Trajectory Tracking Control Law Research Articles

Trajectory-Driven Adaptive Control of Autonomous Unmanned Aerial Vehicles with Disturbance Accommodation

This paper presents the development of direct adaptive control laws to enable an autonomous unmanned aerial vehicle (UAV) to track reference trajectories in the presence of external disturbances. A maneuver database of reference trajectories is computed offline from a linear UAV dynamic model using an optimization routine. Each maneuver in the database is therefore represented as a state trajectory, as well as the control input sequence that generates that trajectory. The trajectory tracking control laws are designed to enable a UAV to follow reference trajectories from this maneuver database. A disturbance accommodating control law is first developed and applied for the tracking of reference trajectories while the UAV is subjected to a persistent external disturbance. This control design requires a state-space disturbance generator model and the derivation of ideal trajectories from a reference model, which requires the solution of a set of matching conditions. A direct adaptive controller is then developed to enable the UAV to track reference trajectories while subject to modeling error and external disturbances. The adaptive controller also requires a disturbance model and the existence of ideal trajectories, but it does not require the explicit solution of the matching conditions. Simulation results for the disturbance accommodating controller and the adaptive controller are presented using a linear six-degree-of-freedom dynamic model that is representative of typical UAV dynamics. The results show that, although both controllers track reference trajectories and provide disturbance rejection, the adaptive controller is better suited for handling modeling errors or uncertainties.

Robust Tracking Control of Quadrotors Based on Differential Flatness: Simulations and Experiments

We introduce a new exponentially convergent trajectory tracking control law based on the fully nonlinear quadrotor model subject to unknown disturbances and modeling uncertainties. The approach takes advantage of the system's differential flatness property to relate the second time derivative of linear accelerations (snap) to the roll and pitch moments. Using these model-based relations, the closed-loop system is transformed to follow an exponentially stable error dynamics that are robust to unknown disturbances and uncertainties bounded on a compact set. It is proven that the control law exponentially stabilizes the position and yaw tracking errors, while the roll and pitch angle tracking errors are ultimately bounded. Simulations and experimental results under windy conditions and without disturbance estimation, demonstrate the effectiveness and robustness of the approach.

Global trajectory tracking control of underactuated surface vessels with non-diagonal inertial and damping matrices

This paper investigates the tracking control problem of underactuated surface vessels with non-diagonal inertia and damping matrices. Based on the inherent cascaded structure of vessel dynamics and the cascaded system theory, the tacking control problem of vessels is converted to the stabilization control problem of two cascaded subsystems. Two trajectory tracking control laws are designed respectively for known and unknown model parameters. The first feedback control law is derived with the aid of Lyapunov method, realizing the global $${\mathscr {K}}$$ -exponential trajectory tracking of vessels with accurate model parameters. As all the state variables in the first law are independent of model parameters, the sliding mode technique is applied to extend the first control scheme to the case of unknown model parameters, resulting into an another tracking control law, which ensures the global $${\mathscr {K}}$$ -exponential stability of the closed-loop error system despite unknown model parameters. Effectiveness of the proposed controllers is demonstrated by numerical simulations.

Sliding mode tracking control of autonomous underwater vehicles with the effect of quantization

This paper develops a trajectory tracking control law for autonomous underwater vehicles (AUVs) with the effect of states and control input quantization. A sliding mode control (SMC) scheme is proposed to conquer the quantization effect by introducing the bound of quantization error into the switching term of the SMC. A finite-time disturbance observer is proposed to observe the unknown time-varying disturbances. The stability analysis demonstrates that the designed tracking controller can force the AUV to track the reference trajectory and guarantee the asymptotic stability of the closed system. Simulation results illustrate the effectiveness of the proposed control method.

