Feasible Reference Trajectories Research Articles

Homing tracking control of autonomous underwater vehicle based on adaptive integral event-triggered nonlinear model predictive control

The homing problem of autonomous underwater vehicle with constraints and bounded disturbances is studied in this paper. More specifically, a nonlinear model predictive control (NMPC) framework based on adaptive integral event-triggered (AIET) mechanism is designed for AUV tracking mobile docking station (DS). Firstly, according to the characteristics of AUV homing, a guidance system based on mobile DS is designed, which can provide a feasible reference trajectory for the subsequent AUV tracking independent of the vehicle model. Then, in the framework of AIET-NMPC control, the designed tracking controller can reduce the computational cost while guaranteeing the control accuracy. The proposed AIET mechanism can dynamically adjust the trigger threshold according to the integral error between the real state and the optimal state of the system. In addition, by designing exponential robust constraints in the NMPC optimization problem, the system stability margin is increased. Finally, it strictly proves the Zeno free behavior, the feasibility of the algorithm, and the stability of the system. Simulation results demonstrate that the proposed control approach yields better effects in terms of tracking control performance and computational performance compared to other methods.

A singularity‐free online neural network‐based sliding mode control of the fixed‐wing unmanned aerial vehicle optimal perching maneuver

AbstractThe perching behavior of birds is very common in nature, but it is extraordinary for fixed‐wing unmanned aerial vehicles (UAVs), because of post‐stall maneuver. The main problems of the perching maneuver are weak control authority and strong model nonlinearity. This paper proposed a control method to realize the fixed‐wing perch maneuver. For the problem of weak control authority, an optimal trajectory is designed. And a feasible reference trajectory is given under the conditions of model dynamic characteristics and actuator constraints. For the problem of strong nonlinearity, a singularity‐free online neural network‐based sliding mode controller is designed. The simulation test shows that the proposed controller can ensure a reliable perching maneuver under the initial state deviation.

Self‐learning‐based optimal tracking control of an unmanned surface vehicle with pose and velocity constraints

AbstractIn this article, subject to both pose and velocity constraints within narrow waters, a self‐learning‐based optimal tracking control (SLOTC) scheme is innovatively created for an unmanned surface vehicle (USV) by deploying actor‐critic reinforcement learning (RL) mechanism and backstepping technique. To be specific, the barrier Lyapunov function (BLF) is devised to uniformly limit the states within a predefined region pertaining to a smoothly feasible reference trajectory. By virtue of a constrained Hamilton–Jacobi–Bellman (HJB) function, an actor‐critic control structure under backstepping is established by employing adaptive neural network identifiers which recursively updates actor and critic, simultaneously. Eventually, theoretical analysis proves that the entire SLOTC scheme can render all the states remain in the predefined compact set while tracking errors converge to an arbitrarily small neighborhood of the origin. Simulation results on a prototype USV demonstrate remarkable effectiveness and superiority.

Nonlinear Control Method for Backflipping with Miniature Quadcopters

The paper proposes a nonlinear control method for performing a backflip maneuver with a nano quadcopter. To perform the maneuver, first a feasible reference trajectory is designed that describes the intended state evolution. Then, the designed trajectory is precisely tracked by a nonlinear geometric controller that is able to track even highly challenging reference trajectories. The performance of the proposed method is evaluated and compared to a simple adaptive feedforward control strategy based on simulations and real-world experiments using Bitcraze Crazyflie nano quadcopters.

Formation Reconstruction and Trajectory Replanning for Multi-UAV Patrol

This article addresses the dynamic formation reconstruction and trajectory replanning problem in the air patrol task using multiple fixed-wing unmanned aerial vehicle formations. Unlike most of the formation flying related work, this article considers a more practical issue that some of the vehicles may break down during operation. In this case, a more reasonable coping strategy is proposed which is to reconstruct the formation such that the task objectives can be achieved optimally. To perform the patrol task, a virtual target is introduced which moves along the patrol path with a predetermined speed. Considering the fact that not all the vehicles have access to the patrol path information, a decentralized estimator is designed for each vehicle to estimate the virtual target state respectively based on which the individual reference trajectories can be generated. As these reference trajectories do not satisfy relevant physical constraints, including system model, control input limits, no-fly zone avoidance, and intervehicle collision avoidance, a novel model predictive trajectory replanning algorithm is developed to generate feasible reference trajectories for each vehicle in real time, which is computationally attractive by incorporating a situation-dependent mechanism. Simulations have been conducted to validate the effectiveness of our proposed algorithm.

