Time-optimal sliding-mode control of a mobile robot in a dynamic environment

Rubagotti, Matteo; Vedova, Marco L. Della; Ferrara, Antonella

doi:10.1049/iet-cta.2010.0678

Cited by 40 publications

(26 citation statements)

References 16 publications

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“…For the robot's feedback model (7) to solve the problem (5), an appropriate value of the feedback operator K has to be available to the robot's controller. Note that there are two methods for determining the LTI feedback operator K :…”

Section: Proposed Lti Feedback Operator Designmentioning

confidence: 99%

“…The optimal feedback operator K can be determined by following the classical Pontryagin's minimum principle, where K is treated as the open-loop control input to the feedback system (7). For that, let vec(K) transforms the matrix K into a column vector, which is formed by stacking the rows of K. The feedback model (7) can be rewritten aṡ…”

Section: Proposed Lti Feedback Operator Designmentioning

confidence: 99%

“…Numerous nonlinear control laws have been proposed in the literature to address the trajectory tracking problem of mobile robots, see [3], [4], [5] for backstepping methods, [6], [7], [8] for sliding mode control, [9], [10], [11] for moving horizon H ∞ tracking control coupled with disturbance effect, 1 http://en.wikipedia.org/wiki/Curiosity (rover) 2 http://en.wikipedia.org/wiki/Google driverless car 3 http://www.youtube.com/watch?v=YgEUrkY80-U 4 http://news.stanford.edu/news/2012/august/surfing-robot-082312.html [12] for transverse function approach, [13], [14] for formation control, and [15] for optimal motion planning. A vector-field orientation feedback control method for a differentially driven wheeled vehicle has been demonstrated in [16].…”

Section: Introductionmentioning

confidence: 99%

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Linear time-invariant feedback operator for mobile robot trajectory tracking

Miah

Gueaieb

Farkas

et al. 2015

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

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Abstract-In this paper we propose a linear time-invariant (LTI) state feedback operator for nonholonomic mobile robots to track a pre-defined trajectory on a 2D planar region. Designing an on-line smooth state feedback control law is still among the major challenges for solving the trajectory tracking problem of nonholonomic systems including differential drive mobile robots. To address this problem, numerous nonlinear feedback control laws have been proposed to date. Most of these feedback control laws yield online solutions to the trajectory tracking problem with satisfactory tracking errors asymptotically. In most cases, they suffer from an overwhelming degree of computational complexity even to track a 2D trajectory using a simple unicyclelike nonholonomic system. The proposed control law offers an advantage of being smooth and LTI state-feedback in addition to its capability to address problems of partially observed systems. The shortcoming of the proposed control law is that the LTI feedback operator is computed off-line before the robot applies its control signal into the left and right wheels through their actuators. The theoretical results are supported by computer simulations followed by experiments with an e-puck mobile robot.

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Section: Proposed Lti Feedback Operator Designmentioning

confidence: 99%

Section: Proposed Lti Feedback Operator Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear time-invariant feedback operator for mobile robot trajectory tracking

Miah

Gueaieb

Farkas

et al. 2015

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

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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

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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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“…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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Time-optimal sliding-mode control of a mobile robot in a dynamic environment

Cited by 40 publications

References 16 publications

Linear time-invariant feedback operator for mobile robot trajectory tracking

Linear time-invariant feedback operator for mobile robot trajectory tracking

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

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

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