Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints.

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the 'explosion of complexity' problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

Integration of path planning and following control for the stratospheric airship with forecasted wind field data.

The absence of real-time airspeed sensors, which was more often ignored in previous studies, and low dynamic characteristics render stratospheric airship control challenging. This study creatively overcomes the aforementioned problems in an integrated path planning and following control scheme using forecasted wind field data. Herein, an efficient and practicable path planning algorithm is designed. Further, a smooth vector field guidance law is proposed for solving the problem of complex path following. Subsequently, an event-triggered neural network-based adaptive tracking controller is designed, considering the wind forecast error influence. Finally, these three parts are organically integrated to achieve autonomous flight. The stability of the closed-loop system and the exclusion of Zeno behavior are rigorously proved. The simulation results reveal that the convergence rate is 63.8% improved, essentially exhibiting better optimization, the tracking errors are eliminated within 80 s, and 99.4% control input updating times are saved.

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

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

Obstacle avoidance in aerial pursuit.

Pursuing prey through clutter is a complex and risky activity requiring integration of guidance subsystems for obstacle avoidance and target pursuit. The unobstructed pursuit trajectories of Harris' hawks Parabuteo unicinctus are well modeled by a mixed guidance law feeding back target deviation angle and line-of-sight rate. Here we ask how their pursuit behavior is modified in response to obstacles, using high-speed motion capture to reconstruct flight trajectories recorded during obstructed pursuit of maneuvering targets. We find that Harris' hawks use the same mixed guidance law during obstructed pursuit but appear to superpose a discrete bias command that resets their flight direction to aim at a clearance of approximately one wing length from an upcoming obstacle as they reach some threshold distance from it. Combining a feedback command in response to target motion with a feedforward command in response to upcoming obstacles provides an effective means of prioritizing obstacle avoidance while remaining locked-on to a target. We therefore anticipate that a similar mechanism may be used in terrestrial and aquatic pursuit. The same biased guidance law could also be used for obstacle avoidance in drones designed to intercept other drones in clutter, or to navigate between fixed waypoints in urban environments.

Visual versus visual-inertial guidance in hawks pursuing terrestrial targets.

The aerial interception behaviour of falcons is well modelled by a guidance law called proportional navigation, which commands steering at a rate proportional to the angular rate of the line-of-sight from predator to prey. Because the line-of-sight rate is defined in an inertial frame of reference, proportional navigation must be implemented using visual-inertial sensor fusion. By contrast, the aerial pursuit behaviour of hawks chasing terrestrial targets is better modelled by a mixed guidance law combining information on the line-of-sight rate with information on the deviation angle between the attacker's velocity and the line-of-sight. Here we ask whether this behaviour may be controlled using visual information alone. We use high-speed motion capture to record n = 228 flights from N = 4 Harris' hawks Parabuteo unicinctus, and show that proportional navigation and mixed guidance both model their trajectories well. The mixed guidance law also models the data closely when visual-inertial information on the line-of-sight rate is replaced by visual information on the motion of the target relative to its background. Although the visual-inertial form of the mixed guidance law provides the closest fit, all three guidance laws provide an adequate phenomenological model of the behavioural data, whilst making different predictions on the physiological pathways involved.

Highly Robust Adaptive Sliding Mode Trajectory Tracking Control of Autonomous Vehicles.

Autonomous driving technology has not yet been widely adopted, in part due to the challenge of achieving high-accuracy trajectory tracking in complex and hazardous driving scenarios. To this end, we proposed an adaptive sliding mode controller optimized by an improved particle swarm optimization (PSO) algorithm. Based on the improved PSO, we also proposed an enhanced grey wolf optimization (GWO) algorithm to optimize the controller. Taking the expected trajectory and vehicle speed as inputs, the proposed control scheme calculates the tracking error based on an expanded vector field guidance law and obtains the control values, including the vehicle's orientation angle and velocity on the basis of sliding mode control (SMC). To improve PSO, we proposed a three-stage update function for the inertial weight and a dynamic update law for the learning rates to avoid the local optimum dilemma. For the improvement in GWO, we were inspired by PSO and added speed and memory mechanisms to the GWO algorithm. Using the improved optimization algorithm, the control performance was successfully optimized. Moreover, Lyapunov's approach is adopted to prove the stability of the proposed control schemes. Finally, the simulation shows that the proposed control scheme is able to provide more precise response, faster convergence, and better robustness in comparison with the other widely used controllers.

Gap selection and steering during obstacle avoidance in pigeons.

