Smooth Time-varying Control Research Articles

Robust PID consensus-based formation control of nonholonomic mobile robots affected by disturbances

In this work, we report a novel controller to solve (globally) the position and orientation consensus-based formation problem of multiple nonholonomic vehicles modelled as differential drive robots affected by external disturbances. The controller has the structure of a simple to implement Proportional Integral Derivative (PID) scheme. In order to satisfy the well-known Brocket stabilisation theorem for nonholonomic systems, we also incorporate a time-varying persistency of excitation term in the angular velocity dynamics. Our proposal reports the first solution to the robust formation problem using a smooth time-varying controller. Simulations are shown to evidence the theoretical findings of this work.

Cascades-Based Leader–Follower Formation Tracking and Stabilization of Multiple Nonholonomic Vehicles

It is known that nonholonomic systems on the plane cannot be stabilized on arbitrary leader's trajectories with piecewise continuous velocities via continuous controllers, even time-varying. In this article, we identify a wide class of smooth bounded reference trajectories (that includes set-points), and we propose a smooth time-varying controller that stabilizes such trajectories, not only for one nonholonomic mobile robot, but also for a network of mobile robots in a leader-follower configuration. We provide new constructions of strict Lyapunov functions with which we establish uniform global asymptotic stability and other strong robustness properties in the formation-error-coordinates space. Thus, our stability statements are unique in the literature and our tools of analysis are original.

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.

A new formation control of multiple underactuated surface vessels

ABSTRACTThis work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example.

The Exponential Stabilization of Uncertain Chained Form Systems of Mobile Robots Based on Visual Servoing

A system for a type of nonholonomic wheeled mobile robots equipped with an uncalibrated camera fixed to the ceiling is investigated. Based on the visual feedback and the state-input transformation, models of uncertain chained form systems are presented for the robot-camera systems. Then, new smooth time-varying feedback controllers are proposed to exponentially stabilize the uncertain chained system by using state-scaling and control theories for two cases. The exponential stabilities of the closed-loop uncertain systems are rigorously proved. Simulation results demonstrate the effectiveness of the proposed strategies.

Simultaneous Stabilization and Tracking of Nonholonomic Mobile Robots: A Lyapunov-Based Approach

A smooth time-varying controller is proposed to simultaneously address the stabilization and tracking problems of nonholonomic mobile robots for most admissible reference trajectories without switching. The controller is developed with the aid of a delicately designed time-varying signal and Lyapunov method. Computational simplification and asymptotic convergence of regulation or tracking errors are achieved by the proposed controller. Our approach provides an interesting way to unify the existing results on point stabilization and trajectory tracking of mobile robots. The simulation and experimental results on a wheeled mobile robot are presented to demonstrate the effectiveness of the proposed controller.

Motion-Estimation-Based Visual Servoing of Nonholonomic Mobile Robots

A 2-1/2-D visual servoing strategy, which is based on a novel motion-estimation technique, is presented for the stabilization of a nonholonomic mobile robot (which is also called the “parking problem”). By taking into account the planar motion constraint of mobile robots, the proposed motion-estimation technique can be applied in both planar and nonplanar scenes. In addition, this approach requires no matrix estimation or decomposition, and it avoids ambiguity and degeneracy problems for the homography or fundamental matrix-based algorithms. Moreover, the field-of-view (FOV) constraint of the onboard camera is largely alleviated because the presented algorithm works well with few feature points. In order to incorporate the advantages of position-based visual servoing and image-based visual servoing, a composite error vector is defined that includes both image signals and the estimated rotational angle. Subsequently, a smooth time-varying feedback controller is adopted to cope with the nonholonomic constraints, which yields global exponential convergent rate for the closed-loop system. On the basis of the perturbed linear system theory, we show that practical exponential stability can be achieved, despite the lack of depth information, which is inherent for monocular camera systems. Both simulation and experiment results are collected to investigate the feasibility of the proposed approach.

Local Exponential Regulation of Nonholonomic Systems in Approximate Chained Form with Applications to Off-Axle Tractor-Trailers

Most of drift-less nonholonomic systems cannot be exactly converted to an nonholonomic chained form, a wealth of design tools developed for the control of nonholonomic chained form are thus not directly applicable to such systems. Nevertheless, there exists a class of systems that may be locally approximated by the nonholonomic chained form around certain equilibrium points. In this work, we propose a discontinuous and a smooth time-varying control laws respectively for the approximated nonholonomic chained form, guaranteeing local exponential convergence of state to the desired equilibrium point. An tractor towing off-axle trailers is taken as an example to illustrate the approaches.

