Finite-Time Sideslip Differentiator-Based LOS Guidance for Robust Path Following of Snake Robots

This paper presents a finite-time sideslip differentiator-based line-of-sight(LOS)guidance method for robust path following of snake robots.Firstly,finite-time stable sideslip differentiator and adaptive LOS guidance method are proposed to counteract sideslip drift caused by cross-track velocity.The proposed differentiator can accurately observe the cross-track error and sideslip angle for snake robots to avoid errors caused by calculating sideslip angle approximately.In our method,the designed piecewise auxiliary function guarantees the finite-time stability of position errors.Secondly,for the case of external disturbances and state constraints,a Barrier Lyapunov functionbased backstepping adaptive path following controller is presented to improve the robot’s robustness.The uniform ultimate boundedness of the closed-loop system is proved by analyzing stability.Additionally,a gait frequency adjustment-based virtual velocity control input is derived to achieve the exponential convergence of the tangential velocity.At last,the availability and superiority of this work are shown through simulation and experiment results.

LSTM-DPPO based deep reinforcement learning controller for path following optimization of unmanned surface vehicle

To solve the path following control problem for unmanned surface vehicles(USVs),a control method based on deep reinforcement learning(DRL)with long short-term memory(LSTM)networks is proposed.A distributed proximal policy opti-mization(DPPO)algorithm,which is a modified actor-critic-based type of reinforcement learning algorithm,is adapted to improve the controller performance in repeated trials.The LSTM network structure is introduced to solve the strong temporal cor-relation USV control problem.In addition,a specially designed path dataset,including straight and curved paths,is established to simulate various sailing scenarios so that the reinforcement learning controller can obtain as much handling experience as possible.Extensive numerical simulation results demonstrate that the proposed method has better control performance under missions involving complex maneuvers than trained with limited scenarios and can potentially be applied in practice.

Constrained Moving Path Following Control for UAV With Robust Control Barrier Function

This paper studies the moving path following(MPF)problem for fixed-wing unmanned aerial vehicle(UAV)under output constraints and wind disturbances.The vehicle is required to converge to a reference path moving with respect to the inertial frame,while the path following error is not expected to violate the predefined boundaries.Differently from existing moving path following guidance laws,the proposed method removes complex geometric transformation by formulating the moving path following problem into a second-order time-varying control problem.A nominal moving path following guidance law is designed with disturbances and their derivatives estimated by high-order disturbance observers.To guarantee that the path following error will not exceed the prescribed bounds,a robust control barrier function is developed and incorporated into controller design with quadratic program based framework.The proposed method does not require the initial position of the UAV to be within predefined boundaries.And the safety margin concept makes error-constraint be respected even if in a noisy environment.The proposed guidance law is validated through numerical simulations of shipboard landing and hardware-in-theloop(HIL)experiments.

Kinematics and Path Following Control of an Articulated Drum Roller

Automatic navigation of an articulated drum roller, which is an articulated steering type vehicle widely used in the construction industry, is highly expected for operation cost reduction and improvement of work effi- ciency. In order to achieve the path following control, considering that its steering system is articulated steering and two frames are articulated by an active revolute joint, a kinematic model and an error dynamic state-space equation of an articulated drum roller are proposed. Besides, a state- feedback control law based on Lyapunov stability theory is also designed, which can be proved to achieve the purpose of control by the analysis of stability. What＇s more, to evaluate the performance of the proposed method, simu- lation under the MATLAB/Simulink and experiments using positioning algorithm and errors correction at the uneven construction site are performed, with initial dis- placement error （-1.5 m）, heading error （-0.11 tad） and steering angle （-0.19 rad）. Finally, simulation and exper- imental results show that the errors and steering angle can decrease gradually, and converge to zero with time. Meanwhile, the control input is not saturated. An articu- lated drum roller can lock into a desired path with the proposed method in uneven fields.

Adaptive sliding-mode path following control system of the underactuated USV under the influence of ocean currents

The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode path-following control system is proposed, which comprises a path-variable updated law,a modified integral line-of-sight(ILOS) guidance law based on a time-varying lookahead distance and adaptive feedback linearizing controllers combined with sliding-mode technique. A more accurate USV model without the assumption of having diagonal inertia and damping matrices is first presented, aiming at improving the performance of the path-following control. Next, the coordinate transformation is adopted to decouple the sway dynamic from the rudder angle, and the path-following errors dynamics without non-singular problem are presented in the moving Frenet-Serret frame. Then, based on the cascaded theorem and the adaptive sliding-mode method, the adaptive control law of position errors and course error are designed, among which the lookahead distance and integral gain are all computed as different functions of cross-track error to estimate and compensate the sideslip angle caused by external disturbances adaptively. Finally, according to the Lyapunov and cascaded theorem, the control system proposed is proved to be uniform globally asymptotic stability(UGAS) and uniform semiglobal exponential stability(USGES) when the control objectives are all achieved. Simulation results illustrate the precision and high-quality performance of this new controller.

