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This paper provides a unified formulation of optimal guidance-to-collision law for a target with an arbitrary acceleration or deceleration. The collision course for general target acceleration or deceleration is first determined from the engagement geometry in conjunction with the nonlinear engagement kinematics in the proposed approach. The heading error de_ned in the collision course is then adopted as a variable to be nullified for accomplishing the intercept condition. The proposed guidance law is derived based on the heading error dynamics and the optimal error dynamics to ensure optimality and finite-time convergence. As illustrative examples, the proposed guidance command for a constant target acceleration and a target deceleration in the form of a quadratic function of speed are provided. Additionally, the time-to-go prediction method is suggested for implementing the proposed method. The characteristics of the proposed guidance command are analytically investigated to provide insight into the proposed method. The key benefits of the proposed method lie in not producing unnecessary guidance commands near a target compared to other methods and ensuring optimality in guidance command even in the nonlinear engagement kinematics. Finally, numerical simulations are performed to validate the proposed method and to show our findings.

This paper addresses the problem of energy-optimal waypoint-following guidance for an Unmanned Aerial Vehicle with the consideration of a general autopilot dynamics model. The proposed guidance law is derived as a solution of a linear quadratic optimal control problem in conjunction with a linearized kinematics model. The algorithm developed integrates path planning and following into a single step and is able to be applied to a general waypoint-following mission. Theoretical analysis reveals that previously suggested optimal point-to-point guidance laws are special cases of the proposed approach. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations.

This paper aims to reveal the hidden physical meaning or the working principle of the three-loop autopilot. First, the minimal control structure that ensures the desired dynamic characteristics is analyzed. The results show that the three-loop autopilot has a redundant feedback loop from the minimal control structure standpoint. Based on this observation, its physical meaning is interpreted by utilizing the closed-loop tracking error dynamics in the presence of aerodynamic uncertainties. It turns out that the three-loop autopilot has the minimal control structure with an additional command which is based on the instantaneous direct model reference adaptive control. A clear mechanism of how the aerodynamic uncertainties are compensated is provided in the three-loop autopilot. Finally, numerical simulations are performed to validate our findings. The analysis results in this paper show the beauty of the three-loop autopilot: it can be considered as the most concise form to achieve desired dynamic characteristics and counteract model uncertainties. The potential importance of the results obtained is that they allow us to properly design the three-loop autopilot by reflecting its physical meaning and have potential directions to improve the performance of the three-loop autopilot as well as the adaptive control.

This paper aims to examine the potential of using the emerging deep reinforcement learning techniques in missile guidance applications. To this end, a Markovian decision process that enables the application of reinforcement learning theory to solve the guidance problem is formulated. A heuristic way is used to shape a proper reward function that has tradeoff between guidance accuracy, energy consumption, and interception time. The state-of-the-art deep deterministic policy gradient algorithm is used to learn an action policy that maps the observed engagements states to a guidance command. Extensive empirical numerical simulations are performed to validate the proposed computational guidance algorithm.

This paper addresses the problem of minimum-effortwaypoint-following guidance with/without arrival angle constraints of an Unmanned Aerial Vehicle. By utilizing a linearized kinematics model, the proposed guidance laws are derived as the solutions of a linear quadratic optimal control problem with an arbitrary number of terminal boundary constraints. Theoretical analysis reveals that both optimal proportional navigation guidance and trajectory shaping guidance are special cases of the proposed guidance laws. The key feature of the proposed algorithms lies in their generic property. For this reason, the guidance laws developed can be applied to general waypoint-following missions with an arbitrary number of waypoints and an arbitrary number of arrival angle constraints. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations.

This paper considers the problem of twodimensional (2D) constrained trajectory optimisation of a pointmass aerial robot for constant-manoeuvring target localisation using bearing-only measurement. A performance metric that can be utilised in trajectory optimisation to maximise target observability is proposed first based on geometric conditions. One-step optimal manoeuvre that maximises the observability criterion is then derived analytically for moving targets. The heading angle constraint is also incorporated in the proposed optimal manoeuvre derivation to support practical application. Numerical simulations with some comparisons are presented to validate the analytical findings.

