Uncertain Nonholonomic Mobile Robots Research Articles

Cost-effective distributed FTFC for uncertain nonholonomic mobile robot fleet with collision avoidance and connectivity preservation

In this paper, the fault-tolerant formation control (FTFC) problem is investigated for a group of uncertain nonholonomic mobile robots with limited communication ranges and unpredicted actuator faults, where the communication between the robots is in a directed one-to-one way. In order to guarantee the connectivity preservation and collision avoidance among the robots, some properly chosen performance functions are incorporated into the controller to per-assign the asymmetrical bounds for relative distance and bearing angle between each pair of adjacent mobile robots. Particularly, the resultant control scheme remains at a cost-effective level because its design does not use any velocity information from neighbors, any prior knowledge of system nonlinearities or any nonlinear approximator to account for them despite the presence of modeling uncertainties, unknown external disturbances, and unexpected actuator faults. Meanwhile, each follower is derived to track the leader with the tracking errors regarding relative distance and bearing angle subject to prescribed transient and steady-state performance guarantees, respectively. Moreover, all the closed-loop signals are ensured to be ultimately uniformly bounded. Finally, a numerical example is simulated to verify the effectiveness of this methodology.

Path-Guided Finite-Time Formation Control of Nonholonomic Mobile Robots Based on an Extended State Observer

In this paper, we study the finite-time formation control problem of uncertain nonholonomic mobile robots following a parameterized path. A path-guided formation control scheme based on an extended state observer is proposed. To compensate for unmeasured velocities and disturbances simultaneously, a third-order fast finite-time extended state observer (FFTESO) is proposed. Then, a distributed formation control solution is developed to achieve the kinematic and dynamic system coordination control of the nonholonomic mobile robots. For the kinematic system control, a path-parameter-updating law is developed for a virtual leader, and the desired linear velocity and heading angle are developed for the mobile robots. For the kinetic control, an anti-disturbance control protocol is designed based on the estimated signals. The salient features of the proposed algorithms lie in that the estimations of disturbances and unmeasured velocities are achieved against the system’s nonholonomic constraints, and the path following the control and cooperative control is synthesized together for path-guided formation, which reduces the complexity of the controller design. Finally, simulation studies are conducted to demonstrate the effectiveness of the proposed algorithm.

Distributed Adaptive Resilient Formation Control of Uncertain Nonholonomic Mobile Robots Under Deception Attacks

This paper investigates the formation control problem for a group of nonholonomic mobile robots (NMRs) with unknown parameters and deception attacks. The information transmitted among different robots is represented by a directed graph and only a subset of the robots can obtain the full information of the desired trajectory directly. For those robots which cannot access to the reference trajectory directly, distributed estimators are designed to estimate the unknown trajectory information by using only locally available information. Besides, the sensor-to-controller transmitting channels and the communication among connected robots are suffering from deception attacks. Adaptive laws and compensation terms are designed to handle the issue of attack-induced uncertainties. Then, a novel distributed resilient formation control scheme is designed, based on which a sufficient condition is developed to guarantee that the formation errors converge to a compact set and all the closed-loop signals are bounded. Experimental results are given to validate the theoretical studies.

Quantized-states-based adaptive control against unknown slippage effects of uncertain mobile robots with input and state quantization

An adaptive tracking design strategy based on quantized state feedback is developed for uncertain nonholonomic mobile robots with unknown wheel slippage effects. All state variables and control torques are assumed to be quantized by the state and input quantizers, respectively, in a network control environment. Thus, the quantized state feedback information is only available for the tracking control design. An approximation-based adaptive controller using quantized states is recursively designed to ensure the robust adaptive tracking against unknown wheel slippage effects where the quantized-states-based adaptive mechanism is derived to compensate for unknown wheel slippage effects, system nonlinearities, and quantization errors. The boundedness of the quantization errors and estimated parameters in the closed-loop system is analyzed by presenting some theoretical lemmas. Based on these lemmas, we prove the uniform ultimate boundedness of closed-loop signals and the convergence of the trajectory tracking error in the presence of wheel slippage effects. Simulations verify the effectiveness of the resulting tracking scheme.