Path Following Control of A Deep-Sea Manned Submersible Based upon NTSM

In this paper, a robust path following control law is proposed for a deep-sea manned submersible maneuvering along a predeterminated path. Developed in China, the submersible is underactuated in the horizontal plane in that it is actuated by two perpendicular thrusts in this plane. The advanced non-singular terminal sliding mode （NTSM） is implemented for the design of the path following controller, which can ensure the convergence of the motion system in finite time and improve its robustness against parametric uncertainties and environmental disturbances. In the process of controller design, the close-loop stability is considered and proved by Lyapunov＇ s stability theory. With the experimental data, numerical simulations are provided to verify the control law for path following of the deep-sea manned submersible.

Path following control of underactuated ships based on nonswitch analytic model predictive control

A path following controller is developed for underactuated ships with only surge force and yaw moment available to follow a predefined path.The proposed controller is based on nonswitch analytic model predictive control.It is shown that the optimal control law for a nonlinear path following system with ill-defined relative degree is continuous and nonsingular.The problem of ill-defined relative degree is solved.The path-following ability of the nonlinear system is guaranteed.Numerical simulations are provided to demonstrate the effectiveness of the proposed control law.

Adaptive back-stepping control on container ships for path following

A feedback-dominance based adaptive back-stepping(FDBAB) controller is designed to drive a container ship to follow a predefined path. In reality, current, wave and wind act on the ship and produce unwanted disturbances to the ship control system.The FDBAB controller has to compensate for such disturbances and steer the ship to track the predefined(or desired) path. The difference between the actual and the desired path along which the ship is to sail is defined as the tracking error. The FDBAB controller is built on the tracking error model which is developed based on Serret-Frenet frame transformation(SFFT). In additional to being affected by external disturbances, the ship has more outputs than inputs(under-actuated), and is inherently nonlinear.The back-stepping controller in FDBAB is used to compensate the nonlinearity. The adaptive algorithms in FDBAB is employed to approximate disturbances. Lyapunov's direct method is used to prove the stability of the control system. The FDBAB controlled system is implemented in Matlab/Simulink. The simulation results verify the effectiveness of the controller in terms of successful path tracking and disturbance rejection.

Dynamic Path Following Control of a Ground Ackerman Steering Robot to Avoid a Collision

A novel method is proposed to dynamically control the path following of a ground Ackerman steering robot to avoid a collision.The method consists of collision prediction module,collision avoidance module and global path following module.The elliptic repulsive potential field method（ER-PFM）and the enhanced vector polar histogram method（VPH＋）based on the Ackerman steering model are proposed to predict the collision in a dynamic environment.The collision avoidance is realized by the proposed cost function and speed control law.The global path following process is achieved by pure pursuit.Experiments show that the robot can fulfill the dynamic path following task safely and efficiently using the proposed method.

A Novel Prescribed-Performance Path-Following Problem for Non-Holonomic Vehicles

The issue of achieving prescribed-performance path following in robotics is addressed in this paper,where the aim is to ensure that a desired path within a specified region is accu-rately converged to by the controlled vehicle.In this context,a novel form of the prescribed performance guiding vector field is introduced,accompanied by a prescribed-time sliding mode con-trol approach.Furthermore,the interdependence among the pre-scribed parameters is discussed.To validate the effectiveness of the proposed method,numerical simulations are presented to demonstrate the efficacy of the approach.

Multi-circular formation control with reinforced transient profiles for nonholonomic vehicles:A path-following framework

This article investigates a multi-circular path-following formation control with reinforced transient profiles for nonholonomic vehicles connected by a digraph.A multi-circular formation controller endowed with the feature of spatial-temporal decoupling is devised for a group of vehicles guided by a virtual leader evolving along an implicit path,which allows for a circumnavigation on multiple circles with an anticipant angular spacing.In addition,notice that it typically imposes a stringent time constraint on time-sensitive enclosing scenarios,hence an improved prescribed performance control(IPPC)using novel tighter behavior boundaries is presented to enhance transient capabilities with an ensured appointed-time convergence free from any overshoots.The significant merits are that coordinated circumnavigation along different circles can be realized via executing geometric and dynamic assignments independently with modified transient profiles.Furthermore,all variables existing in the entire system are analyzed to be convergent.Simulation and experimental results are provided to validate the utility of suggested solution.