This paper addresses the problem of maneuver recognition and behavior anomaly detection for generic targets by means of pattern matching techniques. The problem analysis is performed making specific reference to moving vehicles in a multi-lane road scenario, but the proposed technique can be easily extended to significantly different monitoring contexts. The potential extensions include, but are not limited to, public surveillance in train station or airport, road incidents and relative precursors detection, and vehicle trajectories monitoring. The overall proposed solution consists of a trajectory analysis tool and a string-matching method. This allows the integration of two different approaches, to detect both a priori defined patterns of interest and generic maneuver/behavior standing out from those regularly exhibited. The proposed string matching algorithm is newly developed in this paper, based on Regular Expressions. For generating reference patterns, a technique for the automatic definition of a dictionary of regular expressions matching the commonly observed target maneuvers is developed. The advantages of the proposed approach are extensively analyzed and tested by means of numerical simulations and experiments.

In this study, the performance characteristics of a rotor used for multirotor are investigated through wind-tunnel tests. The rotor is tested at several flow speeds and angles to approximate the actual flying condition. A high resolution six-axis force/moment sensor is utilized to record the forces and moments in three directions. Wind tunnel results show the changes in the rotor performance with the variation in flying speed, flying angle, and rotor revolution. The results also demonstrate that the aerodynamic characteristics of the rotor quite differ from those in the hovering state when the vehicle is flying forward. Finally, aerodynamic models of the rotor in forward state are provided.

This chapter proposes a new optimal guidance law to enhance target observability for passive guidance with bearing-only measurement. A performance index that considers terminal miss distance, control effort and target observability criterion in an integrated manner is proposed first. The proposed guidance law is then derived analytically by solving the optimization problem formulated. Under certain conditions, it is proved that the guidance law developed gradually switches from retro PNG to classical PNG as time goes. The closed-form solutions of ZEM and guidance command are also derived to provide better insights of the proposed guidance law. Nonlinear numerical simulations are conducted to support the analytical findings.

This chapter proposes a new optimal guidance law based on PI concept to reduce the sensitivity to unknown target maneuvers. By augmenting the integral ZEM as a new system state, a linear quadratic optimization problem is formulated and then the proposed guidance law is analytically derived through optimal control theory. The closed-form solution of the proposed guidance law is presented to provide better insight of its properties. Additionally, the working principle of the integral command is investigated to show why the proposed guidance law can be utilized to reduce the sensitivity to unknown target maneuvers. The analytical results reveal that the proposed optimal guidance law is exactly the same as an instantaneous direct model reference adaptive guidance law with a specified reference model. The potential significance of the obtained results is that it can provide a point of connection between PI guidance laws and adaptive guidance laws. Therefore, it allows us to have better understanding of the physical meaning of both guidance laws and provides the possibility in designing a new guidance law that takes advantages of both approaches. Finally, the performance of the guidance law developed is demonstrated by nonlinear numerical simulations with extensive comparisons.

This chapter addresses the problem of energy-optimal waypoint-following guidance for an UAV with the consideration of arbitrary number of obstacles. The proposed guidance law is derived as a solution of a linear quadratic optimal control problem in conjunction with convex parameter optimization. The algorithm developed integrates path following and obstacle avoidance into a single step and is able to be applied to a general waypoint-following mission. Several particular cases of the proposed guidance law are presented to provide better insights of the proposed algorithm. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations.

This chapter develops a new optimal gravity-turn-assisted intercept angle guidance law for an exo-atmospheric interceptor. The analytical guidance command is derived as a solution of a finite-time optimal regulation problem by using the Lagrange multiplier approach. The convergence of the instantaneous ZEM and intercept angle error is theoretically analyzed based on the instantaneous linear time-invariant system concept. We also reveal that existing optimal impact angle constrained guidance laws are the special cases of the proposed formulation. Numerical simulations with some comparisons clearly demonstrate the effectiveness of the proposed guidance law.

This chapter proposes a new trajectory shaping guidance law for impact time control and impact angle control with seeker’s field-of-view (FOV) limit. The proposed guidance law is derived by using the concept of biased PNG (BPNG). The guidance law developed leverages a nonlinear function to ensure the boundedness of velocity lead angle to cater for seeker’s FOV constraint. The finite-time convergence of the impact time error and impact angle error is theoretically analyzed. By investigating the optimality of the biased command, the physical meaning of the proposed trajectory shaping guidance law is revealed to support practical applications. Numerical simulations clearly demonstrate the effectiveness of the proposed formulation.

