Analytical approximation for the double-stance phase of a walking robot

Shahbazi, Mohammad; Babuška, Robert; Lopes, Gabriel

doi:10.1109/icra.2015.7140005

Cited by 5 publications

(7 citation statements)

References 15 publications

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“…We have recently introduced the first approximation to the DS dynamics of the lossless B-SLIP model [28]. The predictive power of the proposed map was investigated through a numerical error analysis, corroborating its effectiveness.…”

Section: Introductionmentioning

confidence: 76%

“…Note that in [28], for the case of lossless B-SLIP, we presented a different approach to finding the equivalency relations. Although the obtained expressions for k k , a t and r rest are different from those derived here, they result in very similar numerical values.…”

Section: At Restmentioning

confidence: 99%

“…For the lossless DS phase, we revisited our previous results [28] by taking a different approach, namely the perturbation-based (PB) approach, wherein we compute the approximations in a single step. Although the new approximations seem more complicated, they are suitable for functional analysis as there is no need for an extra iteration in the calculations.…”

Section: Introductionmentioning

confidence: 99%

“…For bt sufficiently close to zero, equation(28) results in invalid values, due to the presence of bt in the denominators. According to our numerical analysis, this holds for ξ 0 < 10 −6 , with ξ 0 = b 0 /(2 √ k 0 m) = bt/ c 2 √ k 0 m(rrest/lrest) 2 .…”

mentioning

confidence: 99%

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Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum

et al. 2016

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This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.

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Section: Introductionmentioning

confidence: 76%

Section: At Restmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum

et al. 2016

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“…Gait stability for these methods has most commonly been studied using Poincaré analysis, which is complicated by the fact that the step-to-step return map does not admit an analytical solution. This property has motivated the development of approximate analytical solutions for the stance evolution of SLIP models [23], [24], which may be used in the design of SLIP controllers [18]. Another promising strategy, proposed by Piovan and Byl [21], is to use partial feedback linearization techniques for leg-length modulation to analytically solve part of the dynamics.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Differentially Flat Two-Dimensional Spring-Loaded Inverted Pendulum Model

Chen

Wensing

Zhang

2020

IEEE Robot. Autom. Lett.

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This paper considers the optimal control problem of an extended spring-loaded inverted pendulum (SLIP) model with two additional actuators for active leg length and hip torque modulation. These additional features arise naturally in practice, allowing for consideration of swing leg kinematics during flight and active control over stance dynamics. On the other hand, nonlinearity and the hybrid nature of the overall SLIP dynamics introduce challenges in the analysis and control of the model. In this paper, we first show that the stance dynamics of the considered SLIP model are differentially flat, which has a strong implication regarding controllability of the stance dynamics. Leveraging this powerful property, a tractable optimal control strategy is developed. This strategy enables online solution while also treating the hybrid nature of the SLIP dynamics. Together with the optimal control strategy, the extended SLIP model grants active disturbance rejection capability at any point during the gait. Performance of the proposed control strategy is demonstrated via numerical tests and shows significant advantage over existing methods.

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Planar hopping control strategy for tail-actuated SLIP model traversing varied terrains

Li²,

Yuan

et al. 2017

2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Analytical approximation for the double-stance phase of a walking robot

Cited by 5 publications

References 15 publications

Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum

Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum

Optimal Control of a Differentially Flat Two-Dimensional Spring-Loaded Inverted Pendulum Model

Planar hopping control strategy for tail-actuated SLIP model traversing varied terrains

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