Intuitive dynamic modeling and flatness-based nonlinear control of a mobile robot

In this paper, a bond graph model of a mobile robot with four Mecanum wheels is developed to extract a dynamic model of the robot. This is achieved using the BG_V21 tool box of MATLAB. The dynamic model thus obtained is used to derive the control law for trajectory tracking by the robot. There are two control algorithms that are used, namely, the flatness-based controller and the backstepping controller. From the simulation results, it is evident that the extracted dynamic model of the robot is accurate. Moreover, the flatness-based controller proved to have the upper hand in performance over the backstepping controller.

Optimal control strategy based on neural model of nonlinear systems and evolutionary algorithms for renewable energy production as applied to biofuel generation

In the renewable energy generation, several processes require the integration of a set of advanced techniques in order to find optimal solutions. Dynamic estimation, stabilizing control for disturbance rejection, optimization for control effort, and parameter tuning are techniques used to address the whole process requirements and obtain optimal results. In this paper, an optimal control strategy for a maximum biofuel production in the presence of disturbances is proposed. First, an integrated optimal control strategy to maximize biofuel production in the presence of disturbances is proposed. Second, due to its high nonlinearity, complex nature, and multiplicity of equilibrium points, a biological process for biofuel generation is described in order to demonstrate the efficiency of the optimal control strategy. A nonlinear discrete-time neural observer for unknown nonlinear systems in the presence of external disturbances and parameter uncertainties is used to estimate unmeasurable variables. An inverse optimal control law for trajectory tracking based on the neural observer is designed such that asymptotic convergence reference trajectory is guaranteed. Differential Evolution and Clonal Selection Algorithms are used to calculate the optimal parameters for neural network training, neural network gains, and feedback control gains. Additionally, a supervisory fuzzy control is proposed in order to select the adequate control action between the closed loop and the open loop and to determine optimal reference trajectories. Simulation results comparison and statistical validation are presented, where it is demonstrated that the optimal control strategy integrated with the Differential Evolution algorithm gives better results to maximize the biofuel production in the presence of disturbances.

Adaptive Trajectory Tracking for Quadrotor MAVs in Presence of Parameter Uncertainties and External Disturbances

This paper presents an adaptive trajectory tracking control strategy for quadrotor micro aerial vehicles (MAVs). The proposed approach, while maintaining the common assumption of an orientation dynamics faster than the translational one, removes the assumption of absence of external disturbances and of geometric center coincident with the Center of Mass (CoM). In particular, the trajectory tracking control law is made adaptive with respect to the presence of external forces and moments (e.g., due to wind) and to the uncertainty of parameters of the dynamic model, such as the position of the CoM. A stability analysis is presented to analytically support the proposed controller, while numerical simulations are provided in order to validate its performance.

A robust back-stepping based trajectory tracking controller for the tanker with strict posture constraints under unknown flow perturbations

This paper proposes a novel robust back-stepping based trajectory tracking controller for the tanker with strict posture constraints under unknown flow perturbations in Autonomous Aerial Refueling (AAR). Firstly, by using the back-stepping technique, the proposed trajectory tracking control law design is separated into five loops. The 6 DOF model for tanker is tactfully transformed into several strict-feedback nonlinear forms, especially the dynamics of the translational kinematics which are originally non-affine nonlinear forms and are intractable for controller design. The influences of the unknown flow perturbations on tanker in each loop are viewed as the components of the “total disturbances” which are estimated and compensated by extended state observer (ESO). Secondly, the uncontrolled Euler angle constraints, which should also be considered in AAR, are transformed into extra boundary commands for the angular rates. And a novel command limiting tracking differentiator (CLTD), which considers not only the controlled but also uncontrolled state constraints, is specially designed for posture control. Thirdly, an integrated robust constrained posture control scheme is proposed for tanker's posture constraints based on Barrier Lyapunov (BL) function and CLTD. Then, with the position and ground velocity controller based on traditional active disturbance rejection control (ADRC) in the outer loop, a novel robust back-stepping based trajectory tracking controller is proposed for tanker in AAR. Finally, extensive simulations and comparisons on the 6 DOF tanker model are carried out to demonstrate the effectiveness of the proposed control scheme.