Evaluation of Dynamic Coupling Intensity and Passive Attitude Control of Underwater Vehicle-Manipulator Systems

In the future, underwater manipulation tasks are intended to be performed by moving base robots, namely Underwater Vehicle-Manipulator Systems (UVMSs). However, the manipulation task induces reaction forces and torques on the underwater vehicle, affecting its positioning. Therefore, it is necessary to compensate for these disturbances to perform the coordinated control of the UVMS or the station keeping of the underwater vehicle. For this sake, this paper presents a new methodology to evaluate the intensity of the dynamic coupling as a function of the working frequency of the manipulator. With such information will be possible to predict the frequency range in which the dynamic coupling is significant. Also, this approach could be used on the task planning level to produce dynamically feasible reference trajectories, improving the control performance. Beyond the identification of a safe frequency range, the obtained results also provide interesting insights about the dynamic coupling influence for the attitude Degrees of Freedom (DoFs) of the underwater vehicle, which can be related to results reported in previous works. Moreover, motivated by the results obtained here and the originality of this application, a passive control is synthesized for the attitude of UVMSs. The simulation results show good attenuation for the pitch oscillations with the proposed control.

Safe and optimal lane-change path planning for automated driving

This paper proposes an integrated lane-change trajectory planning method for advanced driver assistance system of connected and automated vehicles. First, the time-based quintic polynomial automated lane-change model is presented, which could adjust longitudinal and lateral velocity simultaneously. By tuning the lane-change duration and longitudinal displacement in the lane-change model, the lane-change reference trajectories satisfying the demands of safety, lane-change duration, travel distance, and comfort were derived under traffic-free condition. All feasible reference trajectories compose a trajectory map, which includes different driving situations, such as quick and comfortable or sudden and safe lane change. Second, the lane-change constraints induced by surrounding vehicles are introduced. The effects of surrounding vehicles on the lane-change performance are investigated by adjusting the speeds and initial gaps of preceding and rear vehicles. In addition, the initial velocity of the host vehicle is optimized to maximize the area of the trajectory map to enable a safer lane change. Finally, within the derived trajectory map, an optimal lane-change trajectory eliminating potential collisions is calculated by minimizing the lane-change duration, travel distance, driving comfort, and fuel consumption.

Predictive pursuit-evasion game control method for approaching space non-cooperative target

This paper designs the predictive pursuit-evasion game-based orbit control method for the chasing spacecraft to approach a space uncooperative maneuvering target. Firstly, the trajectory planning algorithm combines RRT⁎ and cubic splines to generate a feasible reference trajectory in the relative motion space for the chaser, which enables to deal with the boundary constraints and avoid collisions with the attachments of target. Then, based on the dynamics model, input constrains and objective functions, the pursuit-evasion game model between the target and the chaser is formulated, in which each one acts independently to satisfy its own objective function. With the game formulation, a predictive pursuit-evasion game controller for the chaser is designed to track reference trajectory. Under the frame of model predictive control, the multiple objective constraint optimization can be transferred into to quadratic programming problem to handle input constraints. By predicting opponent’s best move and changing its optimal strategy for its benefit iteratively, the saddle points of the game can be obtained without opponent’s maneuvering. Numerical simulations verify the effectiveness of the predictive pursuit-evasion game control method for approaching an uncooperative target.

MPC approaches for modulating air-to-water heat pumps in radiant-floor buildings

A modulating heat pump and water tank result in a nonlinear model due to the load dependency of the heat pump performance, and variable water flows. Nonlinear model predictive control is an effective way to deal with many physical constraints and nonlinear formulations. Alternatively, linear time-varying MPC can be used, based on successive linearizations around a reference trajectory. The goal of the paper is to analyze the advantages and disadvantages of those MPC techniques for temperature control in radiant-floor buildings. The results show that nonlinear on-line optimization is real-time feasible for the application considered here, as the slow dynamics allows for a fairly long sampling time. Alternatively, the linear time-varying MPC approach shows a significantly better performance compared to the Standard MPC scheme if a feasible reference trajectory is provided. Nonlinear MPC can save up to 6% energy and improve the comfort by 4% with respect to Standard MPC for the given application, while its difference with LTV-MPC is negligible. Moreover, a robustness analysis has been conducted, showing the impact of the heat pump efficiency on the control performance.

