Global Trajectory Tracking Control Research Articles

Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups

The trajectory tracking problem is a fundamental control task in the study of mechanical systems. Hamiltonian systems are posed on the cotangent bundle of configuration space of a mechanical system, however, symmetries for the full cotangent bundle are not commonly used in geometric control theory. In this paper, we propose a group structure on the cotangent bundle of a Lie group and leverage this to define momentum and configuration errors for trajectory tracking, drawing on recent work on equivariant observer design. We show that this error definition leads to error dynamics that are themselves “Euler-Poincare like” and use these to derive simple, almost global trajectory tracking control for fully-actuated Euler-Poincare systems on a Lie group state space.

Uncertainty and disturbance estimator‐based geometry tracking control for quadrotors without linear velocity measurements

AbstractThis paper addresses the trajectory tracking control problem of a quadrotor under uncertain model parameters, external disturbances, and unmeasurable linear velocity. The main contribution of this paper is to present a geometric control strategy with a simple structure and easily adjustable parameters, which combines the differentiator and uncertainty and disturbance estimator techniques to achieve global trajectory tracking control. First, a cascade control framework is introduced to solve the strong coupling and underactuated problems of quadrotors. Furthermore, an antidisturbance outer‐loop differentiator‐based position controller is designed based on the uncertainty and disturbance estimators (UDE) to achieve accurate quadrotor tracking of the desired trajectory. The higher order control inputs of the translational dynamics are estimated using a differentiator to determine the desired angular velocity and its derivative. Then, a robust inner‐loop geometric controller is derived in Lie algebraic space using the rotation matrix. After that, the stability analysis of the closed‐loop system is executed using the Lyapunov stability theory. Finally, the numerical simulation verifies that the method enables the quadrotor to have strong robustness and excellent tracking capability in the presence of large initial angles, time‐varying disturbances, and unmeasured linear velocity.

Lyapunov based global trajectory tracking control of wheeled mobile robot

This paper considers the global trajectory tracking control problem of wheeled mobile robot. A novel tracking controller for the kinematic model of wheeled mobile robot is presented based on the cascaded approach theory. Meanwhile, by using the Lyapunov stability theory, the stability of the controller is proved. Finally, the proposed scheme is implemented on the wheeled mobile robot. The simulation results show the effectiveness of the controller.

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

On global trajectory tracking control of robot manipulators with a delayed feedback

In this paper, the trajectory tracking control problem of a robot manipulator with cylindrical joints is considered by means of a nonlinear PD controller taking into account the delayed feedback structure. The conclusion about stability of a closed-loop system is obtained on the basis of the development of the direct Lyapunov method in the study of the stability property for a non-autonomous functional differential equation by constructing a Lyapunov functional with a semi-definite time derivative.

Finite‐time rotation‐matrix‐based tracking control for autonomous underwater vehicle with input saturation and actuator faults

AbstractThis article tackles the finite‐time global trajectory tracking control problem of the autonomous underwater vehicle (AUV) in presence of input saturation constraints, actuator faults, unknown dynamics, and external disturbances. First, we describe the orientation of the AUV by rotation matrix instead of classical Euler angle or unit quaternion such that the AUV's dynamics could be globally formulated without singularity and unwinding phenomenon. After that, a smooth dead zone‐based model is introduced here to linearize the actuator model, leaving that the adaptive laws could be suitable for the solution of input saturation and actuator faults. Considering that the difficulty of model dynamic acquirement, together with the complicity of rotation‐matrix‐based representation, would trouble deployment of the controller. The minimum learning parameter technology is thereby utilized to approximated the dynamic nonlinearity of the AUV. On the basis of these, a rotation‐matrix‐based sliding mode control scheme is technically proposed. It is proved that the tracking errors can be stabilized to a small neighborhood of origin within a settling time. Finally, several set numerical experiments are conducted to assess the effectiveness and show the advantages of the proposed control scheme.