This paper proposes a new optimal guidance law that directly uses (instead of compensating for) gravity for accelerating missiles. The desired collision triangle that considers both gravity and the vehicle’s axial acceleration is analytically derived based on geometric conditions. The concept of instantaneous zero-effort-miss is introduced to allow for analytical guidance command derivation. By formulating a finite time instantaneous zero-effort-miss regulation problem, the proposed optimal guidance law is derived through Schwarz’s inequality approach. The relationships of the proposed formulation with conventional proportional navigation guidance and guidance-to-collision are analyzed, and the results show that the proposed guidance law encompasses previously suggested approaches. The significant contribution of the proposed guidance law lies in that it ensures zero final guidance command and enables energy saving with the aid of using gravity turn. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed approach.

This paper proposes a new composite guidance law to intercept manoeuvring targets without line-of-sight (LOS) angular rate information in the presence of autopilot lag. The presented formulation is...

This paper proposes a new optimal guidance law to enhance target observability for passive guidance with bearing-only measurement. A performance index that considers terminal miss distance, control effort and target observability criterion in an integrated manner is proposed first. The proposed guidance law is then derived analytically by solving the optimization problem formulated. Under certain conditions, it is proved that the guidance law developed gradually switches from retro proportional navigation guidance to classical proportional navigation guidance as time goes. The closed-form solutions of zero-effort-miss and guidance command are also derived to provide better insights of the proposed guidance law. Nonlinear numerical simulations are conducted to support the analytical findings.

A new composite guidance law for intercepting manoeuvring targets with desired terminal line-of-sight (LOS) angle constraint is proposed in this paper. The presented guidance law is derived through generalized model predictive control (GMPC) augmented by a target manoeuvre estimator. More specifically, the target manoeuvre estimator is used to estimate and compensate for the unknown target manoeuvre online while the GMPC is used to obtain optimal LOS angle tracking performance. Stability analysis shows that the LOS angle tracking error and the LOS angular rate can converge to a sufficiently small region around zero asymptotically. The effectiveness of the proposed guidance law is validated by applying it to a surface-to-air missile for intercepting a head-on manoeuvring target under different scenarios.

This paper investigates the problem of coning motion stability of spinning missiles equipped with strapdown seekers. During model derivation, it is found that the scaling factor error between the strapdown seeker and the onboard gyro introduces an undesired parasitic loop in the guidance system and, therefore, results in stability issues. Through stability analysis, a sufficient and necessary condition for the stability of spinning missiles with strapdown seekers is proposed analytically. Theoretical and numerical results reveal that the scaling factor error, spinning rate and navigation ratio play important roles in stable regions of the guidance system. Consequently, autopilot gains must be checked carefully to satisfy the stability conditions.

This article investigates the problem of designing robust guidance laws for intercepting maneuvering targets with desired terminal line-of-sight angle constraint. Based on generalized model predictive control for the nominal system, the discontinuous and continuous integral sliding mode control laws are, respectively, developed. Stability analysis shows that the proposed guidance law can ensure the optimal tracking characteristic of generalized model predictive control algorithm and the line-of-sight angle tracking error as well as the line-of-sight angular rate can converge to zero asymptotically. The effectiveness of the proposed guidance law is validated by applying it to a surface-to-air missile for intercepting a head-on maneuvering target under different scenarios.

This paper aims to develop a new finite‐time convergent guidance law for intercepting maneuvering targets accounting for second‐order autopilot lag. The guidance law is applied to guarantee that the line of sight (LOS) angular rate converges to zero in finite time and results in a direct interception. The effect of autopilot dynamics can be compensated based on the finite‐time backstepping control method. The time derivative of the virtual input is avoided, taking advantage of integral‐type Lyapunov functions. A finite‐time disturbance observer (FTDOB) is used to estimate the lumped uncertainties and high‐order derivatives to improve the robustness and accuracy of the guidance system. Finite‐time stability for the closed‐loop guidance system is analyzed using the Lyapunov function. Simulation results and comparisons are presented to illustrate the effectiveness of the guidance strategy.

