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Kinematic and adaptive dynamic trajectory tracking controller for mobile robots
Abstract
This paper addresses the design of an adaptive controller to guide a unicycle-like mobile robot while tracking a trajectory. The controller is designed considering the complete dynamic model of the robot, and consists of two parts. The first one is based on the kinematic model of the robot, and plays the role of generating the desired linear and angular velocities values. These desired values are the inputs to the second part, which compensates the robot dynamics and generates the linear and angular velocities commands to the robot. The parameters representing the robot dynamics are updated on-line so that the controller adapts itself to the robot dynamics. This provides smaller errors and better performance in case of parameter uncertainties, such as load changes for different tasks. A proof of the stability of the whole control system is presented. Experimental results show the good performance of the proposed controller for trajectory tracking and robot positioning.
... Se utiliza el modelo de De La Cruz (2006) en (Martins et al., 2007) para desarrollo de un controlador adaptable, que tiene la capacidad de adaptarse online a partir de la excitación de la dinámica del vehículo. Resultados de los experimentos realizados con un robot Pioneer 3-DX son presentados en dicho trabajo. ...
... El controlador de seguimiento de trayectoria a ser utilizado es el propuesto en (Martins et al., 2007), que es un controlador dinámico adaptable. La Fig. 5 ilustra la estructura de dicho controlador. ...
... El modelo dinámico de la silla de ruedas presentado en la Sección III, el controlador de seguimiento de trayectoria desarrollado en (Martins et al., 2007), así como el sistema de generación de trayectoria de la Sección V, han sido implementados en Matlab/Simulink ® . El mapa del ambiente de navegación discreteado (Fig. 8), así como las localizaciones iniciales y de destino del vehículo móvil, sirven como entradas al sistema. ...
... For testing the controller performance, different three dynamic loads are used from references of [18][19][20][21] with different loads of 10 kg, 55 kg and 125 kg respectively. The control was designed based on the dynamics of a Pioneer 2-DX wheel chair [13] weighing of 10 kg. ...
... The parameter updating law (18) works as an integrator and can cause robustness problems in case of measurement errors, noise or disturbances. A possible way of preventing parameter drifting is to turn parameter updating off when the error value is smaller than a certain bound, as illustrated in [20]. Another known way of preventing parameter drifting is to change the parameter updating law by introducing a Leakage term, or a σ -modification [4,15]. ...
An important issue in the field of motion control of wheeled mobile robots is that the design of most controllers is based only on the robot’s kinematics. However, when high-speed movements and/or heavy load transportation are required, it becomes essential to consider the robot dynamics as well. The control signals generated by most dynamic controllers reported in the literature are torques or voltages for the robot motors, while commercial robots usually accept velocity commands. In this context, we present a velocity-based dynamic model for differential drive mobile robots that also includes the dynamics of the robot actuators. Such model has linear and angular velocities as inputs and has been included in Peter Corke’s Robotics Toolbox for MATLAB, therefore it can be easily integrated into simulation systems that have been built for the unicycle kinematics. We demonstrate that the proposed dynamic model has useful mathematical properties. We also present an application of such model on the design of an adaptive dynamic controller and the stability analysis of the complete system, while applying the proposed model properties. Finally, we show some simulation and experimental results and discuss the advantages and limitations of the proposed model.
... A lei de atualização de parâmetros (13) funciona como um integrador, e, portanto, pode causar problemas de robustez quando ocorrem erros de medição, ruídos ou distúrbios no sinal medido. Uma possível forma de evitar a divergência dos parâmetros é desativar a adaptação quando o valor de erro for menor do que um limite, como mostrado em (Martins et al., 2007). Outra maneira de se evitar tal divergência é introduzir uma modificação sigma na lei de atualização dos parâmetros, como mostrado em (Kaufman, Barkana e Sobel, 1998) e exemplificado em (Nasisi e Carelli, 2003), que apresenta um controlador servovisual com modificação sigma aplicado a um manipulador robótico. ...