Tracking control of a marine surface vessel with full-state constraints

ABSTRACTIn this paper, a trajectory tracking control law is proposed for a class of marine surface vessels in the presence of full-state constraints and dynamics uncertainties. A barrier Lyapunov function (BLF) based control is employed to prevent states from violating the constraints. Neural networks are used to approximate the system uncertainties in the control design, and the control law is designed by using the Moore-Penrose inverse. The proposed control is able to compensate for the effects of full-state constraints. Meanwhile, the signals in the closed-loop system are guaranteed to be semiglobally uniformly bounded, with the asymptotic tracking being achieved. Finally, the performance of the proposed control has been tested and verified by simulation studies.

Observer-Based Adaptive Neural Network Trajectory Tracking Control for Remotely Operated Vehicle.

This paper focuses on the adaptive trajectory tracking control for a remotely operated vehicle (ROV) with an unknown dynamic model and the unmeasured states. Unlike most previous trajectory tracking control approaches, in this paper, the velocity states and the angular velocity states in the body-fixed frame are unmeasured, and the thrust model is inaccurate. Obviously, it is more in line with the actual ROV systems. Since the dynamic model is unknown, a new local recurrent neural network (local RNN) structure with fast learning speed is proposed for online identification. To estimate the unmeasured states, an adaptive terminal sliding-mode state observer based on the local RNN is proposed, so that the finite-time convergence of the trajectory tracking error can be guaranteed. Considering the problem of inaccurate thrust model, an adaptive scale factor is introduced into thrust model, and the thruster control signal is considered as the input of the trajectory tracking system directly. Based on the local RNN output, the adaptive scale factor, and the state estimation values, an adaptive trajectory tracking control law is constructed. The stability of the trajectory tracking control system is analyzed by the Lyapunov theorem. The effectiveness of the proposed control scheme is illustrated by simulations.

Energy Shaping for Tracking Control of 4-DOF Crane

In this paper the nonlinear tracking control methodology is proposed for 4–DOF (degree of freedom) overhead crane system using energy shaping. The 4–DOF underactuated overhead crane system has an extra DOF compared with the popular 3–DOF variant. The 4-DOF crane modeling represents strong state coupling and more complicated system dynamics which makes it challenging control problem. The control methodology begins with the first step of decoupling the crane dynamics into two subsystems using collocated partial feedback linearization. The passivating outputs of the modified subsystems are identified which are further utilized for energy shaping to obtain the nonlinear state feedback control law which effectively achieves the objective of trajectory tracking with fast elimination of payload swings. The energy shaping procedure obviates the need for solving PDEs to derive the control law. The trajectory tracking control law represents generalization of the position regulation problem. The simulation results are presented to validate the control law and superior performance is demonstrated over the existing control methodologies.

Rapid maneuvering of multi-body dynamic systems with optimal motion compensation

Rapid maneuvering of multi-body dynamical systems is an important, yet challenging, problem in many applications. Even in the case of rigid bodies, it can be difficult to maintain precise control over nominally stationary links if it is required to move some of the other links quickly because of the various nonlinearities and coupled interactions that occur between the bodies. Typical control concepts treat the multi-body motion control problem in two-stages. First, the nonlinear and coupling terms are treated as disturbances and a trajectory tracking control law is designed in order to attenuate their effects. Next, motion profiles are designed, based on kinematics parameterizations, and these are used as inputs to the closed loop system to move the links. This paper describes an approach for rapid maneuvering of multi-body systems that uses optimal control theory to account for dynamic nonlinearities and coupling as part of the motion trajectory design. Incorporating appropriate operational constraints automatically compensates for these multi-body effects so that motion time can be reduced while simultaneously achieving other objectives such as reducing the excitation of selected links. Since the compensatory effect is embedded within the optimal motion trajectories, the performance improvement can be obtained even when using simple closed-loop architectures for maneuver implementation. Simulation results for minimum time control of a two-axis gimbal system and for rapid maneuvering of a TDRS single-access antenna, wherein it is desired to limit the excitation of the satellite body to which the antenna is attached, are presented to illustrate the concepts.

