A Continuous Control for Stabilizing the Extended Nonholonomic Double Integrator

2011 ◽  
Vol 464 ◽  
pp. 217-220
Author(s):  
Yan Peng ◽  
Mei Liu ◽  
Qing Jiu Huang ◽  
Shao Rong Xie
Keyword(s):  
Mobile Robot ◽  
Dimensional Space ◽  
Control Law ◽  
Continuous Control ◽  
Time Varying ◽  
Higher Dimensional ◽  
Control Scheme ◽  
And Performance ◽  
Time Invariant ◽  
Double Integrator

The extended nonholonomic double integrator (ENDI) cannot be asymptotically stabilized by a continuous and time-invariant feedback controller since it violates the Brockett’s condition. In this paper, a new continuous control scheme is proposed to stabilize the ENDI system without drift. The dynamics of an ENDI system is enlarged to a higher dimensional space where a continuous but time-varying control law is designed for its stabilization. Besides the theoretical proofs, simulations conducted on the dynamics of a mobile robot are also presented to demonstrate the validity and performance of the proposed method.

A Continuous Control for Stabilizing the Extended Nonholonomic Double Integrator: Theory and Simulation Results

2010 ◽  
Vol 44-47 ◽  
pp. 3987-3991
Author(s):  
Yan Peng ◽  
Mei Liu ◽  
Shao Rong Xie ◽  
Jun Luo
Keyword(s):  
Dimensional Space ◽  
Control Law ◽  
Continuous Control ◽  
Time Varying ◽  
Higher Dimensional ◽  
Control Scheme ◽  
Simulation Results ◽  
And Performance ◽  
Time Invariant ◽  
Double Integrator

The extended nonholonomic double integrator (ENDI) cannot be asymptotically stabilized by a continuous and time-invariant feedback controller since it violates the Brockett’s condition. In this paper, a new continuous control scheme is proposed to stabilize the ENDI system without drift. The dynamics of an ENDI system is enlarged to a higher dimensional space where a continuous but time-varying control law is designed for its stabilization. Besides the theoretical proofs, simulations conducted on the dynamics of a mobile robot are also presented to demonstrate the validity and performance of the proposed method.

scholarly journals An Adaptive Control Scheme for Nonholonomic Mobile Robot with Parametric Uncertainty

10.5772/5801 ◽  
2005 ◽  
Vol 2 (1) ◽  
pp. 8 ◽  
Author(s):  
F. Mnif ◽  
F. Touati
Keyword(s):  
Mobile Robot ◽  
Parametric Uncertainty ◽  
Lyapunov Stability Theory ◽  
Original System ◽  
Stability And Convergence ◽  
Nonholonomic Mobile Robot ◽  
Control Scheme ◽  
The Stability ◽  
Invariant Control ◽  
Time Invariant

This paper addresses the problem of stabilizing the dynamic model of a nonholonomic mobile robot. A discontinuous adaptive state feedback controller is derived to achieve global stability and convergence of the trajectories of the of the closed loop system in the presence of parameter modeling uncertainty. This task is achieved by a non smooth transformation in the original system followed by the derivation of a smooth time invariant control in the new coordinates. The stability and convergence analysis is built on Lyapunov stability theory.

PD-like controller with impedance for delayed bilateral teleoperation of mobile robots

Robotica ◽  
2015 ◽  
Vol 34 (9) ◽  
pp. 2151-2161 ◽  
Author(s):  
E. Slawiñski ◽  
S. García ◽  
L. Salinas ◽  
V. Mut
Keyword(s):  
Mobile Robot ◽  
Mobile Robots ◽  
Force Feedback ◽  
Robot Motion ◽  
Time Varying ◽  
Control Parameters ◽  
Bilateral Teleoperation ◽  
Teleoperation System ◽  
Control Scheme ◽  
The Stability

SUMMARYThis paper proposes a control scheme applied to the delayed bilateral teleoperation of mobile robots with force feedback in face of asymmetric and time-varying delays. The scheme is managed by a velocity PD-like control plus impedance and a force feedback based on damping and synchronization error. A fictitious force, depending on the robot motion and its environment, is used to avoid possible collisions. In addition, the stability of the system is analyzed from which simple conditions for the control parameters are established in order to assure stability. Finally, the performance of the delayed teleoperation system is shown through experiments where a human operator drives a mobile robot.