Finite-time path following control of a sailboat with actuator failure and unknown sideslip angle

Suffering from actuator failure and complex sideslip angle,the motion control of a sailboat becomes challenging.In this paper,an improved double finite-time observer-based line-of-sight guidance and finite-time control(IDFLOS-FC)scheme is presented for path following of sailboats.The salient features of the proposed IDFLOS-FC scheme are as follows:(1)Considering the problem of actuator failure,an actuator failure model is introduced into the dynamics model of a sailboat.(2)The time-varying sideslip angle of the sailboat is accurately observed by the double finite-time sideslip observers(DFSOs),which reduces the error in line-of-sight(LOS)guidance.(3)A radial basis function(RBF)neural network is used to fit the uncertainty of the model,and the upper bound of the sum of fault effects and external disturbances is estimated based on adaptive theory,so that the controller has accurate tracking and interference suppression.(4)According to the Lyapunov method,the system is finite-time stable.Finally,simulation was used to validate the effectiveness of the method.

Time-Coordinated Path Following for Multiple Agile Fixed-Wing UAVs with End-Roll Expectations

This paper presents a control strategy for multiple unmanned aerial vehicle systems(multi-UAVs)time-coordinated path following with desired endpoint roll attitudes.It utilizes the strong maneuvering capabilities of agile fixed-wing UAVs and incorporates an end-roll expectation.The strategy consists of four steps:time-coordinated control,position control,roll angle planning and attitude control.The position and attitude controllers exhibit Lyapunov exponential stability.The time-coordinated controller addresses the synchronization problem by adjusting the speed based on the coordinated state to achieve progress adjustment.The position controller operates based on the cross-track error and altitude error in the Gravity-Referenced Moving frame.By employing an optimization approach and designing a penalty function,the roll angle sequence is computed.The attitude inner-loop control operates in the SO(3)space and allows for control of large deviations.High-fidelity simulation validates the effectiveness of the proposed method,with normalized coordination error and following error controlled within 2%and 1.2m.

Control of a Spherical Robot: Path Following Based on Nonholonomic Kinematics and Dynamics

This paper presents the controller design for the path following of a spherical mobile robot, BHQ-1. Firstly, a desired velocity for the reference path is deduced from the kinematic model, which cannot be transformed into the classic chained form. Secondly, a necessary torque for the desired velocity is obtained based on the dynamic model. As to the kinematics, a one-dimensional function is selected to measure the two-directional tracking error, and the velocity of rolling forward is reasonably assumed to be constant; therefore the multiple-input multiple-output （MIMO） system is transformed into a single-input single-output （SISO） system. As to the dynamics, both exact dynamics and inexact dynamics with modeling error as well as bounded unknown disturbance are taken into account, based on which a proportional-derivative （PD） controller and a sliding mode controller with adaptive parameters are proposed respectively. Finally, convergence analysis and simulation results are provided to validate these controllers.

Aircraft-on-ground path following control by dynamical adaptive backstepping

The necessity of improving the air traffic and reducing the aviation emissions drives to investigate automatic steering for aircraft to effectively roll on the ground. This paper addresses the path following control problem of aircraft-on-ground and focuses on the task that the aircraft is required to follow the desired path on the runway by nose wheel automatic steering. The proposed approach is based on dynamical adaptive backstepping so that the system model does not have to be transformed into a canonical triangular form which is necessary in conventional backstepping design. This adaptive controller performs well despite the lack of information on the aerodynamic load and the tire cornering stiffness parameters. Simulation results clearly demonstrate the advantages and effectiveness of the proposed approach.