UAV Flyable Trajectory Generation and Its Tracking Control

For the complex combat environment, considering the flyable performance constrains and the safety constrains, an online trajectory planning algorithm of UAVs(Unmanned Aerial Vehicles) based on Pythagorean Hodograph (PH) curve is put forward, which is easy to traced. When the unexpected obstacles are detected, based on the velocity obstacles avoidance method, the collision avoidance trajectory is planned online. The position of the interrupt point and the direction of the UAV turn are calculated. To fully use the PH trajectories performance that the curvature of the curve is continuous and precisely known, the location and crossing heading error equations were established within the Serret-Frenet coordinates. The corresponding asymptotically stable convergence backstepping trajectory tracking control law was designed based on the error formulations. The autonomous collision avoidance trajectory simulation result and its tracking control result show that the proposed trajectory generation method and the corresponding adaptive tracking control method are effective and can improve the tracking accuracy.

Nonlinear Dynamic Inversion and Neural Networks for a Tilt Tri-Rotor UAV

A small scale tri-rotor test bed with tilting propellers has been built to test flight control laws in view of the construction of a larger tilt rotor UAV. As a first step to achieve autonomous flight capabilities, a nonlinear dynamic inversion based flight controller is developed. This controller is designed on the basis of a time-scale principle with two levels. A lower level, fast control action, designed to achieve attitude control and stability goals, is driven by a higher level trajectory tracking control law. To achieve robust stability and performance in the presence of parametric variations and modelling uncertainties, an adaptive flight control law correction based on neural networks is investigated. A RBF neural network is implemented to mitigate the effects of imprecise inverse dynamics. The overall proposed flight controller performance are tested via numerical simulations on the mathematical model of the small scale tri-rotor. Preliminary results on the full tilt rotor are also shown.

Supervised coverage control of multi-agent systems

In this paper, we consider a dynamic coverage problem for multi-agent systems, where the main objective of a group of mobile agents is to explore a given compact region. We propose a novel control scheme, where we introduce a supervisor that assists a group of agents with the centralized coverage control law and the global trajectory tracking control law. The coverage control law ensures the coverage task is done until the agents end up in local minima, and when they do, the global trajectory tracking control law ensures that the agents are deployed to uncovered regions. Our control scheme is designed to be decoupled such that only one control law is active at a given time. In addition to the coverage objective, we design control laws for coverage agents to avoid collisions and maintain proximity to a supervisor. Moreover, we utilize feedback linearization to use the proposed control scheme for coverage control of kinematic unicycle agents. We validate our approach via numerical simulations.

A Designing Method of Underwater Controller Based on Trajectory-Tracking Control Law for Underwater Profile Monitoring Vehicle

An Underwater part including hardware and software of distributed controller for underwater profile monitoring vehicle is investigated. A finite-time tracking control law based on finite-time trajectory-tracking control method is proposed to make an automation control of the vehicle and a manual/auto swtiched distributed controller on Underwater Profile Monitoring Vehicle is desinged. We give the designing procedure of hardware and software of the controller.

Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing

Nowadays, autonomously operated nonholonomic vehicles are employed in a wide range of applications, ranging from relatively simple household chores (e.g. carpet vacuuming and lawn mowing) to highly sophisticated assignments (e.g. outer space exploration and combat missions). Each application may require different levels of accuracy and capabilities from the vehicles, yet, all expect the same critical outcome: to safely complete the task while avoiding collisions with obstacles and the environment. Herein, we report on a bounded control law for nonholonomic systems of unicycle-type that satisfactorily drive a vehicle along a desired trajectory while guaranteeing a minimum safe distance from another vehicle or obstacle at all times. The control law is comprised of two parts. The first is a trajectory tracking and set-point stabilization control law that accounts for the vehicle’s kinematic and dynamic constraints (i.e. restrictions on velocity and acceleration). We show that the bounded tracking control law enforces global asymptotic convergence to the desired trajectory and local exponential stability of the full state vector in the case of set-point stabilization. The second part is a real-time avoidance control law that guarantees collision-free transit for the vehicle in noncooperative and cooperative scenarios independently of bounded uncertainties and errors in the obstacles’ detection process. The avoidance control acts locally, meaning that it is only active when an obstacle is close and null when the obstacle is safely away. Moreover, the avoidance control is designed according to the vehicle’s acceleration limits to compensate for lags in the vehicle’s reaction time. The performance of the synthesized control law is then evaluated and validated via simulation and experimental tests.