Sufficient Conditions for Closed-Loop Asymptotic Controllability and Stabilization by Smooth Time-Varying Feedback Integrator

For general finite-dimensional time-varying nonlinear systems, we derive sufficient conditions for closed-loop asymptotic controllability and asymptotic stabilization by means of a smooth ordinary time-varying feedback integrator. The main hypotheses are based on the existence of an almost smooth time-varying control Lyapunov function. The corresponding results generalize earlier works in the literature concerning dynamic stabilization for autonomous systems.

A time-varying cascaded design for trajectory tracking control of non-holonomic systems

This paper deals with the tracking control problem of a general class of nonholonomic dynamic systems with reference signals that may exponentially decay. By introducing a time-varying coordinate transformation and using the cascaded-design approach, smooth time-varying controllers are constructed, which render the tracking error dynamics globally -exponentially stable. The result shows that the persistent-excitation condition or not coverging to zero for reference signals is not necessary even for the globally -exponential tracking of nonholonomic systems. The proposed method is applied to the tracking control of an underactuated surface vessel.

Smooth time-varying stabilization of driftless systems over communication channels

We address the problem of smooth time-varying stabilization of port-interconnected driftless passive systems. The benchmark that we study is reminiscent of driftless systems interconnected over communication channels and constitutes a generalization of the well-known chained-form nonholonomic systems. Our contribution consists in proposing a smooth time-varying controller that guarantees uniform global asymptotic stability; moreover, a necessary condition is also stated. Both the sufficient and necessary conditions are formulated in terms of the so-called δ -persistency of excitation previously used in set-point control of nonholonomic systems. The proof of sufficiency relies on a recently reported extended Matrosov's theorem which may be regarded as an extension of Krasovskı˘i-La Salle's invariance principle to the case of nonautonomous systems.

Control of a planar space robot: Theory and experiments

In this paper the attitude control problem of planar space robot is addressed and new feedback control scheme is proposed. Since control laws are synthesized via theory of geometric phase, the proposed control laws contain smooth functions of states and time. The usefulness and validity of this control scheme can be demonstrated by hardware experiments. In experiments to simulate the space environment prototype of the planar space robot is floated by air on the horizontal plane. Experimental results show that the proposed smooth time-varying control laws stabilize the attitude of the planar space robot sufficiently.

Global time-varying stabilization of underactuated surface vessel

This note considers the stabilization problem of an underactuated surface vessel. Three global smooth time-varying control laws are proposed with the aid of different techniques. The first proposed control law makes the state of the closed-loop system asymptotically converge to zero, while the second and the third control laws make the state of the closed-loop system globally exponentially converge to zero. Moreover, the exponential convergence rate of the state of the closed-loop system can be arbitrarily assigned with the third control law. Simulation results show that the proposed control laws are effective.

Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control

A general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems, extended power systems, underactuated surface vessel systems etc. By introducing an assistant state variable and a time-varying state transformation based on the concept of minimal dilation degree, this class of nonholonomic systems is transformed into linear time-varying control systems, and the asymptotic exponential stability is thus achieved by using a smooth time-varying feedback control law. The existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions.

UGAS of Skew-symmetric Time-varying Systems: Application to Stabilization of Chained Form Systems

The contribution of this communication is twofold: firstly, we will present a theorem guaranteeing uniform global asymptotic stability of a class of stable nonlinear systems, known in the literature of nonholonomic systems as skew-symmetric. These are systems of the form x ˙ = − A ( t , x ) x where A ( . , . ) e R n × n is skew-symmetric except for the (1,1) element which is non-zero. Secondly, we extend previous results for the nonholonomic integrators to the case of systems with n>3 states. Our smooth time-varying controllers are called δ-persistently exciting since they are based on a property which generalizes for nonlinear functions of the state, the persistency of excitation concept originally defined for time functions, in the context of systems identification.

UGAS of Skew-Symmetric Systems: Application to the Nonholonomic Integrator

The contribution of this communication is twofold: firstly, we will present a theorem guaranteeing uniform global asymptotic stability of a class of stable nonlinear systems, known in the literature of nonholonomic systems, as "skew-symmetric"(the use of quotes"" is motivated by having one non-zero element in the main diagonal). Secondly, we extend previous results for the nonholonomic integrators to the case of systems with n > 3 states. Our smooth time-varying controllers are called δ-persistently exciting since they are based on a property which generalizes, for nonlinear functions of the state, the persistency of excitation concept originally defined in the context of systems identification for time functions.

Robust friction compensation for precise and smooth position regulation

In this paper, a smooth robust time-varying controller is proposed to regulate a servo-system with stick-slip friction. The controller has the advantage of simultaneously achieving zero regulating error and smoothness of motion. Only an upper bound on the maximum static friction torque is required for controller design. Lyapunov's second method is employed to prove the global asymptotic stability of the closed-loop system. Numerical simulations of regulating a servo-system with friction are presented as an illustration.