Quantized feedback control strategy for tracking performance guarantee of nonholonomic mobile robots with uncertain nonlinear dynamics

This paper discusses a quantized feedback tracker design problem of nonholonomic mobile robots with uncertain nonlinear dynamics in a network environment with state and input quantization. Quantized state feedback information of mobile robots is only used for the tacker design. Compared with existing control approaches for uncertain nonholonomic mobile robots, the primary contribution of our study is to develop quantized-states-based low-complexity tracking and stability methodologies for ensuring the predesignated performance of tracking errors. A robust tracking scheme using quantized state variables is designed without any adaptive mechanisms to compensate for nonlinear dynamic uncertainties. The boundedness of the quantization errors of the closed-loop signals is derived from a theoretical lemma. Using this lemma, the closed-loop stability is analyzed with the predesignated performance guarantee of tracking errors in the Lyapunov sense. A robot simulation verifies the resulting theoretical tracking strategy.

Connectivity-preserving-based distributed adaptive asymptotically synchronised tracking of networked uncertain nonholonomic mobile robots with actuator failures and unknown control directions

This brief addresses a distributed adaptive asymptotically synchronous tracking problem based on guaranteed connectivity for networked uncertain nonholonomic mobile robots (NMRs) with actuator failures and unknown control directions. First, a radial basis function (RBF) neural network is used to approximate the unknown nonlinear functions, and a distributed nonlinear error surface is introduced to achieve synchronous tracking between NMRs and maintain the initial connectivity patterns. Then, a conditional inequality that allows multiple piecewise Nussbaum functions to achieve robust control is proposed to solve the problem of unknown actuator failures and unknown control directions. Moreover, the proposed protocol ensures that all signals in the closed-loop system are globally bounded and the tracking errors converge asymptotically to zero. Finally, a simulation example verifies the effectiveness of the proposed adaptive laws.

Output-feedback formation tracking control of networked nonholonomic multi-robots with connectivity preservation and collision avoidance

This paper studies the problem of adaptive output-feedback formation tracking control for networked uncertain nonholonomic mobile robots (NMRs) with different limited communication distances, while achieving connectivity preservation and collision avoidance. In robot control, equipping all the speed sensors not only increases the cost of the system but also risks losing accuracy and reliability. In this paper, it is assumed that the velocities of the nonholonomic mobile robots in this paper are unknown, they are estimated according to the output of the systems by an adaptive observer via a neural network. The designed dynamic surface based on nonlinear transformation errors can achieve the above three control objectives at the same time, avoiding the situation of using multiple potential functions to solve such problems, which will lead to conflicts in the selection of the design parameters. Compared with the existing references about formation tracking to maintain connectivity and avoid collisions, the main contribution of this paper is to design an observer of robot speed estimation and use only a neural network to estimate the unknown nonlinear term of the system itself. The unknown nonlinearity produced in the process of controller design does not need an additional neural network. Furthermore, the effectiveness of the proposed strategy is verified by simulation examples.

Distributed approximation-free design for ensuring network connectivity of uncertain nonholonomic multi-robot synchronized tracking systems with disturbances

A distributed approximation-free design for maintaining initial connectivity of uncertain nonholonomic multi-robot synchronized tracking systems is developed under limited communication ranges where the models of followers are regarded as the kinematics and dynamics of uncertain nonholonomic mobile robots. All nonlinearities and external disturbances in the followers’ dynamics are assumed to be unknown. The primary improvement in the current development is that local trackers for ensuring connectivity among robots are designed by using only relative posture errors and adaptive function approximators such as neural networks or fuzzy logic systems are not utilized despite unknown nonlinearities in the robot dynamics. This improvement has been done by transforming individual linear position errors among mobile robots to individual nonlinear position errors using connectivity-preserving functions with communication ranges. The predefined synchronized tracking performance and the guaranteed connectivity of the overall closed-loop system are proved via the Lyapunov stability theorem.

