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

Hamzaçebi, Hasan; Morgül, Ömer

doi:10.1007/s11071-016-3307-y

Cited by 16 publications

(8 citation statements)

References 37 publications

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“…Descriptions of different extended SLIP models can be found in [20]. The use of models to control legged robots is also reported [21][22][23][24][25][26]. In addition to single-leg models, bipedal models and their controls have been widely studied [6,7,27].…”

Section: Introductionmentioning

confidence: 99%

The generalized spring-loaded inverted pendulum model for analysis of various planar reduced-order models and for optimal robot leg design

Lu,

Lin

2024

Bioinspir. Biomim.

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This paper proposes a generalized spring-loaded inverted pendulum (G-SLIP) model to explore various popular reduced-order dynamic models' characteristics and suggest a better robot leg design under specified performance indices. The G-SLIP model’s composition can be varied by changing the model’s parameters, such as ground contacting type and spring property. It can be transformed into four widely used models: the spring-loaded inverted pendulum (SLIP) model, the two-segment leg (TSL) model, the SLIP with rolling foot (SLIP-RF) model, and the rolling SLIP (R-SLIP) model. The effects of rolling contact and spring configuration on the dynamic behavior and fixed-point distribution of the G-SLIP model were analyzed, and the basins of attraction (BOA) of the four described models were studied. By varying the parameters of the G-SLIP model, the dynamic behavior of the model can be optimized. Optimized for general locomotion running at various speeds, the model provided leg design guidelines. The leg was empirically fabricated and installed on the hexapod for experimental evaluation. The results indicated that the robot with a designed leg runs faster and is more power-efficient.

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Section: Introductionmentioning

confidence: 99%

The generalized spring-loaded inverted pendulum model for analysis of various planar reduced-order models and for optimal robot leg design

Lu,

Lin

2024

Bioinspir. Biomim.

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“…In addition to added torque at the hip, Hamzacebi and Morgul added another linear actuator to the TD-SLIP model to control the leg length and improve stability [11]. Later, they studied a multi-actuated dissipative SLIP model, which further added a damper to the leg [12]. Similarly, both studies were undertaken analytically and through simulation without experimental applications.…”

Section: Introductionmentioning

confidence: 99%

A Torque-actuated dissipative spring loaded inverted pendulum model with rolling contact and Its application to hexapod running

Wang²,

Huang

et al. 2019

Bioinspir. Biomim.

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We report on the development and analysis of a new torque-actuated dissipative spring loaded inverted pendulum model with rolling contact (TDR-SLIP), which is a successor to the previously developed spring loaded inverted pendulum model with rolling contact (R-SLIP) model. The stability properties of the models were analyzed numerically via steps-to-fall analysis and return map analysis, wherein the dimensionless parameters are varied to analyze their effects on the dynamic performance of the model, including torque, damping constant, spring constant, touchdown angle, touchdown speed, and landing angle. Because the involvement of torque and damping in the TDR-SLIP model is similar to other recently developed torque-actuated dissipative spring loaded inverted pendulum studies, their performance was compared so that the unique features of the TDR-SLIP model, such as rolling contact, could be investigated. To undertake the comparison, a method for yielding parameter equivalency between these two models is also reported. In addition to its analytical role, the TDR-SLIP model served as a template to initiate the stable running behavior of the empirical robot acted as the anchor. Two sets of legs were evaluated-the original compliant halfcircular leg of the robot and the new mechanical legs, which resemble the morphology of the TDR-SLIP model. Two types of control strategies were tested-position-based control and hybrid control. The experimental results reveals that the low-damped compliant half-circular leg and the mechanical leg match the behaviors of the R-SLIP model and the TDR-SLIP model, respectively, and the robot with hybrid control performs more stably and more closely to the model profile. In addition, when the robot's motion follows the template's stable dynamics, the energy cost of the leg in stance can be significantly lower than that in flight.

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“…Initial formulations of this type of systems are generally modeled as nonlinear hybrid dynamical * Correspondence: uyanik@jhu.edu This work is licensed under a Creative Commons Attribution 4.0 International License. systems that include some state-dependent scheduling functions [12][13][14][15]. However, a vast majority of the system identification studies for such systems focus on their local behavior around a periodic orbit.…”

Section: Introductionmentioning

confidence: 99%

“…The class of systems we consider appears in a wide range of dynamical phenomena from biology to engineering, such as legged locomotion [6,8], helicopter rotor dynamics [9], inverter locomotives [10], and wind turbines [11]. Initial formulations of this type of systems are generally modeled as nonlinear hybrid dynamical systems that include some state-dependent scheduling functions [12][13][14][15]. However, a vast majority of the system identification studies for such systems focus on their local behavior around a periodic orbit.…”

Section: Introductionmentioning

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

Cited by 16 publications

References 37 publications

The generalized spring-loaded inverted pendulum model for analysis of various planar reduced-order models and for optimal robot leg design

The generalized spring-loaded inverted pendulum model for analysis of various planar reduced-order models and for optimal robot leg design

A Torque-actuated dissipative spring loaded inverted pendulum model with rolling contact and Its application to hexapod running

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

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