Vector Field Guidance Law Research Articles

Data-Driven Hazard Avoidance Landing of Parafoil: A Deep Reinforcement Learning Approach

This paper examines a couple of realizations of autonomous landing hazard avoidance technology of parafoil: a reinforcement-learning-based approach and a rule-based approach, advocating the former. Furthermore, comparative advantages and behavioral analogies between the two approaches are presented. In the data-driven approach, a decision process observing only a series of nadir-pointing images is designed without explicit augmentation of vehicle dynamics for the homogeneity of observation data. An agent then learns the hazard avoidance steering law in an end-to-end fashion. On the contrary, the rule-based approach is facilitated via explicit notions of guidance-control hierarchy, vehicle dynamic states, and metric details of ground obstacles. The soft actor–critic method is applied to learn a policy that maps the down-looking images to parafoil brakes, whereas a vector field guidance law is employed in the rule-based approach, considering each hazard as a repulsive source. This paper then presents empirical equivalences in designing both approaches and their distinctions. Numerical experiments in multiple test cases validate the reinforcement learning method and present comparisons between the approaches regarding their resultant trajectories. The interesting behaviors of the resultant policy of the data-driven approach are emphasized.

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.

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.

Modified vector field and nonlinear guidance law for low-cost UAV path following

Purpose The purpose of this paper is to present a high accuracy path following method for low-cost fixed-wing UAVs. Design/methodology/approach The original vector field (VF) algorithm is condensed. A spatial integration mechanism is added to the existing VF and nonlinear guidance law, aiming to decrease steady-state cross-track-error and cope with long-term disturbance. Findings Numerical simulations show the proposed method could diminish steady-state cross-track-error effectively. Test flights show the proposed method is applicable on low-cost fixed-wing UAVs. Practical implications The path following accuracy shown in simulations and test flights indicates the proposed method could be deployed in scenarios including inflight rendezvous, formation, trafficway take-off and landing. Originality/value This paper provides an improved high-accuracy path following method for low-cost fixed-wing UAVs.

VECTOR FIELD GUIDANCE LAW FOR CURVED PATH FOLLOWING OF AN UNDERACTUATED AUTONOMOUS SHIP MODEL

A vector field guidance law and control system for curved path following of an underactuated surface ship model is presented in this paper. In order to obtain the curved path, continuous derivatives piecewise cubic Hermite interpolation is applied for path generation based on the predefined waypoints. A heading autopilot controller is designed based on 2nd order Nomoto’s model and its stability is guaranteed by the Diagram of Vyshnegradsky method. The parameters of Nomoto model are estimated using least square support vector machine based on the manoeuvring tests. The vector field guidance law is applied for both straight and curved path-following control of an underactuated surface ship model. In order to demonstrate the performance, the classical guidance law based on line-of-sight, is adopted for comparison. The results show that the vector field method is capable to solve the guidance problem of underactuated surface ships.

Design of Standoff Cooperative Target-Tracking Guidance Laws for Autonomous Unmanned Aerial Vehicles

This paper investigates two guidance laws of standoff cooperative tracking static and moving of multiple autonomous unmanned aerial vehicles for targets from the perspective of the control system design. In the scheme of the proposed guidance laws, one vehicle is chosen as leader and others as followers. The leader only needs the measurement of the target, and the followers only measure the leader and its neighbors in the communication topology network. By using the proposed guidance laws, it is guaranteed that all vehicles can track a static or moving target with an evenly spaced formation of circle. Considering the coupling of tracking and cooperation, the stability analysis is performed by constructing two relatively independent subsystems based on Lyapunov theory, and the corresponding rigorous proofs of stability are given. By comparing with the Lyapunov vector field guidance law, the simulation results verify the effectiveness and superiority of the proposed guidance laws.

Vector Field Guidance Law for Curved Path Following of an Underactuated Autonomous Ship Model

A vector field guidance law and control system for curved path following of an underactuated surface ship model is presented in this paper. In order to obtain the curved path, continuous derivatives piecewise cubic Hermite interpolation is applied for path generation based on the predefined waypoints. A heading autopilot controller is designed based on 2nd order Nomoto’s model and its stability is guaranteed by the Diagram of Vyshnegradsky method. The parameters of Nomoto model are estimated using least square support vector machine based on the manoeuvring tests. The vector field guidance law is applied for both straight and curved path-following control of an underactuated surface ship model. In order to demonstrate the performance, the classical guidance law based on line-of-sight, is adopted for comparison. The results show that the vector field method is capable to solve the guidance problem of underactuated surface ships.