The ability of birds to fly through cluttered environments has inspired biologists interested in understanding its underlying mechanisms, and engineers interested in applying its underpinning principles. To analyse this problem empirically, we break it down into two distinct, but related, questions: How do birds select which gaps to aim for? And how do they steer through them? We answered these questions using a combined experimental and modelling approach, in which we released pigeons (Columbia livia domestica) inside a large hall with an open exit separated from the release point by a curtain creating two vertical gaps - one of which was obstructed by an obstacle. We tracked the birds using a high-speed motion capture system, and found that their gap choice seemed to be biased by their intrinsic handedness, rather than determined by extrinsic cues such as the size of the gap or its alignment with the destination. We modelled the pigeons' steering behaviour algorithmically by simulating their flight trajectories under a set of six candidate guidance laws, including those used previously to model target-oriented flight behaviours in birds. We found that their flights were best modelled by delayed proportional navigation commanding turning in proportion to the angular rate of the line-of-sight from the pigeon to the midpoint of the gap. Our results are consistent with this being a two-phase behaviour, in which the pigeon heads forward from the release point before steering towards the midpoint of whichever gap it chooses to aim for under closed-loop guidance. Our findings have implications for the sensorimotor mechanisms that underlie clutter negotiation in birds, uniting this with other kinds of target-oriented behaviours including aerial pursuit.

A Predefined-Time Control for the Laser Acquisition in Space Gravitational Wave Detection Mission.

The establishment of a laser link between satellites, i.e., the acquisition phase, is a key technology for space-based gravitational detection missions, and it becomes extremely complicated when the long distance between satellites, the inherent limits of the sensor accuracy, the narrow laser beam divergence and the complex space environment are considered. In this paper, we investigate the laser acquisition problem of a new type of satellite equipped with two two-degree-of-freedom telescopes. A predefined-time controller law for the acquisition phase is proposed. Finally, a numerical simulation was conducted to demonstrate the effectiveness of the proposed controller. The results showed that the new strategy has a higher efficiency and the control performance can meet the requirements of the gravitational detection mission.

A Nonlinear Finite-Time Robust Differential Game Guidance Law.

In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton-Jacobi-Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception.

Measurement Compensation for Time-Delay Seeker and Three-Dimensional Adaptive Guidance Law Design.

The time delay of seekers has grown to be a serious issue for tactical missile guidance with the development of flight vehicle technologies. To address the problem, a measurement compensation system for the seeker, with lags and delays based on predictive active disturbance rejection control, is proposed. In addition, to eliminate the effects of target maneuvers to the tactical missile guidance, an adaptive finite-time convergent sliding mode guidance law, based on super-twisting algorithm, is proposed in three-dimensional missile-target engagement kinematics. Specifically, the compensation system consists of a predictive tracking structure and an active disturbance rejection control system, which could follow a virtual measurement without lags and delays. The compensation system has advantages in disturbance rejection and model inaccuracy addressing, compared with existing compensation methods for seeker measurement. As for the sliding mode guidance law design, the proposed approach is based on an improved super-twisting algorithm with fast convergent adaptive gains, which has advantages in addressing unknown but bounded target maneuvers and avoiding chattering of the classical sliding mode control. As a result, the measurement compensation system and the adaptive sliding mode guidance law is verified robust and effective under the proposed constraints by the simulation examples.

Extending Quantum Probability from Real Axis to Complex Plane.

Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle's random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle's position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker-Planck equation. It is shown that quantum probability Ψ2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.

A Semi-Physical Platform for Guidance and Formations of Fixed-Wing Unmanned Aerial Vehicles.

Unmanned Aerial Vehicles (UAVs) have multi-domain applications, fixed-wing UAVs being a widely used class. Despite the ongoing research on the topics of guidance and formation control of fixed-wing UAVs, little progress is known on implementation of semi-physical validation platforms (software-in-the-loop or hardware-in-the-loop) for such complex autonomous systems. A semi-physical simulation platform should capture not only the physical aspects of UAV dynamics, but also the cybernetics aspects such as the autopilot and the communication layers connecting the different components. Such a cyber-physical integration would allow validation of guidance and formation control algorithms in the presence of uncertainties, unmodelled dynamics, low-level control loops, communication protocols and unreliable communication: These aspects are often neglected in the design of guidance and formation control laws for fixed-wing UAVs. This paper describes the development of a semi-physical platform for multi-fixed wing UAVs where all the aforementioned points are carefully integrated. The environment adopts Raspberry Pi's programmed in C++, which can be interfaced to standard autopilots (PX4) as a companion computer. Simulations are done in a distributed setting with a server program designed for the purpose of routing data between nodes, handling the user inputs and configurations of the UAVs. Gazebo-ROS is used as a 3D visualization tool.

Improved adaptive integral line-of-sight guidance law and adaptive fuzzy path following control for underactuated MSV.

