Nonholonomic Systems In Chained Form Research Articles

Predefined-time VFO control design for unicycle-like mobile robots

The paper presents a predefined-time Vector-Field-Orientation (VFO) control law for unicycle-like nonholonomic mobile robots. We consider a set-point control problem in the presence of strict time constraints, which has to guarantee satisfaction of a prescribed upper bound of the settling time for the configuration errors. The control law is based on the VFO methodology, which is characterized by non-oscillatory and well-predictable time evolution of transient states for unicycle-like robots. A formal stability analysis based on the Lyapunov theory is provided for the closed-loop dynamics. Then, the results of extensive numerical simulations as well as experimental tests illustrate the resultant control performance where time constraints are considered. The proposed approach is compared with an alternative predefined-time stabilizer, recently introduced for nonholonomic chained-form systems.

Adaptive Multiple-Surface Sliding Mode Control of Nonholonomic Systems With Matched and Unmatched Uncertainties

The problem of stabilizing a class of nonholonomic systems in chained form affected by both matched and unmatched uncertainties is addressed in this paper. The proposed design methodology is based on a discontinuous transformation of the perturbed nonholonomic system to which an adaptive multiple-surface sliding mode technique is applied. The generation of a sliding mode allows to eliminate the effect of matched uncertainties, while a suitable function approximation technique enables to deal with the residual uncertainties, which are unmatched. The control problem is solved by choosing a particular sliding manifold upon which a second order sliding mode is enforced via a continuous control with discontinuous derivative. A positive feature of the present proposal, apart from the fact of being capable of dealing with the presence of both matched and unmatched uncertainties, is that no knowledge of the bounds of the unmatched uncertainty terms is required. Moreover, the fact of producing a continuous control makes the proposed approach particularly appropriate in nonholonomic applications, such as those of mechanical nature.

Finite-Time Discontinuous Control of Nonholonomic Chained-Form Systems

A finite-time discontinuous control method is proposed for controlling nonholonomic chained-form systems. Through a general discontinuous coordinate transformation, the nonholonomic system is transformed into two decoupled subsystems that are independently stabilized with control laws. Sufficient conditions for the existence of decoupled subsystems and finite-time convergence of system states are given. Furthermore, the finite-time discontinuous control laws are proposed to ensure that the system states reach the equilibrium in a finite time. Simulation results are presented to demonstrate the effectiveness and advantages of the proposed approach.

Event-triggered tracking control for a class of nonholonomic systems in chained form

Event-triggered tracking control for a class of nonholonomic systems in chained form

Fast finite-time consensus protocol of multi-agent systems with nonholonomic constraints

In this paper, a fast finite-time consensus protocol for multi-agent systems with nonholonomic constraints is studied. First, the chained form nonholonomic systems are transformed into two subsystems, which are the first-order subsystem and the reduced-order subsystem. Based on graph theory content and fast finite-time control theory, the fast finite-time consensus problems of the two subsystems are taken into consideration separately. Second, a switching control strategy is proposed to ensure that all states of multiple nonholonomic systems converge instantly to the same state in finite time. Finally, a numerical example is given to verify the effectiveness of the proposed control algorithm.

Prescribed-time control of high-order nonholonomic systems in chained form by time-varying feedback

In this paper, the prescribed-time control problem for a class of high-order nonholonomic systems is investigated. With the aid of a novel state transformation, the nonholonomic systems are decoupled. Further, a time-varying high-gain feedback controller is constructed by backstepping. It is shown that the proposed control law can achieve the prescribed-time convergence for high-order nonholonomic systems and the controller is bounded. Numerical examples verify the effectiveness of the method proposed in this paper.

Fixed-Time Fractional-Order Global Sliding Mode Control for Nonholonomic Mobile Robot Systems under External Disturbances

The present study addresses the problem of fixed-time stabilization (FTS) of mobile robots (MRs). The study’s distinguishing aspects are that the system under examination is subjected to external disturbances, and the system states are pushed to zero in a finite time. This paper suggests new control techniques for chained-form nonholonomic systems (CFNS) subjected to disturbances. First, a switching fractional-order (FO) control approach is proposed for a first-order subsystem (FOS) of an MR under complex disturbances. Secondly, an FO generic global sliding mode control approach is designed for the second-order system (SOS) of the MR in the presence of disturbances. The suggested sliding manifold for the SOS of the MR guarantees global system stability and reduces the chattering problem during control operations. A conventional quadratic Lyapunov function (QLF) is used to converge to the origin in a finite time (FnT). Through this study, a stabilizer for an MR in the presence of disturbances based on an FO switching time-varying controller that can stabilize immeasurable states in a fixed time is proposed. Finally, three case simulations are provided to demonstrate the efficacy of the control strategy proposed in this work against external disturbances.

