Fully-actuated System Research Articles

Predefined-Time Hybrid Tracking Control for Dynamic Positioning Vessels Based on Fully Actuated Approach

This study investigates the problem of tracking the trajectory of a dynamic positioning (DP) ship under sudden surges of elevated sea states. First, the tracking problem is reformulated as an error calibration problem through the introduction of fully actuated system (FAS) approaches, thereby simplifying controller design. Second, a predefined-time control term is designed to maintain the convergence time of the trajectory tracking error within a specified range; however, the upper bound of the perturbation must be estimated in advance. The high sea state during operation can result in an abrupt change in the upper bound of disturbance, thereby affecting the control accuracy and stability of the system. Therefore, a linear control matrix is developed to eliminate the system’s dependence on the estimation of the upper bound of disturbance following smooth switching, thereby achieving control decoupling and providing a conservative switching time. Additionally, a nonlinear reduced-order expansion observer (RESO) is constructed for feedforward compensation. The stability of the system is demonstrated using the Lyapunov function, indicating that the selection of appropriate poles can theoretically enhance the system’s convergence with greater control accuracy and robustness after switching. Finally, the effectiveness of the proposed method is validated through simulations and comparative experiments.

Adaptive RISE-based tracking control of uncertain nonlinear systems: A FAS approach

A fully actuated system (FAS) approach integrated with adaptive robust integral of the sign of the error (ARISE) feedback control strategy is proposed for multi-input multi-output nonlinear systems in the presence of both external disturbances and parametric uncertainties. Owing to an inability to eliminate unmeasured disturbances and model inaccuracies simultaneously, the existing results based on the FAS approaches are typically limited to the uniformly ultimate boundedness of the tracking errors. To achieve the asymptotic tracking performance confronted with parametric uncertainties and time-varying disturbances, an ARISE feedback controller with desired compensation is synthesized to suppress the adverse effects arising from nonlinearity and uncertainty of the system. The improvements compared to the traditional RISE feedback control are attributed to two aspects: (i) the feedback gains in the RISE term are adjustable-online without having to know the prior bounds of disturbances and their time derivatives; (ii) a desired compensation-based adaptive feedforward term, primarily employing the desired trajectories in place of the measured states, could weaken the underlying interaction between the adaptive compensation and robustness part. A rigorous stability analysis is provided to demonstrate that the system state can asymptotically track a bounded desired trajectory in spite of bounded disturbances and parametric uncertainties. Comparative simulations on an under-actuated planar manipulator, possessing an equivalent multi-order FAS model, have been conducted to verify the effectiveness and merits of the developed controller. Experimental validation on a two-wheeled self-balancing robot is also provided to show the feasibility of the proposed approach.

Neuroadaptive high-order fully-actuated system approach for roll autopilot with unknown uncertainties

In this paper, a neuroadaptive high-order fully-actuated system approach control scheme incorporating the disturbance observer technique is proposed for the missile roll autopilot, subject to model uncertainties generated by the induced roll moment, along with actuator control efficiency deterioration and external disturbance. To address model uncertainties, the radial basis function neural network is implemented. The external disturbance and approximation error are treated as compound disturbances and estimated by a nonlinear disturbance. To avoid the “differential explosion” inherent in the backstepping technique, the high-order fully-actuated system approach is invoked to track the desired roll angle command. The semi-globally uniformly bounded of the closed-loop system is demonstrated via the Lyapunov method. Numerous simulations under various conditions have been conducted to verify the effectiveness of the proposed roll autopilot.

Finite-Time Fault-Tolerant Control via Fully Actuated System Approaches.

In this article, a finite-time fault-tolerant controller based on the fully actuated system (FAS) theory is presented to realize system stabilization and trajectory tracking. Paralleling to first-order nonlinear state space theory, the high-order FAS (HOFAS) theory contains rich controller design approaches. The existing FAS approaches can only give general global asymptotic stability results. In order to enhance the applicability of FAS approaches in fast control systems, a parameterized FAS stabilization controller based on the homogeneity principle is established for global finite-time stability. Moreover, a finite-time FAS tracking controller based on a finite-time observer is proposed for a HOFAS model with process faults. The proposed observer can yield zero-value convergence of state estimation error and fault estimation error in a finite time, and the proposed fault-tolerant controller can yield zero-value convergence of tracking error in a finite time. The main results are proved theoretically and illustrated experimentally.