This paper presents an adaptive fuzzy path following control law based on an improved adaptive integral line-of-sight (IAILOS) guidance law for the underactuated marine surface vessel (MSV) exposed to the time-varying ocean currents and time-varying sideslip angle. Initially, the IAILOS guidance law is proposed which can not only calculate the desired yaw angle but also estimate the time-varying ocean currents and time-varying sideslip angle simultaneously. Furthermore, the adaptive fuzzy path following control law is established by combining with the estimator to cope with the MSV's attitude tracking control and velocity tracing control problem via backstepping technique. Specifically, the dynamic uncertainties and unknown environment disturbances are compensated by the fuzzy logic system with fuzzy updating law based on estimation error rather than tracking error. Additionally, two high-order tracking differentiators (TDs) are designed to construct derivatives of virtual control vector and reduce computational complexity inherent in backstepping method. It is proved that the proposed adaptive fuzzy path following control law can drive the vessel to track the desired path and tracking error can converge to an arbitrarily small compact set, while guaranteeing all signals in the closed-loop control system are uniformly ultimately bounded. Finally, simulation results and comparisons are carried out to demonstrate the effectiveness of the proposed control approach.

Terminal attack trajectories of peregrine falcons are described by the proportional navigation guidance law of missiles.

The ability to intercept uncooperative targets is key to many diverse flight behaviors, from courtship to predation. Previous research has looked for simple geometric rules describing the attack trajectories of animals, but the underlying feedback laws have remained obscure. Here, we use GPS loggers and onboard video cameras to study peregrine falcons, Falco peregrinus, attacking stationary targets, maneuvering targets, and live prey. We show that the terminal attack trajectories of peregrines are not described by any simple geometric rule as previously claimed, and instead use system identification techniques to fit a phenomenological model of the dynamical system generating the observed trajectories. We find that these trajectories are best-and exceedingly well-modeled by the proportional navigation (PN) guidance law used by most guided missiles. Under this guidance law, turning is commanded at a rate proportional to the angular rate of the line-of-sight between the attacker and its target, with a constant of proportionality (i.e., feedback gain) called the navigation constant (N). Whereas most guided missiles use navigation constants falling on the interval 3 ≤ N ≤ 5, peregrine attack trajectories are best fitted by lower navigation constants (median N < 3). This lower feedback gain is appropriate at the lower flight speed of a biological system, given its presumably higher error and longer delay. This same guidance law could find use in small visually guided drones designed to remove other drones from protected airspace.

Adaptive internal model guidance law for weaving maneuvering target.

For the terminal phase guidance problem of the missile intercepting weaving maneuvering target, an adaptive internal model guidance laws in the three-dimensional (3-D) engagement space is proposed in this paper. The guidance law adopts the disturbance rejection theory by treating the target weaving maneuvering accelerations as external disturbance, which comprises of nominal part and adaptive part. The nominal part based on feedback linearization method ensures the whole guidance system stable and the adaptive part based on internal model principle is used to recover the disturbance signals on-line to reject the target maneuver asymptotically. The algorithm guarantees the whole guidance system with satisfying performance both in transient and steady state on the effect of target maneuver on guidance system. The stability analyses and theory proof are provided in this paper. At last, numerical simulations are carried out to illustrate the effectiveness of the proposed guidance law.

A novel guidance law using fast terminal sliding mode control with impact angle constraints.

This paper is concerned with the question of, for a missile interception with impact angle constraints, how to design a guidance law. Firstly, missile interception with impact angle constraints is modeled; secondly, a novel guidance law using fast terminal sliding mode control based on extended state observer is proposed to optimize the trajectory and time of interception; finally, for stationary targets, constant velocity targets and maneuvering targets, the guidance law and the stability of the closed loop system is analyzed and the stability of the closed loop system is analyzed, respectively. Simulation results show that when missile and target are on a collision course, the novel guidance law using fast terminal sliding mode control with extended state observer has more optimized trajectory and effectively reduces the time of interception which has a great significance in modern warfare.

Guidance law against maneuvering targets with intercept angle constraint.

This study explores the guidance law against maneuvering targets with the intercept angle constraint. The limitation of the traditional guidance law, which simply treats the unknown target acceleration as zero, has been analyzed. To reduce this limitation, a linear extended state observer is constructed to estimate the acceleration of the maneuvering target to enhance the tracking performance of the desired intercept angle. Furthermore, a nonsingular terminal sliding mode control scheme is adopted to design the sliding surface, which is able to avoid the singularity in the terminal phase of guidance. Simulation results have demonstrated that the proposed guidance law outperforms the traditional guidance law in the sense that more accurate intercept angle can be achieved.