This paper proposes an adaptive controller to guide a unicycle-like mobile robot during trajectory tracking. First, the desired values for the linear and angular velocities are generated based on the kinematic model of the robot. Such values are then dealt with to compensate the robot dynamics and to generate the robot commands. The parameters representing the robot dynam-ics are updated on-line, thus providing smaller errors and better performance. Stability proofs for the control system thus de-signed are presented. Simulation and experimental results are also presented, and show the good performance of the proposed controller for trajectory tracking and robot positioning as well. Keywords⎯ Dynamic model, mobile robots, non-linear systems, trajectory tracking, adaptive controller. Resumo⎯ Este artigo apresenta um controlador adaptativo que permite a um robô móvel uniciclo seguir uma trajetória. Primeiro os valores desejados para as velocidades linear e angular do robô são gerados com base em sua cinemática. Esses valores são, en-tão, tratados para compensar a dinâmica do robô e enviar os comandos para seu acionamento. Os parâmetros que representam a dinâmica do robô são adaptados on-line, resultando em redução de erros e melhoria de desempenho perante incerteza em tais pa-râmetros. Provas de estabilidade para o sistema proposto são apresentadas. Resultados de simulação e experimentais mostram que o controlador proposto apresenta bom desempenho para objetivos de seguimento de trajetória e de posicionamento do robô. Palavras-chave⎯ Modelo dinâmico, robôs móveis, sistemas não lineares, seguimento de trajetória, controlador adaptativo.
... However, the parameter-updating law in (13) works as an integrator and, therefore, can cause robustness problems in the presence of measurement errors, noise or disturbances. One possible way to prevent parameter drift is then to turn off the parameter-updating when the error is smaller than a boundary value, as shown in (Martins, Celeste, Carelli, Sarcinelli Filho, & Bastos Filho, 2007). Another well known way to avoid parameter drift is to change the parameter-updating law by introducing a smodification (Kaufman, Barkana, & Sobel, 1998;Sastry & Bodson, 1989). ...
This paper develops a new representation for the dynamic model of unicycle-like mobile robots, discusses some properties of it, and proposes an adaptive dynamic compensation controller based on such model. The proposed dynamic model has linear and angular velocities as inputs, which is usual in commercial mobile robots but not in the literature, thus increasing the significance of the model itself. Important properties of such model are summarized, and some of those are considered in the design of the dynamic compensation controller and in the stability analysis of the equilibrium of the closed-loop system. A robust updating law is applied to avoid parameter drifting and it is shown that the system can deal with bounded parameter variations, keeping the control errors inside a bounded region. Performance comparison shows that the proposed dynamic compensation scheme improves robot's performance in trajectory tracking, compared to the case in which only a kinematic controller is used. Finally, experimental results illustrate the performance of the proposed scheme when applied to a commercial mobile robot.
... As DK is symmetric and positive definite, From (15) and (16) However, the parameter updating law in (13) works as an integrator and, therefore, can cause robustness problems in the presence of measurement errors, noise or disturbances. One possible way to prevent parameter drift is then to turn off the parameter-updating when the error is smaller than a boundary value, as shown in (Martins et al., 2007). Another well known way to avoid parameter drift is to change the parameter updating law by introducing a -modification (Kaufman, Barkana and Sobe, 1998;Sastry and Bodson, 1989). ...
This paper proposes an adaptive controller to guide an unicycle-like mobile robot during trajectory tracking. Initially, the desired values of the linear and angular velocities are generated, considering only the kinematic model of the robot. Next, such values are processed to compensate for the robot dynamics, thus generating the commands of linear and angular velocities delivered to the robot actuators. The parameters characterizing the robot dynamics are updated on-line, thus providing smaller errors and better performance in applications in which these parameters can vary, such as load transportation. The stability of the whole system is analyzed using Lyapunov theory, and the control errors are proved to be ultimately bounded. Simulation and experimental results are also presented, which demonstrate the good performance of the proposed controller for trajectory tracking under different load conditions.
