Saturated stabilization and tracking of a nonholonomic mobile robot

Jiang, Zhong Ping; Lefeber, Erjen; Nijmeijer, Henk

doi:10.1016/s0167-6911(00)00104-3

Cited by 226 publications

(140 citation statements)

References 19 publications

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“…Theorem 2 (Adapted from [56]) Consider the robot's linear kinematic model (25) and its quadratic cost functional given by (28). The optimal linear-quadratic state feedback control law is given by…”

Section: Neighboring Optimal Controlmentioning

confidence: 99%

“…For wheeled mobile robots, conventional control laws have been applied for solving tracking problems [58,30,32,43,1,23,49] and stabilization problems [3,17,51,54,8]. For example, see [29,28,39,48,12,14] for backstepping methods [11,24,53] for sliding mode control, [9,34,18] for moving horizon H ∞ tracking control coupled with disturbance effect, and [47] for transverse function approach. A vector-field orientation feedback control method for a differentially driven wheeled vehicle has been demonstrated in [46].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

RFID-Based Mobile Robot Trajectory Tracking and Point Stabilization Through On-line Neighboring Optimal Control

Miah

Gueaieb

2014

J Intell Robot Syst

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In this manuscript, we propose an on-line trajectorytracking algorithm for nonholonomic Differential-Drive Mobile Robots (DDMRs) in the presence of possibly large parametric and measurement uncertainties. Most mobile robot tracking techniques that depend on reference RF beacons rely on approximating line-of-sight (LOS) distances between these beacons and the robot. The approximation of LOS is mostly performed using Received Signal Strength (RSS) measurements of signals propagating between the robot and RF beacons. However, accurate mapping between RSS measurements and LOS distance remains a significant challenge and is almost impossible to achieve in an indoor reverberant environment. This paper contributes to the development of a neighboring optimal control strategy where the two major control tasks, trajectory tracking and point stabilization, are solved and treated as a unified manner using RSS measurements emitted from Radio Frequency IDentification (RFID) tags. The proposed control scheme is divided into two cascaded phases. The first phase provides the robot's nominal control inputs (speeds) and its trajectory using full-state feedback. In the second phase, we design the neighboring optimal controller, where RSS measurements are used to better estimate the robot's pose by employing an optimal filter. Simulation and experimental results are presented to demonstrate the performance of the proposed optimal feedback controller for solving the stabilization and trajectory tracking problems using a DDMR. Keywords Mobile robot navigation · RFID systems · optimal control · trajectory tracking · robot stabilization · nonholonomic systems. Frequently Used Symbols K(t)Feedback control gain at time t H K Hamiltonian's gradient with respect to K s Number of RFID tags in the environment ψ Costate variable (Lagrange multiplier)Robot's actual and desired pose at time t q j t ∈ R 3 jth tag position in 3D space t 0 ,t f Initial and final time instantsRobot's control input vector at time t ξ (t) Robot's actuator noise at time t ζ (t)Measurement noise vector at time t (·) o , (·) ε , (·) ad Optimal, perturb, admissible value of (·) L Lebesgue measurable function space ν T dJ(·) Gateaux (directional) derivative of J in direction ν 1 Introduction

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Section: Neighboring Optimal Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

RFID-Based Mobile Robot Trajectory Tracking and Point Stabilization Through On-line Neighboring Optimal Control

Miah

Gueaieb

2014

J Intell Robot Syst

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“…This control law is modified to include path following [Fierro and Lewis, 1995] and stabilization by utilizing the averaging approach that yields a smooth transition between trajectory tracking and stabilization [Pettersen and Nijmeijer, 1999]. A control law exploiting backstepping and boundedness of the sine of a term divided by that term yields global asymptotic stability [Jiang and Nijmeijer, 1997], which is expanded to include saturation phenomena [Jiang et al, 2001]. Exploiting the triangular structure of the error variables coming about due to a transformation to the body frame.…”

Section: Trajectory Trackingmentioning

confidence: 99%

Modeling, Identification, and Control of an Unmanned Surface Vehicle

Sonnenburg

Woolsey

2013

Journal of Field Robotics

140

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This dissertation addresses the modeling, identification, and control of an automated planing vessel. To provide motion models for trajectory generation and to enable model-based control design for trajectory tracking, several experimentally identified models are compared over a wide range of speed and planing conditions for the Virginia Tech Ribcraft Unmanned Surface Vehicle. The modeling and identification objective is to determine a model which is sufficiently rich to enable effective model-based control design and trajectory optimization, sufficiently simple to allow parameter identification, and sufficiently general to describe a variety of hull forms and actuator configurations. Beginning with a 6 degree of freedom nonlinear dynamic model, several linear steering and speed models are obtained as well as a thruster model.The Ribcraft USV tracks trajectories generated with the selected maneuvering models by using a backstepping trajectory controller. A PD cascade trajectory control law is also developed and the performance of the two controllers is compared using aggressive trajectories. The backstepping control law compares favorably to the PD cascade controller. The backstepping control law is then further modified to account for nonlinear sternward dynamics and for a constant or slowly varying fluid flow. ACKNOWLEDGMENTSThis dissertation is the product of the culmination of years of research and field experimentation that required the collective abilities only found in a group of skilled researchers. There are many people that guided me through the higher level decision-making and advising process as well as the more laborious experimentation and implementation efforts. Without these people I would not have been able to finish a dissertation even approaching this quality.

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“…An electromagnetic approach for path guidance of a mobile-robot-based automatic transport service system with a PD control algorithm was investigated by Wu et al (2001). Jiang, et al (2001) developed a model-based control design strategy that deals with global stabilization and global tracking control for the kinematic model with a nonholonomic WMR in the presence of input saturations. An adaptive robust controller was proposed for the global tracking problem for the dynamic of the non-holonomic systems with unknown dynamics (Dong, 1999).…”

Section: Controllers For Autonomous Mobile Robotsmentioning

confidence: 99%