Natural Storage Function for Passivity-Based Trajectory Control of Hydraulic Actuators

A passivity framework for hydraulic actuators is developed by considering the compressibility energy function for a fluid with a pressure-dependent bulk modulus. It is shown that the typical actuator's mechanical and pressure dynamics model can be obtained from the Euler-Lagrange equations for this energy function and that the actuator is passive with respect to a hydraulic supply rate which contains, in addition to the flow work (PQ), the compressibility energy also, which has often been ignored. A storage function for the pressure error is then proposed and the pressure error dynamics are shown to be a passive two-port subsystem. Trajectory tracking control laws are then derived using the storage function. A case study is presented to compare the new passivity-based approach and the traditional backstepping approach using a quadratic pressure error term. In this example, the proposed approach has one fewer parameter to tune, is less sensitive to velocity measurement error, and requires lower feedback gains than the traditional approach.

A modified genetic algorithm for UAV trajectory tracking control laws optimization

Purpose – The purpose of this paper is to gain trajectory-tracking controllers for autonomous aircraft are optimized using a modified evolutionary, or genetic algorithm (GA). Design/methodology/approach – The GA design utilizes real representation for the individual consisting of the collection of all controller gains subject to tuning. The initial population is generated randomly over pre-specified ranges. Alternatively, initial individuals are produced as random variations from a heuristically tuned set of gains to increase convergence time. A two-point crossover mechanism and a probabilistic mutation mechanism represent the genetic alterations performed on the population. The environment is represented by a performance index (PI) composed of a set of metrics based on tracking error and control activity in response to a commanded trajectory. Roulette-wheel selection with elitist strategy are implemented. A PI normalization scheme is also implemented to increase the speed of convergence. A flexible control laws design environment is developed, which can be used to easily optimize the gains for a variety of unmanned aerial vehicle (UAV) control laws architectures. Findings – The performance of the aircraft trajectory-tracking controllers was shown to improve significantly through the GA optimization. Additionally, the novel normalization modification was shown to encourage more rapid convergence to an optimal solution. Research limitations/implications – The GA paradigm shows much promise in the optimization of highly non-linear aircraft trajectory-tracking controllers. The proposed optimization tool facilitates the investigation of novel control architectures regardless of complexity and dimensionality. Practical implications – The addition of the evolutionary optimization to the WVU UAV simulation environment enhances significantly its capabilities for autonomous flight algorithm development, testing, and evaluation. The normalization methodology proposed in this paper has been shown to appreciably speed up the convergence of GAs. Originality/value – The paper provides a flexible generalized framework for UAV control system evolutionary optimization. It includes specific novel structural elements and mechanisms for improved convergence as well as a comprehensive PI for trajectory tracking.

Trajectory Tracking Control for Actuator Arrays

Actuator arrays are planar arrangements of actuators with two degrees of freedom that cooperatively translate and orient objects for efficient manipulation. This brief describes a trajectory tracking control law for macroscopic actuator arrays and its convergence properties. The control law is designed on the basis of the kinematics of an object on the array. Its convergence properties are found using a direct solution of the Kalman-Yakubovich-Popov equations. Simulations show that the control law is effective and that the bounds are useful for objects under no-slip contact. Experimental results from a 20-unit prototype array demonstrate the controller performance.