Uma proposta de modelagem da dinâmica de robôs móveis tipo uniciclo é aqui apresentada e utilizada no projeto de controladores para os referidos robôs; inclusive num contexto de controle de formação. A dinâmica dos robôs móveis é modelada através de uma nova abordagem; baseada em um modelo dinâmico que aceita sinais de velocidades linear e angular como entradas. O novo modelo dinâmico apresentado tem suas propriedades estudadas e posteriormente utilizadas no desenvolvimento de controladores adaptativos; para compensar os efeitos da dinâmica de robôs móveis quando realizam tarefas de seguimento de trajetória; posicionamento e controle de formação. A teoria de Lyapunov é utilizada para analisar a estabilidade do equilíbrio para cada caso; também sendo realizada análise de robustez à variação de parâmetros e à presençaa de distúrbios não modelados. A influência da compensação da dinâmica é estudada; e sua importância evidenciada através do cálculo de um índice de desempenho obtido em simulações e experimentos. Três estratégias de controle de formação com compensação dinâmica são apresentadas; sendo uma de controle descentralizado tipo líder-seguidor e duas de controle centralizado tipo estruturas virtuais. Uma das estratégias de controle centralizado é aqui proposta; sendo apresentado o desenvolvimento do Esquema de Controle Multicamadas. Tal esquema permite que cada parte do problema de controle de formação seja resolvido por um módulo independente; aumentando sua flexibilidade. É proposto um controlador de formação que posiciona os robôs numa formação que pode ser fixa ou variável; tanto em posição como em forma; sendo possível enfatizar a importância do controle de posicionamento ou de forma da formação. A influência da compensação dinâmica neste controle de formação é analisada e ilustrada através de resultados de simulação e também de experimentos.
A landmark based navigation system for robotic wheelchairs is developed. The proposed navigation system is robust in the localization procedure which is the major problem in robotic navigation systems. Every landmark is composed of a segment of metallic path and a radio-frequency identification (RFID) tag. The odometry information is used for localization, which is corrected on-line every time the robotic wheelchair is over a landmark. A topological map is generated using such landmarks to compute the shortest path. A technique to generate the topological map for this navigation system and an obstacle avoidance strategy are also developed.
A novel tracking and positioning adaptive control for mobile robots is designed using Lyapunov theory. Then, a switching control that changes the parameter updating law is used to improve the adaptive control in the sense of reducing high accelerations of the robot and avoiding the parameter drifting. Experimental results show a good performance of the adaptive control and its improvement with the switching control.
The so-called RoboGuard is a mobile security device which is tightly integrated into the existing surveillance framework developed and marketed by Quadrox, a Belgian SME. Robo-Guards are semi-autonomous mobile robots providing video streams via wireless Intranet-connections to existing watchguard systems, supplemented by various basic and optional be-haviors. RoboGuards fill several market-niches. Especially, they are a serious alternative to the standard approach of using Closed Circuit Television (CCTV) for surveillance. The paper describes how the main challenges from the telematics viewpoint, namely ensuring Quality of Service (QoS) and Fail-Safe Guarantees (FSG), are solved in this system.
This article describes RISCBOT ( RISCBOT name has been derived from RISC lab and 'bot' of robot), a modular 802.11 b-enabled mobile autonomous robot built at the RISC lab of the University of Bridgeport. RISCBOT localizes itself and successfully fulfills www - enabled online user requests and navigates to various rooms, employing a visual recognition algorithm. This article describes the mechanical design, hardware and software algorithms of the robot, and the web-based interface for communicating with the robot.
In this paper mobile robot control laws, including obstacle avoidance based on distance seasonal information are proposed. The mobile robot is assumed to evolve in a semi-structured environment. The control systems are based on the use of the extended impedance concept, in which the relationship between fictitious forces and motion error is regulated. The fictitious forces are generated from the information provided by sensors on the distance from the obstacle to the robot. The control algorithms also prevent from the potential problem of control command saturation. The paper includes the stability analysis of the developed control systems, using positive definite potential functions.
