Analytical design of the Acrobot exponential tracking with application to its walking

Anderle, Milan; Čelikovský, Sergej

doi:10.1109/icca.2009.5410363

Cited by 14 publications

(15 citation statements)

References 12 publications

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“…In [9] a high performance nonlinear tracking algorithm was developed based on partial feedback linearization proposed in [10]. In this example we will design an approximate nonlinear Kalman filter for state estimation that will be combined with this nonlinear tracking algorithm.…”

Section: Example: Kalman Filtering For Nonlinear Tracking Of Walmentioning

confidence: 99%

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Kalman filter under nonlinear system transformations

Dolinsky

Čelikovský

2012

2012 American Control Conference (ACC)

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This article deals with state estimation and filtering in nonlinear systems. More precisely the design of approximate nonlinear Kalman filter for nonlinear systems linearizable by a nonlinear coordinate transformation with possible application of nonlinear output injection is studied. The main idea is to reduce the errors introduced by the linearization used by the approximate filter using exact full or partial linearization of the system. Underlying transformations of both deterministic and stochastic signals are studied. An example of designing such an approximate nonlinear filter for nonlinear tracking of walking like motion of bipedal robot is given.

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Section: Example: Kalman Filtering For Nonlinear Tracking Of Walmentioning

confidence: 99%

“…where µ 1 (t), µ 2 (t), µ 3 (t) are known smooth functions [9]. Using Theorem 3.1 from [9] the one can stabilize (52) and solve the tracking problem by using the following state feedback…”

Section: B Equations Of Motionmentioning

confidence: 99%

Kalman filter under nonlinear system transformations

Dolinsky

Čelikovský

2012

2012 American Control Conference (ACC)

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“…5], while the feedback control law ( (12) and (14)) has created a zero dynamics of the stance phase dynamics, it has not created a hybrid zero dynamics (HZD), that is, the zero dynamics considering the impact model (2). If the control law could be modified so as to create a HZD, then the study of the swing phase zero dynamics (15) and the impact model would be sufficient to determine the stability of the complete system of the robot, thereby leading to a reduced-dimension stability test [18].…”

Section: The Hybrid Zero Dynamicsmentioning

confidence: 99%

“…There exist various studies about the walking control of the under-actuated mechanical systems [1][2][3][4][5]. Most controllers of these systems are based on tracking reference motions.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and time-varying walking control for an under-actuated planar biped robot

Wang¹,

Chevallereau²

2011

Robotics and Autonomous Systems

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“…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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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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Analytical design of the Acrobot exponential tracking with application to its walking

Cited by 14 publications

References 12 publications

Kalman filter under nonlinear system transformations

Kalman filter under nonlinear system transformations

Stability analysis and time-varying walking control for an under-actuated planar biped robot

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

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