial function of range‐to‐go. The order of the polynomial function is selected according to the number of constraints. Coefficients of the polynomial function are determined by the boundary conditions and solved through a simple integral equation, which facilitates the onboard implementation. Guidance command is designed in a state feedback form to track the shaped trajectory. The proposed guidance law shows some advantages over several similar polynomial shaping based guidance laws. Multiple simulation studies demonstrate the effectiveness of the proposed guidance law.

Cooperative guidance law for intercepting a hypersonic target with impact angle constraint

AbstractThe cooperative guidance problem of multiple inferior missiles intercepting a hypersonic target with the specific impact angle constraint in the two-dimensional plane is addressed in this paper, taking into consideration variations in a missile’s speed. The guidance law is designed with two subsystems: the direction of line-of-sight (LOS) and the direction of normal to LOS. In the direction of LOS, by applying the algebraic graph theory and the consensus theory, the guidance command is designed to make the system convergent in a finite time to satisfy the goal of cooperative interception. In the direction of normal to LOS, the impact angle is constrained to transform into the LOS angle at the time of interception. In view of the difficulty of measuring unknown target acceleration information in real scenarios, the guidance command is designed by utilising a super-twisting algorithm based on a nonsingular fast-terminal sliding mode (NFTSM) surface. Numerical simulation results manifest that the proposed guidance law performs efficiently and the guidance commands are free of chattering. In addition, the overall performance of this guidance law is assessed with Monte Carlo runs in the presence of measurement errors. The simulation results demonstrate that the robustness can be guaranteed, and that overall efficiency and accuracy in intercepting the hypersonic target are achieved.

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.

Adaptive Fast Fixed-Time Three-Dimensional Guidance Law With Acceleration Saturation Constraints

This paper investigates continuous anti-saturation three-dimensional guidance law against maneuvering target at the desired line-of-sight (LOS) angles. Firstly, in the light of fixed-time stability, fast nonsingular terminal sliding mode is designed without the limitation of odd-ratio fractional order. Then, with the limits of lateral acceleration saturation, continuous guidance law is proposed to guarantee that desired LOS angles are reached and maintained after the specified time, while adaptive law is implemented to estimate the information on maneuver accelerations of the attacking missile. Finally, numerical simulations are presented to validate the effectiveness and rationality of the designed scheme.

Fixed-time cooperative guidance for multiple missiles with impact angle constraint

For the guidance problem of multiple missiles attacking a maneuvering target simultaneously in plane, a novel fixed-time distributed cooperative guidance law with impact angle constraint is designed in this paper. The design process of distributed cooperative guidance law can be roughly divided into two parts. First, based on the nonsingular terminal sliding mode control, a cooperative guidance law on the line-of-sight (LOS) direction is developed, which can guarantee that all missiles hit the maneuvering target simultaneously. Second, another guidance law in normal direction of the LOS direction is designed to achieve the fixed-time convergence of LOS angular rate and LOS angle. Finally, numerical simulations verify the effectiveness of the proposed cooperative guidance law for different engagement scenarios.

Line-of-sight rate construction for a roll-pitch gimbal via a virtual pitch-yaw gimbal

In this paper, a method to construct the line of sight rate of a target with a roll-pitch gimbal and tracker is described. Construction of line-of-sight rate is performed via utilizing a virtual pitch-yaw gimbal. Kinematics of both the roll-pitch and pitch-yaw gimbals are described. A dynamical model for the roll-pitch gimbal is developed, and a nested control structure is designed to control the angular rates and line of sight angles. A kinematic model of the tracker is developed and a tracker controller is designed to keep the target in the field of view. Conversion equations between roll-pitch and pitch-yaw gimbal configurations are provided. Finally, constructed line of sight rates are compared to true line of sight rates via simulations. Obtained results indicate that the constructed line of sight rates pertaining to a target satisfactorily converge to the actual line of sight rates.