L1 adaptive backstepping control for path-following of underactuated marine surface ships

A L1 adaptive backstepping controller is proposed for path-following control of an underactuated ship based on a nonlinear steering model, and the control law is derived using Lypunov control function. L1 adaptive controller is a novel technology considering both the robustness and fast adaptation. The closed-loop control system is proved to be uniformly global asymptotically stable. A novel guidance law, time-varying vector field, is proposed for the guidance system. The kinematic analysis of path-following shows that the guidance and control systems are coupled, and the guidance system is affected by the performance of the controller. The Lyapunov method is employed to show that the equilibrium point of the whole system is uniformly global asymptotically stable. Path-following simulations are carried out to validate the performance of the proposed control law and vector field guidance law using a fully nonlinear manoeuvring mode of an underactuated tanker in the presence of stochastic ocean current.

Characteristic model-based path following controller design for the unmanned surface vessel

This paper proposed a path following controller for the unmanned surface vessel (USV) by taking advantage of the vector field (VF) guidance method and the characteristic model-based heading angle and speed tracking approach. Considering the fact that the motions of USVs without professional design were difficult to be accurately modeled due to the high complexity in terms of nonlinearity and coupling, the second-order characteristic model was determined to be the investigated plant which was regarded as the control model. The parameters involved in the model were estimated using forgetting factor recursive least square (FFRLS). Based on the characteristic model of the USV, the intelligent adaptive control method was applied to design the controller for tracking the heading angle and speed. Then, the path following controller was designed for the USV based on the vector field guidance law and the characteristic model-based heading angle and speed controller. Finally, experimental results with comparisons indicate the developed path following controller can simultaneously ensure accuracy in the expected range and defend negative effects induced by slight environmental disturbances, which implied the robustness and preciousness of the proposed controller. The attractive merits of the proposed path following controller mainly thanks to the flexibility and simplicity of the investigated plant (i.e. the second-order characteristic model) and the outperformance of the characteristic model-based controller.

Integral vector field control for three-dimensional path following of autonomous underwater vehicle

A new control method for autonomous underwater vehicle (AUV) is developed to achieve three-dimensional (3D) path following under ocean current disturbances when AUV lacks lateral and vertical driving forces. To make the control system more convenient for practical application and reduce the energy consumption of AUV, the controller is designed with relative velocities. To avoid the singularity problem of curve path following, the Serret–Frenet frame is introduced as virtual target and the error model is defined. The adaptive law of the virtual target and an integral vector field (IVF) guidance law are designed in the kinematic controller. The back-stepping method and adaptive dynamical sliding mode control (BADSMC) technology are applied in the design of dynamic controller. The Lyapunov theory and nonlinear cascade system theory are applied to prove the closed-loop stability. Finally, the performances of the IVF + BADSMC and ILOS + PID algorithm are compared through simulation. Simulation results demonstrate that the proposed controller can realize the path following of AUV under disturbances of ocean current and can improve the following quality.

Moving Path Following With Prescribed Performance and Its Application on Automatic Carrier Landing

This article studies the moving path following (MPF) problem where a desired path attached to a moving object must be followed. Focusing on the problem that the classical guidance vector field is not suitable for an MPF, we present a time-varying vector field guidance law, which is qualified for following a path expressed with respect to a moving target frame. Moreover, a prescribed performance method is embedded to the time-varying vector field law to further enhance the control performance. By combining the prescribed performance, the tracking errors are ensured not to exceed the predefined arbitrary small residual sets. Subsequently, the proposed guidance laws are applied to a typical MPF mission - the automatic carrier landing. An active disturbance rejection attitude controller is designed as the “low-level” controller with backstepping as the main frame. To eliminate the potential problem of external disturbances and parameter uncertainties, extended state observers are adopted in the controller. Besides, tracking differentiators are integrated with the controller to avoid complex derivative calculations in backstepping. Finally, comparative simulations are conducted, the results clarify and verify the proposed methods.

Use of AIS data for guidance and control of path-following autonomous vessels

This paper carries out research on the prototype of an autonomous vessel that is normally used for passenger transportation. A path generation system is proposed using a dynamic time warping algorithm based on Automatic Identification System history data. In order to ensure strong stability properties, a nonlinear controller with globally exponentially stability is introduced for the heading controller. The least square support vector machine is employed to estimate the parameters of the control model based on full-scale manoeuvring tests. The identified results are validated with analytical values. The kinematics and control object of path-following are presented, and a time-varying vector field guidance law is proposed for the path-following control of autonomous vessels. The guidance and control subsystems are interconnected and form a cascade structure. The stability of the coupled guidance and control system is carried out using the cascaded system theory. The proof ensures that the equilibrium point of the cascaded system is uniformly semiglobally exponentially stable. Path following scenario was considered in the presence of currents based on a nonlinear manoeuvring model. Simulation studies were used to verify the theoretical results.

