Robust and efficient walking with spring-like legs

Rummel, Juergen; Blum, Yvonne; Seyfarth, André

doi:10.1088/1748-3182/5/4/046004

Cited by 65 publications

(80 citation statements)

References 34 publications

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“…They contain no information about the magnitude of perturbations that can be mitigated, that is, the size of the basin of attraction. In the two-dimensional model, Rummel et al [11] showed that the stability, indicated by the magnitude of the largest eigenvalue of the return map, is not correlated to the robustness as indicated by the size of the basin of attraction. Computing the robustness is beyond the scope of this study.…”

Section: Stability Analysismentioning

confidence: 99%

Walking in circles: a modelling approach

Maus

Seyfarth

2014

J. R. Soc. Interface.

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Blindfolded or disoriented people have the tendency to walk in circles rather than on a straight line even if they wanted to. Here, we use a minimalistic walking model to examine this phenomenon. The bipedal spring-loaded inverted pendulum exhibits asymptotically stable gaits with centre of mass (CoM) dynamics and ground reaction forces similar to human walking in the sagittal plane. We extend this model into three dimensions, and show that stable walking patterns persist if the leg is aligned with respect to the body (here: CoM velocity) instead of a world reference frame. Further, we demonstrate that asymmetric leg configurations, which are common in humans, will typically lead to walking in circles. The diameter of these circles depends strongly on parameter configuration, but is in line with empirical data from human walkers. Simulation results suggest that walking radius and especially direction of rotation are highly dependent on leg configuration and walking velocity, which explains inconsistent veering behaviour in repeated trials in human data. Finally, we discuss the relation between findings in the model and implications for human walking.

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Section: Stability Analysismentioning

confidence: 99%

Walking in circles: a modelling approach

Maus

Seyfarth

2014

J. R. Soc. Interface.

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“…In terms of stability and energy requirements of the SLIP model, Rummel et al (2010) make the following generalizations:…”

Section: Discussionmentioning

confidence: 99%

Optimization of the visco-elastic parameters describing the heel-region of a prosthesis

Johnston

Hubbard

2012

Journal of Theoretical Biology

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“…In [14], the selection of gait patterns based on studying the interplay between robustness against perturbations and leg compliance is investigated.…”

Section: State Of the Artmentioning

confidence: 99%

Perturbation theory to plan dynamic locomotion in very rough terrains

Sentis¹,

Fernández²

2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-Although the problem of dynamic locomotion in very rough terrain is critical to the advancement of various areas in robotics and health devices, little progress has been made on generalizing gait behavior with arbitrary paths. Here, we report that perturbation theory, a set of approximation schemes that has roots in celestial mechanics and nonlinear dynamical systems, can be adapted to predict the behavior of nonintegrable state-space trajectories of a robot's center of mass, given its arbitrary contact state and center of mass (CoM) kinematic path. Given an arbitrary kinematic path of the CoM and known step locations, we use perturbation theory to determine phase curves of CoM behavior. We determine step transitions as the points of intersection between adjacent phase curves. To discover intersection points, we fit polynomials to the phase curves of neighboring steps and solve their differential roots. The resulting multi-step phase diagram is the locomotion plan suited to drive the behavior of a robot or device maneuvering in the rough terrain. We provide two main contributions to legged locomotion: (1) predicting CoM state-space behavior for arbitrary paths by means of perturbation theory, and (2) finding step transitions by locating common intersection points between neighboring phase curves. Because these points are continuous in phase they correspond to the desired contact switching policy. We validate our results on a human-size avatar navigating in a very rough environment and compare its behavior to a human subject maneuvering through the same terrain. I. STATE OF THE ARTIn dynamic walking we can classify techniques in various categories: (1) trajectory-based techniques, (2) limit cycle-based techniques, (3) prediction of contact, and (4) hybrids of the previous three.Trajectory-based techniques are techniques that track a timebased joint or task space trajectory according to some locomotion model such as the Zero Moment Point (ZMP). The state of the art of these methods includes generalized multi-contact locomotion behaviors, developed in [1] and more recenlty, a time delay extension to the ZMP method for locomotin in moderately uneven terrain, developed by [2].Prediction of contact placement are techniques that use dynamics to estimate suitable contact transitions to produce locomotion or regain balance. In [3], simple dynamic models are used to predict the placement of next contacts to achieve desire gait patterns. Finding feasible CoM static placements given frictional constraints was tackled in [4], [5]. In [6], stable locomotion, in the wide sense of not falling down, is studied by providing velocity based stability margins. This work is used to regain stability when the robot's is pushed out, and lead to the concept of Capture Point.Limit cycle based techniques were pioneered by McGeer [7] through the field of passive dynamic walking. In [8] the authors study orbital stability, and the effect of feedback control to achieve asymptotic stability. Optimization of open-loop stability is in...

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Robust and efficient walking with spring-like legs

Cited by 65 publications

References 34 publications

Walking in circles: a modelling approach

Walking in circles: a modelling approach

Optimization of the visco-elastic parameters describing the heel-region of a prosthesis

Perturbation theory to plan dynamic locomotion in very rough terrains

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