Nonholonomic Chained Form Research Articles

Global formation control of nonholonomic unicycle vehicles with guaranteed rate of convergence

AbstractThis paper studies the full‐state formation control problem of multiple nonholonomic unicycle vehicles. Firstly, the formation error model is transformed into standard nonholonomic chained form, including orientation and position error subsystems. For orientation subsystem, an angular velocity control law is designed to be a cooperative term plus an exponential decay function of time, ensuring orientations reach an agreement on a common value. For position error subsystem, a time‐varying output‐like variable is carefully constructed to ensure a stable zero dynamics, that is, the consensus of these output variables guarantees position formation, overcoming the intrinsic underactuated control difficulty. Then, a linear velocity control law is derived to realize consensus of outputs. It is proved that the proposed distributed time‐varying controller is capable of steering the vehicles to globally exponentially make into desired geometric position shape with the same orientations and vanishing velocities, provided that the communication topology is directed and having a spanning tree. The calculated convergence rates are shown dependent on controller coefficients; thus, the controller is modified to additionally reach a prescribed rate of convergence by redesigning conditions of controller parameters. Finally, two numerical simulations are implemented for five unicycle vehicles, demonstrating the effectiveness of the proposed control scheme.

Global Finite-Time Partial Stabilization for a Class of Nonholonomic Mobile Robots Subject to Input Saturation

In this paper, the global finite-time partial stabilization problem is discussed for a class of nonholonomic mobile wheeled robots with continuous pure state feedback and subject to input saturation. Firstly, for the mobile robot kinematic model, a “3 inputs, 2 chains, 1 generator” nonholonomic chained form systems can be obtained by using a state and input transformation. The continuous, saturated pure state feedback control law is proposed such that the special chained form systems can be stabilized to zero (except an angle variable) in a finite time, i.e., finite-time partial stabilization. Secondly, the rigorous stability analysis of the corresponding closed-loop system is presented by applying Lyapunov theorem combined with the finite-time control theory, and the angle variable can be proved to converge to a constant, moreover, its convergent limit may be accurately estimated in advance. Finally, the simulation results show the correctness and the validity of the proposed controller not only for the chained system but also for the original mobile robots system.

Consensus of multiple nonholonomic chained form systems

Consensus problems of multiple nonholonomic systems are considered in this paper. This problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems. Continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems. Consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not. Different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant, the condition on the group reference signal have been further relaxed in this paper. Simulation results using Matlab have illustrated the effectiveness of the results presented in this paper.

Finite-time Stabilization for Nonholonomic Chained Form Systems with Communication Delay

In this paper, the problem of finite-time stabilization is developed for nonholonomic chained form systems with communication delay in the input. The finite-time control laws are presented by utilizing the switching control strategy and the theory of finite-time stability, which can make the states of the nonholonomic chained form systems to converge from any non-equilibrium state to the equilibrium or a given point in a finite time. Finally, the simulation results show the effectiveness of the proposed control approach.

Robust Stabilization of Nonholonomic Chained Form Systems with Uncertainties

A summary of recent developments concerning robust stabilization problems for the nonholonomic chained form systems with uncertainties is provided. Firstly, various models, main approaches, and results over past ten years for the uncertain chained form systems are presented. Then, several new exciting uncertain chained form models of special interest are proposed for the nonholonomic wheeled mobile robots. They are obtained by using the state and input transformations based on the visual servoing feedback. Finally, the novel robust regulation controllers are addressed for some new uncertain chained models by using two-steps technology, visual feedback, state-scaling and switching strategy. It is expected that this investigation will provide a good introduction about the development of robust stabilization for uncertain chained form systems.

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.

Neural network solution for suboptimal control of non-holonomic chained form system

In this paper, we develop fixed-final time nearly optimal control laws for a class of non-holonomic chained form systems by using neural networks to approximately solve a Hamilton—Jacobi—Bellman equation. A certain time-folding method is applied to recover uniform complete controllability for the chained form system. This method requires an innovative design of a certain dynamic control component. Using this time-folding method, the chained form system is mapped into a controllable linear system for which controllers can systematically be designed to ensure exponential or asymptotic stability as well as nearly optimal performance. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. The results of this paper are demonstrated in an example.

Global κ-exponential Tracking Control of Nonholonomic Systems in Chained-form by Output Feedback

The output tracking control problem of nonholonomic chained form systems is studied in this paper and global κ-exponential output trackers are presented without persistent excitation or not-converging to zero on reference trajectories. First, a time-varying coordinate transformation is introduced to avoid manipulating exponentially converging signals. Then, with the help of theory of cascaded systems and linear perturbed systems, global κ-exponential output trackers are successfully obtained. A new feature of the proposed controller is that the output tracking control problem of nonholonomic chained form systems is also resolvable without the popular condition of persistent excitation or not converging to zero on reference signals in the previous works. The proposed method is demonstrated and discussed by means of nonholonomic mobile robots and cars with one trailer.

Adaptive tracking control for nonholonomic systems with unknown parameters

An adaptive control method for a special chained form system with drift terms and unknown parameters is discussed. Tracking controllers have been considered to be effective for solving the problem of the stability of nonholonomic control systems. Since a tracking control system can be transformed to the special chained form system, a tracking controller using the backstepping method is proposed for the nonholonomic chained form system. The asymptotic stability of the system is guaranteed by using Lyapunov's direct method and using adaptive control method, an adaptive controller is proposed for the nonholonomic system with unknown parameters. The ability of the proposed controller is illustrated by simulations. Furthermore, based on a nonholonomic mobile robot, a typical example of nonholonomic system, we demonstrate the efficiency of the proposed method.

A recursive technique for tracking control of nonholonomic systems in chained form

The authors address the tracking problem for a class of nonholonomic chained form control systems. A recursive technique is proposed which appears to be an extension of the currently popular integrator backstepping idea to the tracking of nonholonomic control systems. Conditions are given under which the problems of semiglobal tracking and global path-following are solved for a nonholonomic system in chained form and its dynamic extension. Results on local exponential tracking are also obtained. Two physical examples of an articulated vehicle and a knife edge are provided to demonstrate the effectiveness of our algorithm through simulations.