Exponential Stabilization of a Wheeled Mobile Robot Via Discontinuous Control

1999 ◽  
Vol 121 (1) ◽  
pp. 121-126 ◽  
Author(s):  
A. Astolfi
Keyword(s):  
Mobile Robot ◽  
State Feedback ◽  
Wheeled Mobile Robot ◽  
State Feedback Control ◽  
Exponential Stabilization ◽  
Control Law ◽  
Model Errors ◽  
Closed Loop System ◽  
Noisy Measurements ◽  
Time Invariant

In the present work the problem of exponential stabilization of the kinematic and dynamic model of a simple wheeled mobile robot is addressed and solved using a discontinuous, bounded, time invariant, state feedback control law. The properties of the closed-loop system are studied in detail and its performance in presence of model errors and noisy measurements are evaluated and discussed.

scholarly journals Delayed Bilateral Teleoperation of Wheeled Robots including a Command Metric

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Franco Penizzotto ◽  
Sebastian García ◽  
Emanuel Slawiñski ◽  
Vicente Mut
Keyword(s):  
Mobile Robot ◽  
System Architecture ◽  
Communication Channel ◽  
Force Feedback ◽  
Time Varying ◽  
Bilateral Teleoperation ◽  
Wheeled Robots ◽  
Teleoperation System ◽  
Control Scheme ◽  
The Stability

This paper proposes a control scheme applied to the delayed bilateral teleoperation of wheeled robots with force feedback, considering the performance of the operator’s command execution. In addition, the stability of the system is analyzed taking into account the dynamic model of the master as well as the remote mobile robot under asymmetric and time-varying delays of the communication channel. Besides, the performance of the teleoperation system, where a human operator drives a 3D simulator of a wheeled dynamic robot, is evaluated. In addition, we present an experiment where a robot Pioneer is teleoperated, based on the system architecture proposed.

On Robust Stability and Performance With Time-Varying Control

1995 ◽  
Vol 117 (4) ◽  
pp. 635-637 ◽  
Author(s):  
Mohammed Dahleh
Keyword(s):  
Performance Improvement ◽  
Robust Stabilization ◽  
Point Of View ◽  
Time Varying ◽  
Discrete Time Systems ◽  
And Performance ◽  
The Stability ◽  
Bounded Perturbations ◽  
Time Invariant ◽  
Time Systems

The analysis of time-varying control for robust stabilization and performance improvement is considered. This problem has been investigated in recent years from the point of view of assessing the capabilities of time-varying control to stabilize plants with structured norm bounded perturbations. In this paper, it is shown that time-varying compensation provides no improvement over time-invariant compensation for the stability and performance robustness of discrete-time systems with structured, causal, time-varying, and norm-bounded perturbations, where the norm on the perturbations is the l2-induced norm. The results of this paper help in completing the picture for the case of time-varying perturbations.

Model Reference Control of a Gas Turbine Engine

1996 ◽  
Vol 210 (4) ◽  
pp. 291-296 ◽  
Author(s):  
R A Perez
Keyword(s):  
Gas Turbine ◽  
Linear Time ◽  
Gas Turbine Engine ◽  
Control Law ◽  
Model Reference ◽  
Turbine Engine ◽  
Linear Time Invariant ◽  
Model Reference Control ◽  
Higher Dimensional ◽  
Time Invariant

A simple control law is developed that guarantees that the outputs of a linear time invariant plant with feedthrough elements will converge asymptotically to a pre-specified set of desired trajectories. This control law is illustrated on a gas turbine engine to demonstrate its applicability to higher dimensional problems and to highlight the fast asymptotic convergence towards the desired trajectories. The algorithm presented here is fairly straightforward to implement, and should be a useful tool for model reference control. The desired model is implemented off-line, thus allowing for a potential real-time application. The only assumption made in this work is that the modes of the ‘actual’ plant are controllable. No assumptions are made or required on the ‘desired’ plant. The dynamic characteristics of both the ‘actual’ and the ‘desired’ plant can actually be quite different. The control law generates an input that forces the ‘actual’ outputs to follow the ‘desired’ trajectories.

Optimal Linear State Feedback Time-Varying Regulator for a Unicycle Mobile Robot

2008 ◽  
Author(s):  
Elvira Rafikova ◽  
Paulo R. G. Kurka ◽  
Marat Rafikov
Keyword(s):  
Mobile Robot ◽  
State Feedback ◽  
Control Design ◽  
State Feedback Control ◽  
Optimal Time ◽  
Control Law ◽  
Time Varying ◽  
Optimal Linear ◽  
Linear State ◽  
Feedback Time

This paper proposes an optimal time-varying linear state feedback control for wheeled mobile robot of the unicycle type. The control law that stabilizes exponentially the motion of the robot to a given desired trajectory is found, after transformation of the cinematic model of the robot into a well-known Brocket integrator [1]. Numerical simulations are presented in order to demonstrate the effectiveness of the proposed control design.

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