Robust contour tracking of nonholonomic mobile robots via adaptive velocity field motion planning scheme

SummaryThis paper aims at designing a contour tracking scheme based on an adaptive velocity field formulation, for the case of uncertain nonholonomic (differential drive) mobile robots, with its dynamic controller. First, to handle kinematic uncertainties that deviate the map of the velocity field into wheel velocities, a linear parameterization of the uncertain Jacobian operator is proposed to synthesize an adaptive kinematic controller that shapes correctly the velocity field. Then, a robust model‐free dynamic controller is proposed to compensate in finite time for uncertain dynamics and disturbances, enforcing the kinematic reference. Finally, a representative simulation study is discussed to show the reliability of the proposed scheme.

Connectivity preservation and collision avoidance in networked nonholonomic multi-robot formation systems: Unified error transformation strategy

This paper proposes a unified error transformation strategy for the distributed formation tracking of networked uncertain nonholonomic mobile robots with different communication ranges. To guarantee the connectivity preservation and collision avoidance of all robots without employing any potential functions, a novel nonlinear formation error function using the relative distance and angles between robots is introduced. Then, the approximation-based local adaptive tracking design methodology using the dynamic surface design technique is recursively established to achieve (i) the connectivity preservation and collision prevention of initially connected robots, (ii) the collision avoidance of initially non-connected robots, and (iii) the desired formation tracking of robots in a fully distributed manner. The stability of the total closed-loop control system is analyzed in the Lyapunov sense.

Connectivity-Preserving Approach for Distributed Adaptive Synchronized Tracking of Networked Uncertain Nonholonomic Mobile Robots.

This paper addresses a distributed connectivity-preserving synchronized tracking problem of multiple uncertain nonholonomic mobile robots with limited communication ranges. The information of the time-varying leader robot is assumed to be accessible to only a small fraction of follower robots. The main contribution of this paper is to introduce a new distributed nonlinear error surface for dealing with both the synchronized tracking and the preservation of the initial connectivity patterns among nonholonomic robots. Based on this nonlinear error surface, the recursive design methodology is presented to construct the approximation-based local adaptive tracking scheme at the robot dynamic level. Furthermore, a technical lemma is established to analyze the stability and the connectivity preservation of the total closed-loop control system in the Lyapunov sense. An example is provided to illustrate the effectiveness of the proposed methodology.

A low-complexity tracker design for uncertain nonholonomic wheeled mobile robots with time-varying input delay at nonlinear dynamic level

A low-complexity design problem of tracking scheme for uncertain nonholonomic mobile robots is investigated in the presence of unknown time-varying input delay. It is assumed that nonlinearities and parameters of robots and their bounds are unknown. Based on a nonlinear error transformation, a tracking control scheme ensuring preassigned bounds of overshoot, convergence rate, and steady-state values of a tracking error is firstly presented in the absence of input delay, without using any adaptive and function approximation mechanism to estimate unknown nonlinearities and model parameters and computing repeated time derivatives of certain signals. Then, we develop a low-complexity tracking scheme to deal with unknown time-varying input delay of mobile robots where some auxiliary signals and design conditions are derived for the design and stability analysis of the proposed tracking scheme. The boundedness of all signals in the closed-loop system and the guarantee of tracking performance with preassigned bounds are established through Lyapunov stability analysis. The validity of the proposed theoretical result is shown by a simulation example.

Predesignated fault-tolerant formation tracking quality for networked uncertain nonholonomic mobile robots in the presence of multiple faults

This paper presents a fault-tolerant formation tracking (FTFT) scheme ensuring predesignated bounds of overshoot, convergence rate, and steady-state values of distributed formation errors for networked nonholonomic mobile robots in the presence of unexpected multiple actuator and system faults. It is assumed that (i) nonlinearities and multiple faults of follower models and their bounds are unknown, and (ii) the time-varying posture information of the leader robot is accessible to only a small fraction of follower robots under directed networks. A continuous local controller for each follower is designed without utilizing any adaptive and function approximation mechanism to compensate for unexpected actuator and nonlinear system faults and computing repeated time derivatives of certain signals. Compared with the related results in the literature, this feature enables the proposed FTFT scheme to be implementable with remarkably low complexity. Theoretical and simulation verifications of our control strategy guaranteeing that the distributed FTFT errors remain within preassigned bounds regardless of the occurrence of unexpected faults are studied in a rigorous manner.