A time-scale transformation approach to prescribed-time stabilisation of non-holonomic systems with inputs quantisation

This article addresses the problem of global stabilisation using state feedback for a kind of uncertain non-holonomic systems in chained form. Two distinct characteristics of this study are that the considered system suffers from the input-quantised actuator, and the system states are expected to converge to zero in prescribed finite time. To address these, a time-scale transformation, that can change the original stabilisation into the finite-time stabilisation of the transformed one, is first introduced. Then, under the new framework of equivalent transformation, a quantised state feedback controller that achieves of the performance requirements is developed with the aid of the recursive technique. Finally, simulation results of a unicycle-type mobile robot are provided to confirm the efficacy of the proposed approach.

Robust finite-time stabilisation of an arbitrary-order nonholonomic system in chained form

We present a robust finite-time stabilising algorithm for an arbitrary-order nonholonomic system in chained form. The state feedback is locally bounded, homogeneous and discontinuous. Its design follows from a generalised circle criterion based on the theory of homogeneous Lyapunov functions and a two-stage homogeneity-preserving strategy proposed by Nakamura.

Bounded Observer-Based Consensus Algorithm for Robust Finite-Time Tracking Control of Multiple Nonholonomic Chained-Form Systems

This article is concerned with the leader–follower consensus tracking problem for multiagent systems with nonholonomic high-order chained-form dynamics subject to external disturbances. A novel distributed and bounded observer is first developed for each follower to estimate the leader information in a finite time. Then, a bounded fast terminal sliding-mode control protocol is constructed for each follower to track the estimated leader's states leading to the fast convergence performance as well as strong robustness. Contrary to some existing finite-time consensus tracking schemes, the control input constraint is taken into account by utilizing hyperbolic tangent saturation function to reduce the risk of the actuator saturation. Moreover, an approximation-based technique is introduced to reduce the conservatism of the upper bound of convergence time. Finally, some simulations for a set of wheeled mobile robots are carried out to demonstrate the efficiency of the proposed control algorithm.

Adaptive output feedback stabilising control of uncertain chained-form non-holonomic systems

In this article, we investigate the global robust stabilisation problem for a class of uncertain chained-form non-holonomic systems. Three types of uncertainties are taken into account, including dynamic uncertainty, unknown control coefficients, and nonlinear parameterisation. Different from the existing works, the input-to-state stability (ISS) with unknown supply rates is used to characterise the system of dynamic uncertainty, and the magnitudes of the control coefficients are not required to be known a priori. The nonlinear parameterisation is well treated with the aid of a parameter separation technique. By constructing a switching control strategy, we propose a discontinuous adaptive stabilising control scheme via output feedback to overcome the serious uncertainties in the chained-form non-holonomic systems. The simulation results illustrate the effectiveness of the presented algorithm.

Output feedback stabilization via nonlinear mapping for time-varying constrained nonholonomic systems in prescribed finite time

This study considers fixed-time stabilization using output feedback for chained-form nonholonomic systems. Notably, the distinctive features of the study are that the system under consideration is adversely affected by time-varying output constraints, and the system states are driven to zero in the prescribed finite time. A time-varying version of the nonlinear mapping is recommended to address the output constraints. The construction of a novel switched time-varying observer that has the capability of estimating the immeasurable states in fixed time enables us to devise an output feedback controller. This controller guarantees the achievement of the performance requirements by employing switching control strategy. Finally, a benchmark example is given to acknowledge the efficacy of the proposed control scheme.

Smooth, time‐invariant regulation of nonholonomic systems via energy pumping‐and‐damping

SummaryIn this article we propose an energy pumping‐and‐damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity‐based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time‐invariant, state‐feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher order nonholonomic systems in chained form, a local convergence result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.