Fully actuated system approach to robust control of uncertain multi‐order sub‐fully actuated systems

AbstractMotivated by the fully actuated system (FAS) approach, this paper proposes a direct robust control method for a type of uncertain multi‐order sub‐fully actuated systems (MOSFASs). Unlike numerous previous results, this paper broadens to a more general multi‐order model and the more challenging sub‐fully actuated case with the presence of singular problems. Firstly, a general uncertain MOSFAS model is presented, where the uncertainty merely needs to satisfy a common assumption. Secondly, a direct robust control method is proposed, giving a robust controller which only needs to satisfy very loose and basic requirements to ensure that the states ultimately converge into an arbitrarily small region. Simultaneously, by constraining the initial values of the states, it is perfectly guaranteed that the states always remain in a “safe” zone free of singular points, thus preserving the realizability of the controller. Finally, under certain conditions, a less conservative robust control scheme is introduced, which can relax the constraint of initial values easily. A simulation for a coarse‐fine angle system demonstrates the validity and value of the proposed robust control method.

Stabilisation of four types of underactuated systems: a FAS approach

ABSTRACT In this paper, four general types of time-varying underactuated systems (UASs) are proposed and investigated with the fully-actuated system (FAS) approach. The proposed UASs consist of both the first-order and the second-order ones, and cover a very wide range of UASs. FAS models for all these types of UASs are obtained under very mild assumptions, and corresponding homeomorphism or diffeomorphism transformations and sets of feasibility are also established. Governed by the FAS theory, once a FAS model of a system is obtained, a stabilising controller for the system can then be easily designed. Particularly, in the case that the set of feasibility coincides with the whole initial value space, a global FAS model is produced for which (and also the original system) global exponential stabilisation is immediately achieved. Otherwise, a sub-FAS with a feasible set is produced for which a sub-stabilising controller can be immediately designed. Meanwhile, a subset in the system initial value space, which is called the region of exponential attraction (REA), is characterised, such that all the solutions of converted sub-FAS starting from this domain are driven exponentially to the origin within the feasible set. Furthermore, in the case that the set of feasibility, or the REA, contains the origin as only a boundary point, the system possesses a ‘nonholonomic’ feature. Several examples are proposed to demonstrate the proposed approach and the power of the FAS approach.

Adaptive stabilisation of second-order strict-feedback systems based on FAS with tuning functions

This paper thoroughly investigates adaptive stabilisation for a specific class of second-order strict-feedback nonlinear systems. Drawing inspiration from the fully actuated system (FAS) approach, an adaptive control scheme incorporating FAS with tuning functions is proposed. Notably, this approach directly addresses second-order systems without the need for reducing them to first-order systems, streamlining the intricate procedures involved. To handle uncertain parameters within the system, a combined scheme of adaptive estimation and tuning functions is employed. Rigorous analysis using Lyapunov stability theory demonstrates that the designed controller ensures the system's asymptotic convergence to the equilibrium point, with all other signals in the closed-loop system bounded. Finally, two simulation experiments verify the effectiveness of the proposed strategy: numerical simulations compared with sliding mode control and backstepping control, and practical application on the single-link robotic arm with a comparative analysis against backstepping control.

Fully actuated system approach for spacecraft rendezvous system with actuator saturation

This paper explores the application of a fully actuated system (FAS) approach to a spacecraft rendezvous system with actuator saturation. A FAS model for the spacecraft rendezvous system is developed, followed by the design of an extended state observer (ESO) to estimate unmeasurable states and the system's nonlinear terms. The saturation issue is addressed using the convex hull method. By the designed ESO, a state feedback controller for the system is designed using the FAS approach, resulting in a constant linear closed-loop system whose eigenvalues can be arbitrarily assigned. This method simplifies the controller design process and provides a more accurate system model without the linearisation of nonlinear terms, thereby improving control accuracy. Simulation results show the effectiveness and usefulness of the proposed method.

High-order fully actuated system models for discrete-time strict-feedback systems with increasing dimensions

This work aims to propose a high-order fully actuated system (FAS) model for discrete-time strict-feedback systems with nonuniform dimensions. In most of existing works, the authors only consider strict-feedback systems with uniform dimension, i.e. all subsystems have the same dimension. In contrast, we assume that the subsystems may have different or nonidentical dimensions. In particular, the dimensions are assumed to be increasing. Both step-forward and step-backward FAS models for discrete-time strict-feedback systems with nonuniform dimensions are given, based on which the exponentially stabilised controllers can be directly obtained. We consider not only first-order strict-feedback systems but also second-order case.

