Nonholonomic Chained Systems Research Articles

Robust and Adaptive Stabilization Controllers of State-Constrained Nonholonomic Chained Systems: A Discontinuous Approach

In this paper, two systematic control design strategies are proposed for strict-feedback nonholonomic systems with full-state constraints to solve stabilization and adaptive stabilization problems. The stabilization schemes involve the introduction of state scaling, the barrier Lyapunov function (BLF), the integrator backstepping method, and the tuning function approach. In addition, a discontinuous switching control strategy is proposed to achieve the control goal if the first system state’s initial state is confined to zero. In both stabilization and adaptive stabilization control, the system states can be regulated at the origin, and meanwhile, the full-state constraints are realized. Finally, it is shown that the simulation results are consistent with the theory analysis results, which further demonstrates the effectiveness of the proposed control schemes.

Adaptive Output Feedback Control for Nonholonomic Chained Systems with Integral Input State Stability Inverse Dynamics.

This paper investigates a class of nonholonomic chained systems with integral input-to-state stable (iISS) inverse dynamics subject to unknown virtual control directions and parameter uncertainty included in drift terms. First, the system is divided into two interconnected subsystems according to the system's structure. Second, one controller is designed using a switch strategy for state finite escape. Then, another controller and adaptive law are designed by combining a reduced-order state observer and backstepping method after input-state scaling. Finally, simulation results validate the feasibility of the proposed control algorithm.

Fractional order uncertainty estimator based hierarchical sliding mode design for a class of fractional order non-holonomic chained system

This paper proposes a novel fractional order sliding mode control approach to address the issues of stabilization as well as tracking of an N-dimensional extended chained form of fractional order non-holonomic system. Firstly, the hierarchical fractional order terminal sliding manifolds are selected to procure the desired objectives in finite time. Then, a sliding mode control law is formulated which provides robustness against various system uncertainties or external disturbances. In addition, a novel fractional order uncertainty estimator is deduced mathematically to estimate and mitigate the effects of uncertainties, which also excludes the requirement of their upper bounds. Due to the omission of discontinuous control action, the proposed algorithm ensures a chatter-free control input. Moreover, the finite time stability of the closed loop system has been proved analytically through well known Mittag-Leffler and Fractional Lyapunov theorems. Finally, the proposed methodology is validated with MATLAB simulations on two examples including an application of fractional order non-holonomic wheeled mobile robot and its performances are also compared with the existing control approach.

Model Predictive Control of Nonholonomic Chained Systems Using General Projection Neural Networks Optimization

In this paper, a class of nonholonomic chained systems is first converted into two subsystems, and then an explicit exponential decaying term is introduced into the input of the first subsystem to guarantee its controllability. After a state-scaling transformation, a model predictive control (MPC) scheme is proposed for the nonholonomic chained systems. The proposed MPC scheme employs a general projection neural network (GPN) to iteratively solve a quadratic programming (QP) problem over a finite receding horizon. The GPN employed in this paper is proved to be stable in the sense of Lyapunov, and its global convergence to the optimal solution is guaranteed for the reformulated QP. A simulation study is performed to show stable and convergent control performance under the proposed method, irrespective of whether the control input $\boldsymbol {u_{1}}$ vanishes or not.

Global Finite-time Stabilization for a Class of Nonholonomic Chained System with Input Saturation

In this paper, for the first time, the finite-time stabilization problem is addressed for the “3 inputs, 2 chains, 1 generator” nonholonomic chained system with input saturation. A saturated controller is presented by applying the three-step switching control strategy and the theory of finite-time stability, the global stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the simulation examples demonstrate the correctness and the validity of the proposed controller.

Output Feedback Stabilization of Uncertain Nonholonomic Chained Systems

In this paper, output feedback stabilization problem of a class of nonholonomic systems in chained form with drift nonlinearity and unknown virtual control coefficients is considered. Observer-based output feedback design is developed when only partial system states are measurable. The control laws are developed using state scaling and backstepping techniques. The proposed control strategies can steer the system globally converge to the origin.

Robust exponential stabilization of uncertain nonholonomic chained systems based on visual feedback

The visual serving stabilization for a kind of nonholonomic mobile robots with uncalibrated camera parameters is investigated based on the visual feedback and the state and input transformations. The authors obtain a new uncertain model of the nonholonomic kinematic system in the image plane, which is a chained form with uncalibrated visual parameters, from the camera robotic system. A new time varying feedback controller is proposed for the exponential stabilization of the nonholonomic chained system with unknown parameters by using state-scaling and switching technique. The exponential stability of the closed loop system is rigorously proved. Simulation results demonstrate the effectiveness of the proposed methods.

Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts

This paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts, including modeled nonlinear dynamics, unmodeled dynamics, and dynamics modeled with unknown parameters. Also the virtual control directions of the system are unknown. The purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable. A novel observer and estimator are introduced for states and parameter estimates, respectively. A constructive procedure of design for an output feedback adaptive controller is given, by using the integrator backstepping approach and based on the proposed observer and parameter estimator. An example is given to show the effectiveness of the proposed scheme.

Continuous Time-Varying Pure Feedback Control for Chained Nonholonomic Systems with Exponential Convergent Rate

In this paper, feedback stabilization problem of nonholonomic chained system is studied. A new continuous and time-varying design approach is proposed and it is a pure state feedback control. By injecting an exponential decaying disturbance scaled by the norm of the states, u1 drives the initial states away from the singular manifold {x|x1 = 0, |x| ≠ 0] that causes singularity. In addition to the continuity, such a control has the exponential convergent rate that discontinuous control has. The enclosed simulation results verified the effectiveness of the proposed approach. Comparisons made with other existing continuous and discontinuous controls show that the proposed control has superior performance.

Global-Stabilizing Near-Optimal Control Design for Nonholonomic Chained Systems

It is well known that a nonlinear optimal control requires the solution to a two-point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration. In this paper, a new and near-optimal control design framework is proposed for controlling any nonholonomic system in the chained form. The proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal system. It is shown that, no matter whether the first component u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1d</sub> (t) of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero, uniform complete controllability of the (nominal) system can be recovered by employing the proposed time-folding/unfolding technique. Upon establishing the common property of uniform complete controllability, the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner. Using duality, uniform complete observability can also be established, a closed-form and exponentially convergent observer can be synthesized, and the controls designed using the proposed framework can be either state-feedback or output-feedback. The tracking controls are designed using the same three-step process. That is, design of the proposed controls starts with optimal control solutions to two linear nominal subsystems, one time-invariant and the other time varying. The two solutions combined together render a globally stabilizing suboptimal control for the overall system. Then, the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one. Consequently, an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form. An example is used to show that regulation control can be designed similarly. All the controls designed are in simple closed forms and hence real-time implementable, they are time varying and smooth, globally and exponentially/asymptotically stabilizing, and they are near optimal since their closeness to the optimal control (attainable only offline) can be measured, monitored on line, and has been minimized

Hybrid Control of Nonholonomic Chained Systems

Hybrid Control of Nonholonomic Chained Systems

Optimal Control of Nonholonomic Chained Systems Using Hybrid Time-State Form

In this paper, we propose a control method for nonholonomic chained systems. We transform the systems into time-invariant linear systems using a hybrid time-state control form and solve an optimal control problem to get an optimal trajectory with a switching point. The optimal input is derived as a feedback controller for the system. We apply the proposed method to a 4-wheeled vehicle and give numerical simulation results to show its effectiveness.

Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot

In this paper it is shown that a class of n-dimensional nonholonomic chained systems can be stabilized using the invariant manifold approach. First, we derive an invariant manifold for this class of systems and we show that, once on it, all the closed-loop trajectories tend to the origin under a linear smooth time-invariant state feedback. Thereafter, it is shown that this manifold can be made attractive by means of a discontinuous time- invariant state feedback. Finally, a mobile robot is taken as an example demonstrating the effectiveness of our study.

Robust Output-Feedback Tracker Design for Nonholonomic Systems

This paper presents new results for the global output-feedback tracking of nonholonomic systems in chained form. The tracking controllers are obtained on the basis of a recursive technique and a full exploitation of the system structure. Sufficient conditions on the reference paths are given to attain global exponential tracking. When disturbances occur in the dynamic extension of a nonholonomic chained system, it is shown how to modify the controller design procedure to yield robust tracking control laws. The proposed method is demonstrated and discussed by means of a benchmark nonholonomic knife-edge mechanical system.

Lyapunov design of global state and output feedback trackers for non-holonomic control systems

In this paper, new results are obtained for the global tracking of a class of non-holonomic dynamic systems via state and output feedback. The tracking controllers are systematically constructed on the basis of a recursive technique and a full exploitation of the system structure. When disturbances occur in a non-holonomic chained system, it is shown how to modify the controller design procedure to yield robust tracking control laws. The proposed method is demonstrated and discussed by means of a benchmark non-holonomic knife-edge mechanical system.

非ホロノミックチェインドシステムの過渡応答を考慮した指数安定化

非ホロノミックチェインドシステムの過渡応答を考慮した指数安定化