Advanced LMI based analysis and design for Acrobot walking

The virtual constraints method is used here to design and control the walking-like trajectory of the 4-link having 4 degrees of freedom: stance angle, 2 knees angles and 1 hip angle and 3 actuators only as the stance leg angle is not actuated. Two different approaches are compared. First, the wellknown approach consists in setting virtual constraints as the dependencies of knees and hip angles on the stance leg angle. Therefore there are 3 virtual constraints enforced by all 3 available inputs and reducing thereby overall 4 degrees of freedom to a single degree of freedom unactuated system. Selecting suitable constraints functions, various walking-like trajectories can be designed. Secondly, this three constraints approach is compared with the alternative one developed very recently. Here, only two constraints are imposed being dependencies of knees angles on the hip angle thereby reducing the 4-link to 2 degrees of freedom system with a single actuator at the hip angle. Such a system may be naturally called as the generalized Acrobot. Comparison of both approaches is performed by numerical simulation using 4-link mathematical model of real laboratory equipement. In the future, the most suitable method would be selected for the real implementation, in particular, based on the current comparative study.

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“…Series of the previous works [9], [1], [3], [4], [5] was related to the control of the Acrobot model, i.e. the model with 2 DOF.…”

Section: B Control Of the 4-link Model Based On Two Virtual Constraintsmentioning

confidence: 99%

“…In particular, numerous techniques and results how to design the walking-like Acrobot trajectory and its exponential tracking has been developed, see [9], [3], [1], [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Virtual constraints for the underactuated walking design: Comparison of two approaches

Anderte

Čelikovský

Ibarra

2013

2013 9th Asian Control Conference (ASCC)

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“…Various techniques are used in [11], [12], [13], [17] provide feedback to stabilize the above error dynamics, among them LMI robust design, high-gain controllers or use of timevarying error dynamics transformations. Their drawbacks are either high degree of conservatism or heuristic character as in case of LMI use.…”

Section: Partial Exact Feedback Linearization Of the Acrobot Modelmentioning

confidence: 99%

“…Physically this quite interestingly corresponds to keeping constant velocity of the center of mass of the Acrobot. Improvement of the tracking feedback was obtained in [12], [13]. In [12], the appropriate exponentially stable tracking was obtained by solving quadratic stability of a linear system with polytopic uncertainty applying LMI methods.…”

Section: Introductionmentioning

confidence: 99%

“…Improvement of the tracking feedback was obtained in [12], [13]. In [12], the appropriate exponentially stable tracking was obtained by solving quadratic stability of a linear system with polytopic uncertainty applying LMI methods. The appropriate exponential tracking presented in [13] was based on the knowledge of the time dependent uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Approximate feedback linearization of the Acrobot tracking error dynamics with application to its walking-like trajectory tracking

Anderle

Čelikovský

2012

2012 20th Mediterranean Conference on Control &Amp; Automation (MED)

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The purpose of this paper is to provide theoretical framework enabling to design tracking feedback for a general Acrobot trajectory which allows rigorous convergence proof. It is based on the partial exact feedback linearization of the Acrobot model followed by further approximate feedback linearization of the tracking error dynamics for arbitrary target trajectory. The approach presented here enables to prove the convergence in a rigorous way at least for small initial tracking errors. The slight novelty here is that neglecting is made with respect to tracking error along any general trajectory to be tracked, not just in some neighborhood of fixed working point. To demonstrate viability of this approach, simulations of a tracking of a walking-like cyclic trajectory are presented. The walking includes several steps including impacts between them. As a matter of fact, the exponentially stable tracking during the swing phase only is capable to stabilize overall walking, including the effect of the impacts.

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Robust and nonlinear control literature survey (no. 21)

2010

Int. J. Robust Nonlinear Control

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In order to keep readers up-to-date, the journal will contain a list of recently published journal articles relevant to the fields of robust and nonlinear control six times a year. This list is compiled from a wide range of journals. Please note that even though the list has been broadly categorized these classifications are by no means strict, and are there to assist the reader. Please also note that inclusion in the list is not an endorsement of a paper's quality. If you have any suggestions or comments, please email Dr Jiqiang Wang at jiqiang.wang@nuaa.edu.cn. THEORETICAL DEVELOPMENTS IN ROBUST CONTROL

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Advanced LMI based analysis and design for Acrobot walking

Cited by 20 publications

References 6 publications

Virtual constraints for the underactuated walking design: Comparison of two approaches

Virtual constraints for the underactuated walking design: Comparison of two approaches

Approximate feedback linearization of the Acrobot tracking error dynamics with application to its walking-like trajectory tracking

Robust and nonlinear control literature survey (no. 21)

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