Controllability and control for discrete periodic systems based on fully-actuated system approach

The problem of controllability and control of linear discrete-periodic systems is investigated in this paper. The high-order fully-actuated models for linear discrete periodic time-varying systems are constructed, and a controllability criterion based on fully-actuated system models is proposed. On this basis, stabilization as the fundamental issue is studied and periodic state-feedback control laws are designed via fully-actuated systems approach and parametric design, which converted the original problem into the pole assignment problem for linear constant systems. Finally, a numerical example is given to verify the validity and feasibility of the proposed method.

Prescribed-time fault-tolerant control for the formation of quadrotors based on fully-actuated system approaches

This paper investigates the problem of prescribed-time fault-tolerant control for the formation of quadrotors by utilising the fully-actuated system approach. Since not all quadrotors can directly access the virtual leader's state, a distributed prescribed-time observer is designed to estimate the state of a virtual leader. Leveraging this observer, a horizontal position controller that combines the fully-actuated system approach with the prescribed-time method, as well as altitude and attitude fault-tolerant controller, are proposed. In the design of control law, two distinct sets of controllers are designed: asymptotically stable controller and prescribed-time controller, each tailored to specific control objectives. The proposed distributed prescribed-time observer can ensure that the estimation error of the leader's state reaches zero within any specified time interval. Finally, the numerical simulation is conducted to demonstrate the effectiveness of the proposed fault-tolerant formation control algorithm.

Comprehensive reconstructions and predictive control for quadrotor UAV information gathering tracking missions based on fully actuated system approaches

This paper introduces a novel approach to the comprehensive reconstruction and predictive control (PC) of the quadrotor UAV for information-gathering missions, employing fully actuated system (FAS) approaches. Unlike conventional PC methods applied to a quadrotor UAV with hybrid constraints, our work integrates reconstructions of the system model, hybrid constraints, and the receding horizon performance index into to an integrated tracking control scheme within the FAS-PC framework. Specifically, the under-actuated quadrotor UAV model is reconstructed into a full-actuated model to inject full-actuation properties. And the implicit hybrid constraints that arise from the model reconstruction are explicitly transformed and decoupled. Simultaneously, the cascaded predictive algorithm is established that the new time-varying input constraints are solved in each predictive horizon, and then the nonlinear optimization problem is decoupled into four linear convex optimization problems subject to the corresponding decoupled linear constraints and the pre-addressed input constraints. Within this framework, the intrinsic complexities, nonlinearities, and interdependencies of the quadrotor UAV system model, along with hybrid constraints and the optimization dilemma, are considerably diminished. This reduction significantly eases computational demands, enabling satisfactory real-time performance. Furthermore, the selection of predictive parameters guarantees the stability of the resultant tracking error closed-loop system. Finally, the efficacy of the proposed method is validated through two sets of flight missions, conducted via simulation and practical experimentation, respectively.

Optimal Fully Actuated System Approach-Based Trajectory Tracking Control for Robot Manipulators.

In this article, a trajectory tracking control strategy is proposed for robot manipulators via a fully actuated system (FAS) approach, which has shown its simplicity and flexibility for most of the nonlinear controller design. However, the motion control for robot manipulators is more complicated since unknown dynamical model, external disturbances, friction forces, and various physical constraints are required to be considered. Therefore, the FAS approach cannot be straightforwardly applied. To address these challenges, the dynamic model of robot manipulators is established via model identification methods. Furthermore, based on the identified model, an FAS composite control strategy with simple structure is designed, which is achieved by integrating a high-order disturbance observer (HODO) in the inner loop, with an FAS trajectory tracking controller in the outer loop. Specifically, the HODO is utilized for handling the uncertain dynamics and external disturbances. Moreover, the controller gains are optimized using a gradient-based optimal parameter tuning method (OPTM). By imposing joint angle constraints, joint angular velocity constraints, and input torque limits into the formulation, the OPTM also ensures the satisfaction of these physical constraints. Numerical simulations and experiments are provided to validate the performance of the proposed controller.

Event-Triggered Adaptive Control of Uncertain Strict-Feedback Nonlinear Systems Using Fully Actuated System Approach.

