Online robust tube-based MPC for time-varying systems: a practical approach

González, Roberto J.; Fiacchini, Mirko; Álamo, T.; Guzmán, José Luís; Rodríguez, Francisco

doi:10.1080/00207179.2011.594093

Cited by 76 publications

(53 citation statements)

References 21 publications

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“…The standard solution to the problem (15) follows from the similar techniques given in [6], [29,Ch. 3], when the robot simultaneously receives measurements from all RF sensors placed in its operating range.…”

Section: ∆Q(t) = F(t)∆q(t)+g(t)∆u(t)+l(t)ξ(t) ∆Q(0) = ∆Qmentioning

confidence: 99%

“…In the technical literature, the trajectory tracking problem of mobile robots has been solved using nonlinear control laws, see [7], [8], [9] for backstepping methods, [10], [11], [12] for sliding mode control, [13], [14], [15] for moving horizon H ∞ tracking control coupled with disturbance effect, and [16] for transverse function approach. A vector-field orientation feedback control method for a differentially driven wheeled vehicle has been demonstrated in [17].…”

Section: Introductionmentioning

confidence: 99%

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Neighboring optimal control for mobile robot trajectory tracking with range-limited sensors

Miah

Gueaieb

Spinello

et al. 2015

2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

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Abstract-Among the major challenges in tracking a predefined trajectory of a nonholonomic mobile robot operating in indoor environments is to determine an appropriate feedback control. In the technical literature, numerous controllers have been proposed to date for solving trajectory tracking and/or regulation problems of mobile robots. Most of them are quite promising to implement and mobile robots can operate in quite complex environments with these controllers. Nevertheless, one of the shortcomings of most of the existing controllers is the requirement of sophisticated hardwares, which, in some cases, more costly than the mobile robot itself. In addition, the analytical expression for most of the controllers is quite complex even for a simple nonholonomic system, an unicycle, for example. In this paper, we propose a neghboring optimal controller coupled with the state estimation for a differential drive mobile robot to track a pre-defined trajectory using signal strength measurements from RF (radio frequency) sensors placed in its operating environment. We emphasize that the RF sensors have limited communication range with the robot. The proposed controller is easy to implement, does not require sophisticated hardware for processing, and has relatively easier expression for the feedback controller. A numerical example is provided to validate the theoretical results. Computer simulations will be backed by experimental results for future investigations.

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Section: ∆Q(t) = F(t)∆q(t)+g(t)∆u(t)+l(t)ξ(t) ∆Q(0) = ∆Qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Neighboring optimal control for mobile robot trajectory tracking with range-limited sensors

Miah

Gueaieb

Spinello

et al. 2015

2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

View full text Add to dashboard Cite

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“…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%

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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“…In some cases, the satisfactory tracking performance is achieved at the cost of vehicle's model simplification, see [20,21], for example. Model predictive control techniques are quite popular and have been extensively used for solving tracking problems of mobile robots in the optimal control literature, see [22,23,24], however, they suffer from defining appropriate feedback laws for partially observed states. Authors in [25,26,27] have recently adopted model predictive control laws for solving the tracking problems of nonholonomic systems.…”

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

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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.

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Online robust tube-based MPC for time-varying systems: a practical approach

Cited by 76 publications

References 21 publications

Neighboring optimal control for mobile robot trajectory tracking with range-limited sensors

Neighboring optimal control for mobile robot trajectory tracking with range-limited sensors

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

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

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