This paper presents a robust observer-based finite-time convergent guidance law to intercept maneuvering targets. To avoid the undesired chattering phenomenon existing in classical sliding mode control, the adaptive super-twisting algorithm is first introduced to design a robust guidance law to drive the line-of-sight (LOS) angular rates to a small region around the origin in finite time. The important feature of the proposed adaptation algorithm is in nonoverestimating the values of the guidance law gains, which is achieved by using a ‘detector’ scheme in the updating law. Moreover, with the proposed adaptive law, the presented guidance law requires no information on target maneuvers. Since the LOS angular rate is difficult for a pursuer to measure accurately for some seekers, a novel adaptive super-twisting observer is proposed to estimate it and a composite guidance law is then synthesized. Detailed finite-time stability analysis and comparison results with other guidance laws demonstrate the superiority of the proposed formulation.

In this paper, a new continuous impact angle constraint guidance law in the presence of actuator fault is presented based on sliding mode control theory. The robustness and finite-time convergence of the basic guidance law is established using Lyapunov stability theory. For actuator compensation, an additional term is augmented in the original guidance law to guarantee finite-time stability of the closed-loop guidance system. Theoretical analysis and simulation results demonstrate the effectiveness of the proposed method.

This paper has proposed two continuous composite finite-time convergent guidance laws to intercept maneuvering targets in the presence of autopilot lag: one is for hit-to-kill and the other is for zeroing the line-of-sight (LOS) angular rate. More specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty online while the finite-time control technique is used to fulfill the design goal in finite time. The key feature in derivation of the proposed guidance law is that two integral-type Lyapunov functions are used to avoid analytic differentiation of virtual control law encountered with traditional backstepping. The finite-time stability of the closed-loop nonlinear observer-controller system is established using finite-time bounded (FTB) function and Lyapunov function methods. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.

This paper presents a new longitudinal autopilot to address the finite-time tracking problem for uncertain agile missiles. The proposed autopilot is essentially a composite control scheme, which is obtained through the finite-time control methodology and the nonlinear disturbance observer NDOB approach. The key idea in this scheme is that the NDOB is adopted to estimate the aerodynamic uncertainties and external disturbances in an integrated manner. With the aid of the finite-time bounded function and the Lyapunov function method, the finite-time stability of the closed-loop system is established, which shows that the angle-of-attack response will converge to the external command signal in finite time. Numerical simulation results are presented to demonstrate the superiority of the proposed scheme.

In this paper, a robust continuous guidance law with terminal angle constraint for intercepting maneuvering targets in the presence of autopilot lag is proposed and its finite-time stability is proved. First, assuming that the missile autopilot is sufficiently fast, a composite fast nonsingular terminal sliding mode guidance (CFNTSMG) law is presented. The proposed guidance law is obtained through a combination of fast nonsingular terminal sliding mode control theory and generalized disturbance observer (GDOB). The presented guidance law requires no priori information on target maneuver, which is estimated and compensated online by GDOB. Moreover, no discontinuous term exists in CFNTSMG law and therefore chattering is eliminated effectively. Next, viewing the missile autopilot as an uncertain second-order system, an integrated guidance and control dynamics is formulated and the systematic step-by-step backstepping technique is used to derive a new robust guidance law, which not only holds the advantages of CFNTSMG law, but also is insensitive to autopilot lag. At each backstepping step, novel continuous virtual/real control laws using finite-time control approach are designed and tracking differentiator is used to overcome the ‘explosion of complexity’ problem encountered with traditional backstepping method. Theoretical analysis and numerical simulations demonstrate the effectiveness of the proposed method.

This paper has proposed a new composite robust guidance law to intercept maneuvering targets without line-of-sight (LOS) angular rate information. The presented guidance law is constructed through a combination of second-order sliding mode, higher-order sliding mode (HOSM) differentiator, and finite-time convergent disturbance observer (FTDOB). More specifically, the HOSM differentiator is used to extract the LOS angular rate information from LOS angle measurement, while the FTDOB is used to estimate and compensate the unknown target maneuvers. The finite-time stability of the closed-loop guidance system is established using finite-time bounded function and Lyapunov function methods. Next, the proposed guidance law is applied to three-dimensional homing engagement, where the FTDOB is used to estimate the target maneuver as well as the cross-coupling terms between the elevation and the azimuth motions. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.