Adaptive path following control of a stratospheric airship with full-state constraint and actuator saturation

In this paper, the path following problem is addressed for a stratospheric airship subject to full-state constraint, input saturation and external disturbances. A novel full-state constrained path-following algorithm, which ensures that all states of the system remain in the predetermined intervals, is proposed based on the theories of barrier Lyapunov function, vector field guidance, adaptive backstepping control and saturation compensator. Firstly, an error-constrained vector field (ECVF) guidance law is presented to handle the position tracking error, which can navigate the stratospheric airship along the predefined path and guarantee that the error is limited by the time-varying asymmetric constraints. Secondly, a state-constrained adaptive attitude controller is introduced to track the desired attitude calculated by the ECVF, in which a saturation compensator of virtual control law is employed to handle the problem of angular velocity constraint. Finally, a state-constrained adaptive velocity controller is designed to maintain an appropriate scheduled velocity. Furthermore, two auxiliary design systems are used to deal with the actuator saturation problem, and adaptive laws are developed for handling dynamic couplings and unknown disturbances. Stability analysis implies that all signals in the closed-loop system are uniformly ultimately bounded, and all path-following state constraint requirements are never violated. Meanwhile, the effectiveness of the proposed control algorithm is demonstrated by comparative simulation results.

Uniformly semiglobally exponential stability of vector field guidance law and autopilot for path-following

A uniform semiglobal exponential stability (USGES) proof for a time-varying vector field guidance law used for path-following control of vehicles is presented. A sliding mode control is introduced for heading autopilot design and Lyapunov methods are used to derive the control law. The equilibrium point of the autopilot error dynamics is proven to be globally exponentially stable (GES). The main result is a time-varying vector field guidance law in cascade with the autopilot. A theorem ensures that the equilibrium point of the cascaded system is uniformly semiglobally exponentially stable. Both straight-line and curved-path path following scenarios are considered in the presence of ocean currents. Simulation studies are carried out to verify the theoretical results. The time-varying guidance laws can also be applied to vehicles in general such as aircraft, underwater vehicles, drones and autonomous vehicles.

Asymmetric error-constrained path-following control of a stratospheric airship with disturbances and actuator saturation

Abstract This paper addresses the asymmetric error-constrained path-following problem of a stratospheric airship with external disturbances and actuator saturation. A path-following algorithm is proposed based on the theories of tan-type barrier Lyapunov function, vector field guidance, adaptive sliding mode control, and radial basis function neural network (RBFNN). First, to satisfy the asymmetric tracking error-constrained requirements of airship position, an asymmetric error-constrained vector field (AECVF) guidance law is presented, which can navigate the stratospheric airship along the predefined path and guarantee that the tracking error is limited by the error constraints. Second, an adaptive sliding mode attitude controller is introduced to track the desired attitudes calculated using the AECVF with disturbances. Finally, an adaptive velocity controller is added to the control algorithm to maintain an appropriate velocity. Moreover, an RBFNN saturation compensator is introduced to solve the actuator saturation problem caused by the low maneuverability. Stability analysis indicates that all the signals in the closed-loop system are uniformly ultimately bounded. Meanwhile, simulation results demonstrate the effectiveness of the proposed control algorithm.

A Comparison Between the ILOS Guidance and the Vector Field Guidance

This paper presents a quantitative comparison between two popular guidance laws for straight line path-following purposes of autonomous marine vehicles: the integral line-of-sight (ILOS) guidance law and the vector field (VF) guidance law. The comparison is based on experimental results and the cross track error measurements as well as the servo command signals are considered in the analysis. Both the guidance schemes are applied to the underactuated LAUV vehicle in the same environmental conditions with the same speed and heading controllers. The comparison separates between transient and steady-state behaviour, with focus on the latter. In particular, the cross-track error transfer functions for small time varying disturbances are derived for the two guidance schemes at equilibrium and similarities are found with the experimental results. The analysis concludes good path following performance for both the VF and the ILOS guidance laws, with the VF controller performing slightly better. However, the VF guidance scheme suffers from significant chattering on the horizontal rudders while the ILOS guidance law gives very smooth servo commands.