Fuzzy logic approach for smooth transition between grid-connected and stand-alone modes of three-phase DG-inverter

In distributed generation systems, the worst case of operation is a sudden transition between Grid-Connected mode (GC) and Stand-Alone mode (SA). In this situation, system state variables, such as abrupt changes in currents, risk to contribute to the destruction of the whole power system. In this work, the use of the Fuzzy Logic (FL)-based approach for smooth transition between GC and SA is investigated. In contrast with the classical approach where the transition is a direct and abrupt change from the GC control mode to the SA mode, the Fuzzy Logic Algorithm (FLA) allows generating a feasible reference trajectory that ensures smooth transition between GC and SA modes through a unified control. Furthermore, the FL is employed to tune the voltage loop control in order to increase the disturbance rejection ability of the voltage loop. Also, the control design and the trajectory planning principle are detailed. The effectiveness of the proposed control is validated by simulation tests and its performance is compared to a conventional control scheme.

Integrated guidance and control strategy for homing of unmanned underwater vehicles

This paper presents a novel integrated guidance and control strategy for homing of unmanned underwater vehicles (UUVs) in 5-degree-of-freedom (DOF), where the vehicles are assumed to be underactuated at high speed and required to move towards the final docking path. During the initial homing stage, the guidance system is first designed by geometrical analysis method to generate a feasible reference trajectory. Then, in the backstepping framework, the proposed trajectory tracking controller can achieve all the tracking errors in the closed-loop system convergence to a small neighbourhood of zero. It means that the vehicle's dynamics are consistent with the reference trajectory derived in the previous step. To demonstrate the effectiveness of the proposed guidance and control strategy, the complete stability analysis used Lyapunov's method is given in the paper, and simulation results of all initial conditions are presented and discussed.

A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes

SummaryIn this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.

A unique robust controller for tracking and stabilisation of non-holonomic vehicles

ABSTRACT It is known that for non-holonomic systems it is impossible to design a universal controller able to asymptotically stabilise any feasible reference trajectory. We present a smooth time-varying controller able to stabilise a wide class of reference trajectories that include converging (parking problem) and persistently exciting (tracking problem) ones, as well as set-points. For the first time in the literature we establish uniform global asymptotic stability for the origin of the closed-loop system in the kinematics state space. We also show that the kinematics controller renders the system robust to perturbations in the sense of integral-input-to-state stability. Then, we show that for the case in which the velocity dynamics equations are also considered (full model), any velocity-tracking controller with the property that the error velocities are square integrable may be used to ensure global tracking or stabilisation even under parametric uncertainty.

Two-Step System Identification and Trajectory Tracking Control of a Small Fixed-Wing UAV

An approach for obtaining dynamically feasible reference trajectories and feedback controllers for a small unmanned aerial vehicle (UAV) based on an aerodynamic model derived from flight tests is presented. The modeling method utilizes stepwise multiple regression to determine relevant explanatory terms for the aerodynamic coefficients. A dynamically feasible trajectory is then obtained through the solution of an optimal control problem using pseudospectral optimal control software. Discrete-time feedback controllers are further designed to regulate the vehicle along the desired reference trajectory. Simulations in a realistic operational environment as well as flight testing of the feedback controllers on the aircraft platform demonstrate the capabilities of the approach.

Attitude tracking of a rigid spacecraft using two internal torques

The attitude-tracking control of a rigid spacecraft using only two internal torques is addressed. First, a given reference trajectory is classified as feasible or unfeasible according to the preservation or violation of the momentum conservation law. The dynamics of the attitude-tracking error is then formulated on the attitude manifold SO(3) with the angular momentum of the actuators as inputs. Given the Lie group structure of SO(3), the transverse function approach is utilized to design an attitude-tracking law ensuring asymptotically ultimately bounded tracking error for any reference trajectory. For feasible reference trajectories satisfying certain persistence conditions, asymptotic tracking is achieved by constructing an asymptotically stable zero dynamics for the closed-loop system. To deliver control torques to the actuator command signals, steering laws are designed for two reaction wheels, two single-gimbal control moment gyros mounted in parallel, and one variable-speed control moment gyro, respectively. The resulting control law can be applied to a spacecraft with different kinds of momentum actuators but underactuated for tasks ranging from bounded tracking of a generic trajectory, three-axis earth pointing to line-of-sight pointing, etc. Numerical examples are presented to verify the effectiveness of the proposed method.