Event‐triggered global trajectory tracking control of a quadrotor: Synthesis, simulations, and experiments

AbstractThis paper presents an event‐triggered controller that solves the problem of trajectory tracking for an aerial vehicle with thrust actuation in a single body‐fixed direction and full angular velocity actuation. Firstly, we design a globally stabilizing hybrid controller and then, using the framework of hybrid dynamical systems, we derive an appropriate event‐triggering mechanism for sampling actuation signals. We prove the global asymptotic stability of a zero tracking error set for the closed‐loop system. For practical implementation of the proposed event‐triggered controller on digital platforms, we restrict the event‐triggering condition and inflate the zero tracking error set to avoid Zeno solutions while achieving global asymptotic stability of the inflated set for the closed‐loop system. The results are illustrated by numerical simulations and further verified by experiments.

Uncertainty and Disturbance Estimator-Based Global Trajectory Tracking Control for a Quadrotor

This article presents an uncertainty and disturbance estimator (UDE) based global trajectory tracking control strategy for a quadrotor. The main contribution of this article is the fusion of the UDE technique with the unit quaternion to achieve the robust global full degrees of freedom trajectory tracking control with experimental demonstrations. The novelty of this article lies in the development of the UDE-based global tracking technique to the overall system (attitude and position) with a quaternion-based nonlinear reference model. The UDE-based attitude and position controllers are derived from the unit quaternion-based quadrotor dynamics with a cascade control structure to deal with underactuation, model uncertainties, and external disturbances. The attitude controllers that are developed with the backstepping techniques avoid the rotation matrix calculation and the unwinding problem. The position controllers are derived using the thrust-vectoring approach. A nonlinear unit quaternion-based reference model is developed to achieve the time-scale separation for the cascade control loops. The stability analysis of the closed-loop system is conducted with the Lyapunov method. Extensive flight experiments are conducted to demonstrate the global singularity-free tracking property and the superior robustness of the proposed controller.

Finite-Time Global Trajectory Tracking Control for Uncertain Wheeled Mobile Robots

In this article, a finite-time global trajectory tracking control is proposed for a class of uncertain wheeled mobile robot systems. It could ensure that the system output tracks the desired trajectory within finite-time. Combined with the dynamic model, the tracking error model is decomposed into an angular velocity error subsystem and a position error subsystem. The finite-time theory is applied to the design of finite-time control law and the stability analysis for the angular velocity error subsystem. Moreover, Backstepping technology is introduced into the position error subsystem. In addition, Fuzzy Logic Systems (FLSs) are investigated to approximate system's unknown smooth function. Theoretical analysis shows that all signals are bounded, and the system has global progressive stability. The simulation verifies the effectiveness of the proposed method.

On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass

On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass

On global trajectory tracking control of robot manipulators in cylindrical phase space

ABSTRACT In this paper a novel approach to the global trajectory tracking control problem for manipulators is presented. The generalised coordinates of such mechanical systems include the link angles, that makes it possible to consider the trajectory tracking control problem in a cylindrical phase space. We propose a design procedure for nonlinear controller with computed feedforward of robot manipulators. Stability proof of the closed-loop system is given by constructing the Lyapunov function which is periodic in angular coordinates with a semi-definite time derivative and using the quasi-invariance principle for non-autonomous systems of ordinary differential equations. We illustrate the implementation of the controller using simulation example.

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.

On Global Trajectory Tracking Control of Robot Manipulators with Flexible Joints

Abstract In this paper a novel approach to the global trajectory tracking control problem for manipulators with flexible joints is presented. The dynamic model of such mechanical systems has a cascade structure that allows to decouple the links dynamics from the actuators ones. We propose a design procedure for nonlinear controller with computed feedforward of robot manipulators with revolute joints in a cylindrical phase space. Stability proof of the closed-loop system is given by constructing a Lyapunov function which is periodic on angular coordinates. We illustrate the implementation of the controller using simulation example.

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.

Modeling and global trajectory tracking control for an over-actuated MAV

This paper deals with an original micro aerial vehicle (MAV) design, the Omnicopter MAV. It has two central coaxial rotors with fixed-pitch propellers and three perimeter mounted ducted fans with servo motors performing thrust vectoring. Compared with traditional rotary wing MAVs that have inherent underactuation, the Omnicopter possesses some advantages in mobility, for example, lateral translation with zero attitude and hover with nonzero attitude. The trajectory tracking control design, global stability analysis, and control allocation are demonstrated through numerical simulation. The advantage of zero attitude translation is illustrated through experimental results.