A dynamical extension that makes possible the integration of a kinematic controller and a torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping, and asymptotic stability is guaranteed by Lyapunov theory. Moreover, this control algorithm can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following, and stabilization about a desired posture. The result is a general structure for controlling a mobile robot that can accommodate different control techniques, rang-ing from a conventional computed-torque controller, when all dynamics are known, to robust-adaptive controllers if this is not the case. A robust-adaptive controller based on neural networks (NNs) is proposed in this work. The NN controller can deal with unmodeled bounded disturbances and/or unstructured unmodeled dynamics in the vehicle. On-line NN weight tuning algorithms that do not require off-line learning yet guarantee small tracking errors and bounded control signals are utilized.
The work presents, first, a complete dynamic model of a unicycle-like mobile robot that takes part in a multi-robot formation. A linear parameterization of the model is also performed. The resulting robot model is input-output feedback linearized. On a second stage, for the multi-robot system, a model is obtained by arranging into a single equation all the feedback linearized robot models. This multi-robot model is expressed in terms of formation states by applying a coordinate transformation. The inverse dynamics technique is then applied to design a centralized formation control. The controller can be applied both to positioning and to tracking desired robot formations. Experimental results validate the theoretical aspects
We consider the tracking control of a nonholonomic mobile robot with parameter uncertainty and unknown dynamics. A new robust adaptive controller is proposed with the aid of adaptive backstepping and robust control techniques. The proposed controller guarantees that the tracking error converges to a small ball containing the origin. The ball's radius can be adjusted by control parameters. Uncertainties in both of kinematics and dynamics of mobile robots are considered of the first time in the frame of robust and adaptive control in this paper. Simulation results show effectiveness of the proposed controller.
In this paper, a system to allow the communication between a human being and a robot, through a human-machine interface (HMI), is proposed. Such HMI makes possible to use electro-biological signals, such as electromyogram (EMG), electrooculogram (EOG) and electroencephalogram (EEG) to control devices like an autonomous wheelchair. An electronic board containing an environmental map has also been developed. Thus, the user selects a cell in the map, through some electro-biological signal, which is understood by the system as the place the mobile vehicle should reach. A control system to guide the robot to seek for this goal is also presented, including experimental results
A real-time multiprocessor system is proposed for the solution of the tracking problem of mobile robots operating in a real context with environmental disturbances and parameter uncertainties. The proposed control scheme utilizes multiple models of the robot for its identification in an adaptive and learning control framework. Radial Basis Function Networks (RBFNs) are considered for the multiple models in order to exploit the net non-linear approximation capabilities for modeling the kinematic behavior of the vehicle and for reducing unmodeled contributions to tracking errors. The training of the nets and the tests of the achieved control performance have been done in a real experimental setup. The proposed control architecture improves the robot tracking performance achieving fast and accurate control actions in presence of large and time-varying uncertainties in dynamical environments. The experimental results are satisfactory in terms of tracking errors and computational efforts.
In this paper, a mobile robot control law for corridor navigation and wall-following, based on sonar and odometric sensorial information is proposed. The control law allows for stable navigation avoiding actuator saturation. The posture information of the robot travelling through the corridor is estimated by using odometric and sonar sensing. The control system is theoretically proved to be asymptotically stable. Obstacle avoidance capability is added to the control system as a perturbation signal. A state variables estimation structure is proposed that fuses the sonar and odometric information. Experimental results are presented to show the performance of the proposed control system.
Adaptive controllers for robot positioning and tracking using direct visual feedback with camera-in-hand configuration are proposed in this paper. The controllers are designed to compensate for full robot dynamics. Adaptation is introduced to reduce the design sensitivity due to robot and payload dynamics uncertainties. It is proved that the control system achieves the motion control objective in the image coordinate system. Simulations are carried out to evaluate the controller performance. Also, discretization and measurement effects are considered in simulations.