Variation-Based Linearization of Nonlinear Systems Evolving on $SO(3)$ and $\mathbb S^{2}$

In this paper, we propose a variation-based method to linearize the nonlinear dynamics of robotic systems, whose configuration spaces contain the manifolds S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and SO(3), along dynamically feasible reference trajectories. The proposed variation-based linearization results in an implicitly time-varying linear system, representing the error dynamics, that is globally valid. We illustrate this method through three different systems: 1) a 3-D pendulum: 2) a spherical pendulum; and 3) a quadrotor with a suspended load, whose dynamics evolve on SO(3), S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and SE(3) × S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively. We show that for these systems, the resulting time-varying linear system obtained as the linearization about a reference trajectory is controllable for all possible reference trajectories. Finally, a linear quadratic regulator-based controller is designed to attenuate the error so as to locally exponentially stabilize tracking of a reference trajectory for the nonlinear system. Several simulations results are provided to validate the effectiveness of this method.

Adaptive sliding mode control of a wheeled mobile robot towing a trailer

Tractor–trailer systems have been widely used to increase load transportation capacity. Control of these systems started from motion aid facilities in human-driven vehicles to fully autonomous mobile robots in recent years. In fact, tractor–trailer wheeled robot has been proposed as a modular robotic system in which an actuated mobile robot tows a passive trailer. This is a highly nonlinear underactuated system subjected to nonholonomic kinematic constraints, stable tracking control of which is investigated in this article. To this end, first dynamic model and nonholonomic constraints of the system will be developed in the presence of uncertainties and external disturbances. Next, feasible reference trajectories for the system are generated considering the system constraints, and a Lyapunov kinematic control law is used to stabilize tracking errors. Then, an adaptive dynamic sliding mode controller is presented to control the wheeled mobile robot in the presence of external disturbances and uncertainties. Appropriate adaptive rules based on vigorous Lyapunov stability theorems are designed to compensate the wheeled mobile robot upper-bounded lumped uncertainties and automatically update controller gains. Next, the experimental setup is described, and the obtained results are presented and discussed. Experimental and comparative results reveal merits of the proposed approach in successful control of the overall system, that is, a wheeled mobile robot towing a passive trailer, leading to asymptotic tracking of reference trajectories.

Robust Adaptive Controller for a Tractor–Trailer Mobile Robot

A tractor-trailer wheeled robot (TTWR) is a kind of modular robotic system that consists of a tractor template attached with a single or multiple trailers, and hence it is a nonlinear and underactuated system subjected to nonholonomic constraints. Tracking control of such a complicated system is a challenging problem, and that is the focus of this paper. To this end, first dynamics model of a TTWR is developed. Next, feasible reference trajectories are generated to define a trajectory tracking problem. Then, a Lyapunov kinematic control law is elaborated to stabilize tracking errors. Subsequently, a feedback linearizing dynamic controller (FLDC) is designed to generate actuator torques. In a wheeled mobile robot (WMR), like most of real engineering applications, it is impossible to obtain an exact dynamics model due to various unknown, or unpredictable and irregular features. Therefore, the robustness of controllers to overcome uncertainties and external disturbances is necessary. So, a robust adaptive feedback linearizing dynamic controller (RAFLDC) is proposed to control the system using estimated upper-bounds of uncertainties. The stability of the control algorithm is verified using the Lyapunov method. Robustness and effectiveness of the proposed controller, and comparison of results for RAFLDC and FLDC algorithms, is investigated using both simulation studies and experimental implementations, and obtained results will be discussed.

Formation control of multiple elliptical agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation. The controllers guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on an algebraic separation condition between ellipses, Lyapunov’s method, and smooth or p-times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings under the agents’ limited sensing ranges.

Formation control of multiple elliptic agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptic shape and limited sensing ranges to perform a desired formation and that guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on explicit algebraic separation conditions between ellipses, root conditions of cubic polynomials, the Lyapunov direct method, and smooth or p-times differentiable step functions. These functions are incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings despite the agents' limited sensing ranges. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society