Moving Horizon ${\cal H}_{\infty}$ Tracking Control of Wheeled Mobile Robots With Actuator Saturation

Chen, Hong; Ma, Miaomiao; Hu, Wang; Liu, Zhiyuan; Cai, Zixing

doi:10.1109/tcst.2008.2000985

Cited by 74 publications

(51 citation statements)

References 23 publications

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“…This is summarized below. Theorem 1 (Adapted from [29]): Consider the robot's linear kinematic model (14) and its quadratic cost functional given by (13). The optimal linear-quadratic state feedback control law is given by…”

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%

See 1 more Smart Citation

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

show abstract

“…These techniques are quite powerful to solve trajectory tracking problems of nonlinear affine systems but require complex feedback law even for a simple unicycle-like affine systems [19]. 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.…”

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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“…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%

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.

show abstract

Moving Horizon ${\cal H}_{\infty}$ Tracking Control of Wheeled Mobile Robots With Actuator Saturation

Cited by 74 publications

References 23 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

Linear Time-Varying Feedback Law for Vehicles With Ackermann Steering

Linear time-invariant feedback operator for mobile robot trajectory tracking

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