Backstepping Control Design on the Dynamics of the Omni-Directional Mobile Robot

Cui, Qing Zhu; Li, Xun; Wang, Xiang Ke; Zhang, Meng

doi:10.4028/www.scientific.net/amm.203.51

Cited by 16 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that this controller is also able to stabilize the robot at a fixed configuration by simply tuning the weight matrices (P(t f ) and Q(t)) of the cost function (14). This is in contrast to many recent RFID-based techniques which usually tackle the localization problem only [16,6,50].…”

Section: Resultsmentioning

confidence: 89%

“…To solve for the nominal optimal trajectory using the feedback system (12) that minimizes the objective functional (14), we need to derive the necessary conditions of optimality. These necessary conditions are most readily found if the integrand of the cost functional (14) is recast in terms of Hamiltonian…”

Section: Nominal Pose and Control Generationmentioning

confidence: 99%

“…Let q(t) ≡ q[t, K(t)] be the solution of the feedback system (12), with the cost functional (14) for any choice of K(t) ∈ K ad . Since K o (t) is optimal with the associated trajectory q o (t), it is clear that J(K o ≤ J(K), ∀ K ∈ K ad .…”

Section: A Appendixmentioning

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 3 more Smart Citations

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

Miah

Gueaieb

2014

J Intell Robot Syst

View full text Add to dashboard Cite

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

show abstract

Section: Resultsmentioning

confidence: 89%

Section: Nominal Pose and Control Generationmentioning

confidence: 99%

Section: A Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Miah

Gueaieb

2014

J Intell Robot Syst

View full text Add to dashboard Cite

show abstract

“…These laws have been explored through a variety of control techniques, such as differential flatness and back-stepping [7,8,9], nonlinear control coupled with data fusion algorithms [10,11], and sliding mode control [12,13,14]. Recently, the trajectory tracking and the set-point stabilization problems of unicycle-type vehicles have been addressed in [15].…”

Section: Introductionmentioning

confidence: 99%

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

Miah¹,

Farkas²,

Gueaieb³

et al. 2017

International Journal of Robotics and Automation

View full text Add to dashboard Cite

In this paper, we propose an optimal state feedback control law for addressing point stabilization and tracking problems of nonholonomic vehicles with Ackermann steering in a unified manner. Unlike other feedback controllers that perform dynamic linearization of vehicle models, the proposed optimal feedback controller provides the state feedback control to the original nonlinear vehicle model for achieving excellent state-tracking performance.In addition, nonlinear control techniques suggested in the literature to date require that the desired trajectory of the robot is generated using persistently excited inputs. This may be too restrictive and non-realistic hypothesis to mimic a real scenario. Here, we address this issue by developing a smooth state-feedback control law that is formulated by modifying the classical Pontryagin's minimum principle. The proposed control law can be applied for solving control problems of a general class of nonlinear affine systems. The proposed control scheme offers a modular solution to other control techniques for a large number of mobile robot applications. The theoretical results are validated through computer simulations.

show abstract