In this paper, a new continuous robust impact angle constraint guidance law with finite-time convergence is proposed for intercepting maneuvering targets with unknown acceleration bounds. The presented guidance law is based on nonsingular terminal sliding mode (NTSM), smooth second-order sliding mode and finite-time convergence disturbance observer (FTDOB). In light of the introduced FTDOB, which is used to estimate and compensate the lumped uncertainty in missile guidance system, no prior knowledge of target maneuver is required. Thus, the proposed guidance law is capable of real implementation. Differently from the widely used boundary layer technique, chattering is eliminated effectively under the proposed guidance law without any performance sacrifice. Using finite-time bounded function approach and Lyapunov stability criteria, rigorous finite-time stability proof in both reaching and sliding phases is given. Theoretical analysis and numerical simulations show that the proposed guidance law can achieve more accurate interception with a wide range of intercept angles and superior overall performance than traditional NTSM algorithm.

This paper presents a robust impact angle guidance law for maneuvering target interception with autopilot dynamics compensation based on a systematic backstepping control technique. Since t...

Summary This paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher-order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line-of-sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher-order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line-of-sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, a new adaptive nonsingular terminal sliding mode control theory based impact angle guidance law for intercepting maneuvering targets was documented. In the design procedure, a new adaptive law for target acceleration bound estimation was presented, which allowed the proposed guidance law to be used without the requirement of the information on the target maneuvering profiles. With the aid of Lyapunov stability criteria, the finite-time convergent characteristics of the line-of-sight angle and its derivative were proven in theory. Numerical simulations were also performed under various conditions to demonstrate the effectiveness of the proposed guidance law.

In this paper, a new robust guidance law is designed to satisfy both impact angle constraint and the seeker’s field-of-view limit for missiles with strapdown seekers. Since the impact angle guidance law needs a highly curved trajectory and most strapdown seekers have a very narrow field-of-view, maintaining the seeker’s lock-on is the key issue for these missiles. To address this problem, a switching logic is adopted, which adds an additional term in the original guidance law when the look angle exceeds the pre-designed boundary value to maintain the seeker’s lock-on. An impact angle guidance law is designed based on terminal sliding mode control theory and the finite time convergence characteristic of the line-of-sight angle, as well as its derivative is proved through the Lyapunov method. Numerical simulations are performed to validate the effectiveness of the proposed guidance law. Some intuitive tunings of the design parameters are also offered in the simulation results to achieve large impact angles.

In this paper, two composite inverse optimal guidance laws against maneuvering targets have been proposed and the stability analysis is also presented. The first guidance law is constructed through a combination of Sontag’s formula and first order sliding mode control. In order to mitigating the undesired chattering caused by the discontinuous sign function, another robust guidance law is then synthesized using adaptive super-twisting algorithm. By virtue of the proposed adaptive law, the second guidance law only requires the time derivatives of the lumped uncertainties are bounded, but their upper bounds can be unknown. An important feature of the proposed adaptive algorithm is in non-overestimating the values of the control gains, which is achieved by introducing a ‘detector’ term in the updating law. Finally, some numerical simulations are carried out to demonstrate the effectiveness of the proposed formulations.

This paper considers the application of compound control method to high-performance autopilot design for aerodynamically controlled agile missiles. The control objective in this paper is to track a reference angle of attack command signal in the presence of external disturbance and aerodynamic coefficient uncertainty with desired performance. The external disturbances and the aerodynamic uncertain terms are first lumped together as the lumped uncertainties, which can be estimated accurately by the introduced extended state observer (ESO). Combining the sliding mode control (SMC) and backstepping techniques, a robust nonsmooth (but continuous) compound control law is developed for angle of attack tracking. With the aid of Lyapunov stability criteria, it is proven that the angle of attack tracking error will converge into a small neighborhood around the origin in finite time. Theoretical analysis and simulation results demonstrate the robustness and effectiveness of the proposed composite method.