Prescribed performance bound‐based adaptive path‐following control of uncertain nonholonomic mobile robots

SummaryIn this paper, we consider the transient performance of path‐following control of nonholonomic mobile robots with parametric uncertainties. By incorporating prescribed performance bound (PPB) technique, the transient performances on position and orientational tracking errors will be guaranteed with convergence rates no less than certain pre‐specified values and sufficiently small maximum overshoots. We also extend the proposed scheme to solve the formation control problem for a group of N unicycle‐type mobile robots without inter‐robot communications. It is ensured that all the robots can track their references with arbitrarily small errors and no collision will occur between any two robots. Simulation studies verify the established theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation

In this paper, the robust stabilization problem is addressed for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation. Firstly, a continuous, time varying, saturated controller is presented for the kinematic system of the robots. Secondly, for the dynamic feedback system, a special derivable, saturated kinematic controller with slope restrictions is selected as a virtual control law that can be tracked by the real generalized velocity in a finite time, furthermore, the dynamic input signals are continuous and saturated at any time. The systematic strategy combines the theory of finite-time stability with the virtual-controller-tracked method. Finally, the simulation results show the effectiveness of the proposed controller design approach.

Practical Stabilization of Uncertain Nonholonomic Mobile Robots Based on Visual Servoing Model with Uncalibrated Camera Parameters

The practical stabilization problem is addressed for a class of uncertain nonholonomic mobile robots with uncalibrated visual parameters. Based on the visual servoing kinematic model, a new switching controller is presented in the presence of parametric uncertainties associated with the camera system. In comparison with existing methods, the new design method is directly used to control the original system without any state or input transformation, which is effective to avoid singularity. Under the proposed control law, it is rigorously proved that all the states of closed-loop system can be stabilized to a prescribed arbitrarily small neighborhood of the zero equilibrium point. Furthermore, this switching control technique can be applied to solve the practical stabilization problem of a kind of mobile robots with uncertain parameters (and angle measurement disturbance) which appeared in some literatures such as Morin et al. (1998), Hespanha et al. (1999), Jiang (2000), and Hong et al. (2005). Finally, the simulation results show the effectiveness of the proposed controller design approach.

Adaptive tracking control for uncertain dynamic nonholonomic mobile robots based on visual servoing

The tracking control of wheeled dynamic mobile robots via visual servoing feedback is considered. A kinematic controller is firstly presented for the kinematic model, and then, an adaptive torque tracking controller is designed for the uncertainty dynamic model in the presence of parametric uncertainty associated with the camera system. The asymptotic convergence of tracking errors to zero is rigorously proved by the Lyapunov method. Simulation results are provided to illustrate the performance of the control law.

A Simple Adaptive Control Approach for Trajectory Tracking of Electrically Driven Nonholonomic Mobile Robots

Almost all existing controllers for nonholonomic mobile robots are designed without considering the actuator dynamics. This is because the presence of the actuator dynamics increases the complexity of the system dynamics, and makes difficult the design of the controller. In this paper, we propose a simple adaptive control approach for path tracking of uncertain nonholonomic mobile robots incorporating actuator dynamics. All parameters of robot kinematics, robot dynamics, and actuator dynamics are assumed to be uncertain. For the simple controller design, the dynamic surface control methodology is applied and extended to mobile robots that the number of inputs and outputs is different. We also adopt the adaptive control technique to treat all uncertainties and derive adaptation laws from the Lyapunov stability theory. Finally, simulation results demonstrate the effectiveness of the proposed controller.

Adaptive formation tracking control of electrically driven multiple mobile robots

An adaptive formation control method is proposed for multiple uncertain non-holonomic mobile robots at the actuator dynamics level. All parameters of the robot kinematics and dynamics, and actuator dynamics are unknown. The virtual structure with path parameters and the dynamic surface design methodology are combined to design a simpler adaptive formation control scheme than the previous backstepping-based control system. Using the Lyapunov stability theorem, the authors present the adaptation laws for tuning all unknown parameters of multiple mobile robots regardless of considering path parameters in the reference trajectories. In addition, it is proved that all signals in the total closed-loop system are semi-globally uniformly bounded and all formation tracking errors and synchronisation errors of the path parameters converge to an adjustable neighbourhood of the origin. Finally, simulation results demonstrate the effectiveness of the proposed approach.