Real‑Time Predictive Control of Path Following to Stabilize Autonomous Electric Vehicles Under Extreme Drive Conditions

A novel real-time predictive control strategy is proposed for path following(PF)and vehicle stability of autonomous electric vehicles under extreme drive conditions.The investigated vehicle configuration is a distributed drive electric vehicle,which allows to independently control the torques of each in-wheel motor(IWM)for superior stability,but bringing control com-plexities.The control-oriented model is established by the Magic Formula tire function and the single-track vehicle model.For PF and direct yaw moment control,the nonlinear model predictive control(NMPC)strategy is developed to minimize PF tracking error and stabilize vehicle,outputting front tires’lateral force and external yaw moment.To mitigate the calcu-lation burdens,the continuation/general minimal residual algorithm is proposed for real-time optimization in NMPC.The relaxation function method is adopted to handle the inequality constraints.To prevent vehicle instability and improve steering capacity,the lateral velocity differential of the vehicle is considered in phase plane analysis,and the novel stable bounds of lateral forces are developed and online applied in the proposed NMPC controller.Additionally,the Lyapunov-based constraint is proposed to guarantee the closed-loop stability for the PF issue,and sufficient conditions regarding recursive feasibility and closed-loop stability are provided analytically.The target lateral force is transformed as front steering angle command by the inversive tire model,and the external yaw moment and total traction torque are distributed as the torque commands of IWMs by optimization.The validations prove the effectiveness of the proposed strategy in improved steering capacity,desirable PF effects,vehicle stabilization,and real-time applicability.

Curvature Adaptive Control Based Path Following for Automatic Driving Vehicles in Private Area

Path following refers to traveling along the desired path with automatic steering control,which is a crucial technology for automatic driving vehicles.Roads in private areas are highly irregular,resulting in a large curvature variation,which reduces the control accuracy of the path following.A curvature adaptive control(CAC)based path-following method was proposed to solve the problem mentioned above.Specifically,CAC takes advantage of the complementary characteristics in response to the path curvature fluctuation of pure pursuit and front-wheel feedback and by combining the two methods further enhances the immunity of the control accuracy in response to a curvature fluctuation.With CAC,the quantitative indices of the path curvature fluctuation and control accuracy were constructed.The model between the path curvature fluctuation and a dynamic parameter was identified using the quantitative index of the control accuracy as the optimization target.The experimental results of a real vehicle indicate that the control accuracy of path following is further enhanced by its immunity in response to curvature fluctuation improved by the CAC.In addition,CAC is easy to deploy and requires low demand for hardware resources.

Extended model predictive control scheme for smooth path following of autonomous vehicles

This paper presents an extended model predictive control(MPC)scheme for implementing optimal path following of autonomous vehicles,which has multiple constraints and an integrated model of vehicle and road dynamics.Road curvature and inclination factors are used in the construction of the vehicle dynamic model to describe its lateral and roll dynamics accurately.Sideslip,rollover,and vehicle envelopes are used as multiple constraints in the MPC controller formulation.Then,an extended MPC method solved by differential evolution optimization algorithm is proposed to realize optimal smooth path following based on driving path features.Finally,simulation and real experiments are carried out to evaluate the feasibility and the effectiveness of the extended MPC scheme.Results indicate that the proposed method can obtain the smooth transition to follow the optimal drivable path and satisfy the lateral dynamic stability and environmental constraints,which can improve the path following quality for better ride comfort and road availability of autonomous vehicles.

Adaptive Path Following Controller of Underactuated Ships Using Serret-Frenet Frame

This paper presents an adaptive path following control law to steer underactuated ships along a predefined path at a constant forward speed with uncertain parameters due to changes of added mass matrices.The proposed controller is based on analytic model predictive control and model reference adaptive control.The SerretFrenet frame is used to describe the ship dynamics.The analytic model predictive control provides a systematic method rather than try-and-error method to get appropriate control parameters to guarantee the stability of the closed-loop system,and the well-defined relative degree is guaranteed by introducing output-redefinition.An identification algorithm based on model reference adaptive control is used to identify the uncertain parameters.Numerical simulations are provided to demonstrate the validity of the proposed control law.

Path Following Control for UAV Using Deep Reinforcement Learning Approach

Unmanned aerial vehicles(UAVs)have been extensively used in civil and industrial applications due to the rapid development of the guidance,navigation and control(GNC)technologies.Especially,using deep reinforcement learning methods for motion control acquires a major progress recently,since deep Q-learning algorithm has been successfully applied to the continuous action domain problem.This paper proposes an improved deep deterministic policy gradient(DDPG)algorithm for path following control problem of UAV.A speci-c reward function is designed for minimizing the cross-track error of the path following problem.In the training phase,a double experience replay bu®er(DERB)is used to increase the learning e±ciency and accelerate the convergence speed.First,the model of UAV path following problem has been established.After that,the framework of DDPG algorithm is constructed.Then the state space,action space and reward function of the UAV path following algorithm are designed.DERB is proposed to accelerate the training phase.Finally,simulation results are carried out to show the e®ectiveness of the proposed DERB–DDPG method.