Identification of a vertical hopping robot model via harmonic transfer functions

Uyanik, Ismail; Ankaralı, Mustafa Mert; Cowan, Noah J.; Saranlı, Uluç; Morgül, Ömer

doi:10.1177/0142331215583327

Cited by 13 publications

(12 citation statements)

References 25 publications

(30 reference statements)

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“…Our assumption only limits the number of unknown Fourier series coefficients of each switching subsystem, ( A i k , B i k ). This is a fair assumption when the switching subsystems are smooth but the resultant system includes many harmonic components (such as in the case of legged locomotion [27]). Thus, we limit the number of Fourier series coefficients for each subsystem, ( A i k , B i k ), to the lowest H frequencies in Eq.…”

Section: Remarkmentioning

confidence: 99%

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Uyanik

Hamzaçebi

Ankaralı

2019

Turk J Elec Eng & Comp Sci

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In this paper, we propose a novel frequency domain state-space identification method for switching linear discrete time-periodic (LDTP) systems with known scheduling signals. The state-space identification problem of linear time-invariant (LTI) systems has been widely studied both in the time and frequency domains. Indeed, there have been several studies that also concentrated on state-space identification of both continuous and discrete linear time-periodic (LTP) systems. The focus in this study is the family of LDTP systems that switch among a finite set of subsystems triggered by known periodic scheduling signals. We address the state-space identification of such systems in frequency domain using input-output data. We also assume that full state measurements are available for the identification process.The major difference of our study is that we explicitly model the known scheduling signals responsible for switching, which greatly reduces the parametric complexity as well as potentially increases the estimation accuracy by avoiding overfitting. In our identification framework, we gather the Fourier transformations of input-output data, known periodic scheduling signals, and state-space system dimensions and fuse them in a linear regression framework. Later, we estimate the Fourier series coefficients of the time-periodic system and input matrices using a least-squares solution. Finally, we illustrate the effectiveness of our method using a switching LDTP system that is based on the damped Mathieu equation.

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Section: Remarkmentioning

confidence: 99%

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Uyanik

Hamzaçebi

Ankaralı

2019

Turk J Elec Eng & Comp Sci

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“…We show that Eqs. (11) and (12) can be solved when partial feedback linearization is used to cancel out some nonlinear terms. Besides, partial feedback linearization can also be used to enforce specific solutions to Eqs.…”

Section: Solving Stance Dynamicsmentioning

confidence: 99%

“…Besides, partial feedback linearization can also be used to enforce specific solutions to Eqs. (11) and (12) such as specifying some desired trajectories to the point mass during its stance locomotion.…”

Section: Solving Stance Dynamicsmentioning

confidence: 99%

“…Therefore, the main research direction in the field of legged locomotion is to first analyze and understand legged locomotion [4,5], then build legged robots with high maneuverability and control their locomotion by inspiring from nature [6]. Detailed reviews about legged robots can be found in [7,8] 1.1 Models for running with legged robots There are various approaches that are used to represent and study legged locomotion such as physicsbased mathematical models [9,10], data-driven models [11] and central pattern generator-based models [12][13][14]. Among these, it would be fair to say that a vast majority of the current literature exclusively focus on developing physics-based mathematical models and performing parametric fit to the data.…”

Section: Introductionmentioning

confidence: 99%

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On the periodic gait stability of a multi-actuated spring-mass hopper model via partial feedback linearization

Hamzaçebi

Morgül

2017

Nonlinear Dyn

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Spring-loaded inverted pendulum (SLIP) template (and its various derivatives) could be considered as the mostly used and widely accepted models for describing legged locomotion. Despite their simple nature, as being a simple spring-mass model in dynamics perspective, the SLIP model and its derivatives are formulated as restricted three-body problem, whose non-integrability has been proved long before. Thus, researchers proceed with approximate analytical solutions or use partial feedback linearization when numerical integration is not preferred in their analysis. The key contributions of this paper can be divided into two parts. First, we propose a dissipative SLIP model, which we call as multi-actuated dissipative SLIP (MD-SLIP), with two extended actuators: one linear actuator attached serially to the leg spring and one rotary actuator attached to hip. The second contribution of this paper is a partial feedback linearization strategy by which we can cancel some nonlinear dynamics of the proposed model and obtain exact analytical solution for the equations of motion. This allows us to investigate stability characteristics of the hopping gait obtained from the MD-SLIP model. We illustrate the applicability of our solutions with open-loop and closed-loop hopping performances on rough terrain simulations.

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“…Most of this previous work, however, uses linear time-invariant (LTI) models to approximate system dynamics and their nominal trajectories. As we have shown in our previous work, such LTI representations can be inadequate in capturing time-varying characteristics of locomotor behaviors where nominal trajectories are large limit-cycles with distinct hybrid phases (Uyanik et al, 2015a;Kiemel et al, 2013;Ankarali and Cowan, 2014;Uyanik et al, 2015b). We now show that linear analysis can still be applied in this context, using the LTP framework to relax the time-invariance assumption, allowing us to identify and analyze input and measurement delays in rhythmic legged locomotor behaviors.…”

Section: Introductionmentioning

confidence: 97%

Independent Estimation of Input and Measurement Delays for a Hybrid Vertical Spring-Mass-Damper via Harmonic Transfer Functions

et al. 2015

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Abstract:System identification of rhythmic locomotor systems is challenging due to the time-varying nature of their dynamics. Even though important aspects of these systems can be captured via explicit mechanics-based models, it is unclear how accurate such models can be while still being analytically tractable. An alternative approach for rhythmic locomotor systems is the use of data-driven system identification in the frequency domain via harmonic transfer functions (HTFs). To this end, the input-output dynamics of a locomotor behavior can be linearized around a stable limit cycle, yielding a linear, time-periodic system. However, few if any modelbased or data-driven identification methods for time-periodic systems address the problem of input and measurement delays in the system. In this paper, we focus on data-driven system identification for a simple mechanical system and analyze its dynamics in the presence of input and measurement delays using HTFs. By exploiting the way input delays are modulated by the periodic dynamics, our results enable the separate, independent estimation of input and measurement delays, which would be indistinguishable were the system linear and time invariant.

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Identification of a vertical hopping robot model via harmonic transfer functions

Cited by 13 publications

References 25 publications

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

On the periodic gait stability of a multi-actuated spring-mass hopper model via partial feedback linearization

Independent Estimation of Input and Measurement Delays for a Hybrid Vertical Spring-Mass-Damper via Harmonic Transfer Functions

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