In this note the trajectory tracking problem for a wheeled mobile base has been addressed, considering the presence of uncertainties in the dynamical model. The proposed solution is based on discrete sliding mode control, in order to ensure both robustness and implementability of the controller. The asymptotic boundedness of the tracking errors has been theoretically proved. The proposed discrete time algorithm has been experimentally tested, performing the experiments on the LABMATE vehicle available at the Robotics Lab of the University of Ancona, and compared with a kinematic controller proposed in the literature.
Addresses the problem of human robot interaction with application to the design of assistive devices. We describe the design and development of a prototype of a smart wheelchair that can be commanded by a rider. Specifically, we focus on (a) the vision-based human interaction interface; (b) the suite of sensors on the chair, and (c) the software architecture and the control algorithms used to control the chair.
The definition of the desired functions and the design of an ultimate versatile personal robot is an ongoing debate. Meanwhile, however, precursors of this yet to evolve species are well on their way to become commercial products. Cleaning robots for public environments as well as for private households seem to be able to provide the breakthrough which the designers of non-industrial robot systems have long awaited.
This survey describes a selection of 30 different cleaning robots, with the first developments reaching back more than 15 years. With a few exceptions we have focused on floor cleaning, in particular indoor floor cleaning. We describe a variety of scrubbing and vacuuming robots which were developed for this task. The described systems range from heavy, large, and expensive industrial cleaning vehicles to small-size, light-weight, low-cost household devices. Thesurvey does not include, however, systems for cleaning facades of buildings, or windows, or production tools.
Although not all of the 30 cleaning robots abovementioned have yet reached the state of commercial products, their number alone certainly reflects the expectations regarding the economic value associated with the automation of cleaning tasks. In Europe only the estimates for the market for cleaning services range up to the order of US$ 100 billion per year. It is therefore not surprising that the cleaning industry and the manufacturers of cleaning devices arerather enthusiastic with respect to the automation of cleaning tasks using (semi-)autonomous mobile robot systems.
Traducción de: Linear algebra Incluye bibliografía e índice
The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.
A novel control scheme with an adaptive neurodynamics and sliding mode control for the dynamic tracking control of a noholonomic mobile robot is presented. A biologically inspired neural model is embedded into the standard backstepping-based velocity controller to eliminate or inhibit the sharp speed jumps of velocity commonly existing in mobile robots due to tracking errors changing suddenly. The proposed control scheme includes a neurodynamics based velocity planner as the kinematics controller and a global sliding mode controller for the dynamics control of mobile robot. A novel neurodynamics model with parameters adaptation is presented for tracking arbitrary paths with different initial posture errors. The simulations demonstrate that the dynamic tracking of mobile robot can be realized by the proposed approach, meanwhile the sharp speed jumps of linear velocity eliminated completely.
In the design of a controller for mobile robot, there are only few
results on the problem of integrating the nonholonomic kinematic
controller and the dynamic controller for mobile robots. Also there are
only few literatures on the robustness of the controller in the presence
of uncertainties or external disturbances in the dynamical model of
mobile robot. In this paper, a robust adaptive controller which can
achieve velocity tracking while considering not only kinematic model but
also dynamic model of mobile robot is proposed. The proposed controller
can overcome model uncertainty or external disturbances by the robust
adaptive technique. The stability of the dynamic system is shown through
the Lyapunov method
This paper concentrates on the discussions on stabilization of
mobile robots with unknown constant-input disturbances. Continuous
time-varying adaptive controllers are designed for mobile robots in a
chain-form by using Lyapunov approach. With the property of homogeneous
systems, uncertain mobile robots governed by the proposed control
algorithms become homogeneous of order zero to achieve exponential
stability. Simulation results validate the theoretical analysis
This paper considers the tracking problem of nonholonomic wheeled
mobile robots with unknown dynamics. A new adaptive robust global
dynamic controller is presented based on the canonical form of the
wheeled mobile robots. This novel controller has low dimension and no
singular points. Simulations show the effectiveness of the control
scheme
The distributed control system employs a Windows network, which
consists of a host computer and several robot controllers. The robots
are tethered mobile robots designed for automating highway maintenance
and construction. The host computer, with live video overlay and
animation, provides the operator with an integrated and interactive
monitoring and control interface. The robot controllers are embedded on
mobile robots and are designed to be independent to the host computer.