Reduced order finite time observers and output feedback for time-varying nonlinear systems

We provide finite time reduced order observers for a class of nonlinear time-varying continuous-time systems. We use the observers to design globally asymptotically stabilizing output feedback controls. We illustrate our work in tracking dynamics for a nonholonomic system in chained form.

Nonlinear mapping-based fixed-time stabilization of uncertain nonholonomic systems with time-varying state constraints

In this paper, the problem of fixed-time stabilization (FxTS) is addressed for a type of uncertain chained-form nonholonomic systems. Remarkably, the study possess two important features: one is that the system under investigation is subject to time-varying state constraints (that are equal to the space constraints of mobile robot or other nonholonomic mechanical systems), and the other is that the design control laws can render the closed-loop system (CLS) states to zero in any prescribed finite time. A novel nonlinear mapping (NM) is introduced to cope with time-varying state constraints. With the help of the adding a power integrator technique and the reasonable switching control strategy, this paper proposes a fixed-time state feedback controller, and completes the performance analysis based on the construction of integral Lyapunov function. Finally, a simulation example is presented to confirm the effectiveness of control strategy.

Barrier Lyapunov functions-based fixed-time stabilization of nonholonomic systems with unmatched uncertainties and time-varying output constraints

The fixed-time stabilization problem is addressed in this paper for a kind of nonholonomic systems in chained form with unmatched uncertainties and time-varying output constraints. A novel tan-type barrier Lyapunov function is introduced to deal with time-varying output constraints. Under the unified framework of the considered system with and without output constraints, a state feedback controller is designed with the aid of adding a power integrator technique and switching control strategy. It is shown that the suggested controller ensures the states of closed-loop system to zero in a given fixed time without disobeying the constraints. Finally, simulation results are given to confirm the efficacy of the presented control scheme.

Fixed-time output tracking control for extended nonholonomic chained-form systems with state observers

This paper deals with the fixed-time tracking control problem of extended nonholonomic chained-form systems with state observers. According to the structure characteristic of such chained-form systems, two subsystems are considered to design controllers, respectively. First of all, using the fixed-time control theory, a controller is proposed to make the first tracking error subsystem converge to zero in bounded time independent initial state. Second, a state observer is proposed to estimate the unmeasurable states of the second subsystem. And the precise state estimation can be presented from the observer within finite time; moreover, the upper bound of time is a constant independent on the initial estimation error. Third, a fixed-time controller is designed to drive all states of the second chained-form subsystem to zero within pre-calculated time. Finally, the effectiveness of the proposed control scheme is validated by simulation results.

Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

Global robust stabilization for nonholonomic systems with dynamic uncertainties

In this paper, we investigate the global robust stabilization problem for a class of uncertain chained-form nonholonomic systems. Remarkably, the studied system allows the nonlinear dynamic uncertainties. Characterizing the system of dynamic uncertainties via Sontag’s input-to-state stability (ISS) and ISS-Lyapunov function, we present a novel robust stabilization scheme via output feedback. The input-state scaling transformation is employed in this procedure to design a discontinuous time-invariant control law. A technical lemma is proposed in this paper to handle the dynamic uncertainties combining with the changing supply rates technique. Moreover, a switching control strategy based on the state magnitude is applied to get around the smooth stabilization burden associated with nonholonomic systems. The simulation results illustrate the efficacy of the presented algorithm.

Robust Fixed-Time Consensus Tracking Control of High-Order Multiple Nonholonomic Systems

Convergence rate is an important performance index in consensus control. Yet, most of the existing results can only achieve asymptotic consensus, or finite-time consensus whose settling time is contingent on initial conditions. This paper studies the robust fixed-time consensus tracking control problem for high-order nonholonomic chained-form systems subject to unknown parameters and nonlinear uncertainties. By using the modified power integrator method, we propose a new robust fixed-time consensus tracking algorithm, with which the consensus tracking can be achieved in a fixed time independent of initial conditions even in the presence of uncertainties. An observer-based fixed-time consensus tracking algorithm is also developed as an alternative method to overcome the communication loop problem. Lyapunov analysis shows the fixed-time stability of the closed-loop system. An application to multiple wheeled mobile robots is presented.