In most existing results, event-triggered controllers are designed based on the backstepping design approach for uncertain strict-feedback nonlinear systems (SFNSs). However, the transmitted signals in the event-triggered scheme (ETS) are discontinuous, which makes the repetitive differentiation of virtual control signals undefined. To overcome this deficiency, this article designs an event-triggered adaptive controller for uncertain SFNSs based on the fully actuated system (FAS) approach. Since the system states and the adaptive parameters are only updated at each triggering instant, the original dynamics cannot be completely removed by using the FAS approach, leading to that the asymptotic stability of the control system is difficult to be guaranteed. To handle such a problem, an ETS with the adaptive parameters is constructed based on Lyapunov method to compensate the effect of triggering. As a result, the asymptotic stability of the system can be guaranteed in the presence of nonlinearities without the global Lipschitz condition, and Zeno behavior can be avoided by using the contradiction method. Furthermore, a positive lower bound for interevent intervals can be got by adding a constant into the ETS, which ensures that the system is practically stabilizable under the bounded nonlinearities. Finally, two simulation examples are presented to demonstrate the superiority and effectiveness of the proposed approach.

Robust Stabilization of Time-Varying Nonlinear Systems With Time-Varying Delays: A Fully Actuated System Approach.

A general time-varying nonlinear uncertain system with time-varying delays is proposed, which is composed of two subsystems: one is an uncertain fully actuated subsystem representing the controllable part in the system, the other is an isolated globally uniformly asymptotically (GUA) stable autonomous subsystem which represents the uncontrollable part in the system. Both the single-order fully actuated system (FAS) and the multiorder FAS representations of the controllable subsystem are introduced. The problem of robust stabilization of such a compound system with full-state feedback can be converted into an input-to-state GUA stabilization problem of the fully actuated subsystem, which is solved for both types of single- and multiorder FASs with very general assumptions on the uncertain perturbed functions. Under certain conditions, the solution reduces to that for robust stabilization with partial-state feedback, and naturally reduce to that for robust stabilization of FASs. Two illustrative examples demonstrate both the effect and the application procedure of the proposed robust stabilization approach.

Impact angle constraint guidance law using fully-actuated system approach

Aiming at the terminal impact-angle constraint in the interception of large maneuvering targets, this paper proposes a three-dimensional (3D) interception guidance law combined with the high-order fully-actuated system approach and the cascaded linear extended state observer (LESO). First, a complete second-order nonlinear model with full actuated characteristics is developed for the missile-target relative dynamics without small-angle assumption. Subsequently, the nonlinear system is transformed into a quasi-feedback system, and then, a high-order fully-actuated model is developed. A cascaded LESO able to estimate the system state and target maneuver information is introduced, and the controller is designed to convert the closed-loop system into a linear time-invariant closed-loop system with the desired characteristic structure, which makes the closed-loop system have the desired closed-loop poles. Finally, the controller parameter matrix is solved using the desired closed-loop poles, and the convergence is validated by the Lyapunov stability theory. Consequently, the linearization of the 3D nonlinear system is realized, and the channel coupling is eliminated. The effectiveness of the proposed method is verified by simulation and analysis.

Leader-Following Formation Tracking Control of Nonholonomic Mobile Robots Considering Collision Avoidance: A System Transformation Approach

In this paper, the obstacle avoidance problem-based leader–following formation tracking of nonholonomic wheeled mobile robots with unknown parameters of desired trajectory is investigated. First, the under-actuated system is transformed into a fully-actuated system by obtaining an auxiliary control variable using the transverse function. Second, by introducing a potential function for each obstacle, the influence of obstacles is considered in trajectory tracking, and the effect of the potential field on mobile robots is taken into account in the system tracking error. Third, the adaptive laws are designed to estimate the unknown parameters of the desired trajectory. Fourth, the results show that the formation error with respect to the actual position and orientation can be arbitrarily small by selecting appropriate design parameters. Finally, simulation examples are used to demonstrate that the proposed control scheme is effective.

Attitude and Orbit Optimal Control of Combined Spacecraft via a Fully-Actuated System Approach

Attitude and Orbit Optimal Control of Combined Spacecraft via a Fully-Actuated System Approach

Fully-Actuated System Approach Based Optimal Attitude Tracking Control of Rigid Spacecraft with Actuator Saturation

Fully-Actuated System Approach Based Optimal Attitude Tracking Control of Rigid Spacecraft with Actuator Saturation

Research on the Trajectory Tracking Control of a 6-DOF Manipulator Based on Fully-Actuated System Models

Research on the Trajectory Tracking Control of a 6-DOF Manipulator Based on Fully-Actuated System Models