By applying the newest PC and embedding technologies, the system has
high flexibility and fault-tolerance for a variety of highway
maintenance operations. Both the hardware design and software
development are described
A dynamical extension that makes possible the integration of a
kinematic controller and a torque controller for nonholonomic mobile
robots is presented. A combined kinematic/torque control law is
developed using backstepping and asymptotic stability is guaranteed by
Lyapunov theory. Moreover, this control algorithm can be applied to the
three basic nonholonomic navigation problems: tracking a reference
trajectory, path following and stabilization about a desired posture. A
general structure for controlling a mobile robot results that can
accommodate different control techniques ranging from a conventional
computed-torque controller, when all dynamics are known, to adaptive
controllers
A stable tracking control rule is proposed for nonholonomic
vehicles. The stability of the rule is proved through the use of a
Liapunov function. Inputs to the vehicle are a reference posture ( x
r, y r, θr)<sup>t
</sup> and reference velocities (νr, ωr)
t. The major objective of this study is to propose a control
rule to find reasonable target linear and rotational velocities (ν,
ω)t. Linearizing the system's differential equation is
useful for deciding parameters for critical dumping for a small
disturbance. In order to avoid slippage, a velocity/acceleration
limitation scheme is introduced. Several simulation results are
presented with or without the velocity/acceleration limiter. The control
rule and limiting method proposed are robot independent and hence can be
applied to various kinds of mobile robots with a dead reckoning ability.
This method was implemented on the autonomous mobile robot Yamabico-11.
Experimental results obtained are close to the results with the
velocity/acceleration limiter
In this paper, a control structure that makes possible the integration of a kinematic controller and an adaptive fuzzy controller for trajectory tracking is developed for nonholonomic mobile robots. The system uncertainty, which includes mobile robot parameter variation and unknown nonlinearities, is estimated by a fuzzy logic system (FLS). The proposed adaptive controller structure represents an amalgamation of nonlinear processing elements and the theory of function approximation using FLS. The real-time control of mobile robots is achieved through the online tuning of FLS parameters. The system stability and the convergence of tracking errors are proved using the Lyapunov stability theory. Computer simulations are presented which confirm the effectiveness of the proposed tracking control law. The efficacy of the proposed control law is tested experimentally by a differentially driven mobile robot. Both simulation and results are described in detail.
A mobile robot is one of the well-known nonholonomic systems. The
integration of a kinematic controller and a torque controller for the
dynamic model of a nonholonomic mobile robot has been presented (Fierro
and Lewis, 1995). In this paper, an adaptive extension of the controller
is proposed. If an adaptive tracking controller for the kinematic model
with unknown parameters exists, an adaptive tracking controller for the
dynamic model with unknown parameters can be designed by using an
adaptive backstepping approach. A design example for a mobile robot with
two actuated wheels is provided. In this design, a new kinematic
adaptive controller is proposed, then a torque adaptive controller is
derived by using the kinematic controller
An exponentially stable controller for a two-degree-of-freedom
robot with nonholonomic constraints is presented. Although this type of
system is open-loop controllable, this system has been shown to be
nonstabilizable via pure smooth feedback. A particular class of
piecewise continuous controllers is shown to exponentially stabilize the
mobile robot about the origin. This controller has the characteristic of
not requiring infinite switching like other approaches, such as the
sliding controller. Simulation results are presented
Linealización con Realimentación del Modelo Dinámico de un Robot Móvil y Control de Seguimiento de Trayectoria
- C. De La Cruz
- R Carelli
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