Stability Analysis of a Clock-Driven Rigid-Body SLIP Model for RHex

Altendorfer, Richard; Koditschek, Daniel E.; Holmes, Philip

doi:10.1177/0278364904047390

Cited by 66 publications

(57 citation statements)

References 21 publications

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“…Notwithstanding a decade's effort [35,[49][50][51], mathematical analysis that can account for the emergence of SLIP dynamics in RHex-style systems has proven challenging. Even the narrower analysis relating open-loop RHex clock control parameter settings to effective SLIP locomotion outcomes has proven mathematically difficult [49]. Moreover, it is not clear that the more tractable active sensor-based closed-loop methods [41,52] for anchoring SLIP dynamics in RHex will yield energetic benefits comparable to their open-loop counterparts.…”

Section: Discussionmentioning

confidence: 99%

Characterization of Dynamic Behaviors in a Hexapod Robot

Komsuoğlu

Majumdar

Ozkan-Aydin

et al. 2014

Experimental Robotics

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This paper investigates the relationship between energetic effi-ciency and the dynamical structure of a legged robot's gait. We present an experimental data set collected from an untethered dynamic hexapod, EduBot [1] (a RHex-class [2] machine), operating in four distinct manually selected gaits. We study the robot's single tripod stance dynamics of the robot which are identified by a purely jointspace-driven estimation method introduced in this paper. Our results establish a strong relationship between energetic efficiency (simultaneous reduction in power consumption and in-crease in speed) and the dynamical structure of an alternating tripod gait as measured by its fidelity to the SLIP mechanics-a dynamical pattern exhibit-ing characteristic exchanges of kinetic and spring-like potential energy [3]. We conclude that gaits that are dynamic in this manner give rise to better uti-lization of energy for the purposes of locomotion. Abstract This paper investigates the relationship between energetic efficiency and the dynamical structure of a legged robot's gait. We present an experimental data set collected from an untethered dynamic hexapod, EduBot [1] (a RHex-class [2] machine), operating in four distinct manually selected gaits. We study the robot's single tripod stance dynamics of the robot which are identified by a purely jointspace-driven estimation method introduced in this paper. Our results establish a strong relationship between energetic efficiency (simultaneous reduction in power consumption and increase in speed) and the dynamical structure of an alternating tripod gait as measured by its fidelity to the SLIP mechanics-a dynamical pattern exhibiting characteristic exchanges of kinetic and spring-like potential energy [3]. We conclude that gaits that are dynamic in this manner give rise to better utilization of energy for the purposes of locomotion.

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Section: Discussionmentioning

confidence: 99%

Characterization of Dynamic Behaviors in a Hexapod Robot

Komsuoğlu

Majumdar

Ozkan-Aydin

et al. 2014

Experimental Robotics

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“…In addition to a few direct experimental inquiries 35,36 and indirect uses in multilegged platforms, 1,5,45 it has received limited attention in the form of an active spring. 30 Recent research also indicates that quadrupedal locomotion uses forward thrust through the use of hip actuators to provide an impulsive energy source. 46 Our use of the hip torque as a means of energy input instead of radial actuation strategies such as tunable springs 47 or toe push-off prior to liftoff is primarily motivated by the ease of incorporating hip actuators within physical robot platforms.…”

Section: Approximate Stance Map For the Forced Td-slipmentioning

confidence: 99%

“…Our approach is based on recently proposed analytic approximations to the dynamics of a dissipative SLIP model, 24 which can capture the effects of viscous damping in the leg much more accurately than previously available methods in the literature that rely on the conservation of energy. [25][26][27][28] Since trajectories of this dissipative model lack symmetry properties necessary to indirectly deduce stability properties without an explicit return map, 29,30 we use our analytic approximations to generalize previous uses of Poincaré methods 26,[31][32][33][34] to the stability analysis of running with a dissipative spring-mass model.…”

Section: Introductionmentioning

confidence: 99%

Stride-to-stride energy regulation for robust self-stability of a torque-actuated dissipative spring-mass hopper

Ankaralı

Saranlı

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Lateral stability of the spring-mass hopper suggests a two-step control strategy for running Chaos: An Interdisciplinary Journal of Nonlinear Science 19, 026106 (2009) In this paper, we analyze the self-stability properties of planar running with a dissipative springmass model driven by torque actuation at the hip. We first show that a two-dimensional, approximate analytic return map for uncontrolled locomotion with this system under a fixed touchdown leg angle policy and an open-loop ramp torque profile exhibits only marginal self-stability that does not always persist for the exact system. We then propose a per-stride feedback strategy for the hip torque that explicitly compensates for damping losses, reducing the return map to a single dimension and substantially improving the robust stability of fixed points. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the behavior of the exact plant model. We illustrate the relevance and utility of our model both through the qualitative correspondence of its predictions to biological data as well as its use in the design of a task-level running controller. © 2010 American Institute of Physics. ͓doi:10.1063/1.3486803͔It has long been established that simple spring-mass systems, such as the well-studied spring-loaded inverted pendulum (SLIP) model, can accurately represent the dynamics of legged locomotion. However, the existing work in this domain almost exclusively focuses on lossless leg models with actuation through tunable leg stiffness, making it difficult to generalize associated results to physical systems. In this paper, we introduce a more realistic model with damping and actuation through a controllable hip torque, subsequently developing a sufficiently accurate analytic approximation to identify and characterize its limit cycles. We show that in the absence of any explicit controls, running with this model is only marginally stable, but when an "energy regulating" feedback law is introduced on the stance hip torque, an open-loop, fixed touchdown angle policy produces asymptotically stable running across a much larger range of states. We also show that the relatively understudied hip torque actuation not only provides robust stability properties, but also has interesting correspondence to data from biological runners, more accurately predicting horizontal ground reaction forces during locomotion.

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“…Despite the availability of methods to analyze stability properties of locomotory behaviors in the absence of closed-form expressions for a Poincaré map [2,3], a number of different possible approaches become available once a sufficiently accurate analytic return map is available. For example, [18] investigates in depth stability properties of a SLIP model attached to a rigid body by neglecting the effects of gravity, which allows for the derivation of suitable closed-form expressions for stride trajectories.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Control of a Dissipative Spring-Mass Hopper with Torque Actuation

Ankaralı

Saranlı

2010

Robotics: Science and Systems VI

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Abstract-It has long been established that simple springmass models can accurately represent the dynamics of legged locomotion. Existing work in this domain, however, almost exclusively focuses on the idealized Spring-Loaded Inverted Pendulum (SLIP) model and neglects passive dissipative effects unavoidable in any physical robot or animal. In this paper, we extend on a recently proposed analytic approximation to the stance trajectories of a dissipative SLIP model to analyze stability properties of a planar hopper with a single rotary actuator at the hip. We first describe how a suitably chosen torque controller can compensate for damping losses, maintaining the same energy level across strides and hence reducing the return map to a single dimension. We then identify and characterize equilibrium points for this return map under a fixed leg placement policy and show that "uncontrolled" asymptotic stability is feasible for this energy-regulated system. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the exact plant model. The paper concludes with the application of our energy-regulation scheme to the design of a task-level gait controller that uses explicit leg placement commands in conjunction with the hip torque.

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Stability Analysis of a Clock-Driven Rigid-Body SLIP Model for RHex

Cited by 66 publications

References 21 publications

Characterization of Dynamic Behaviors in a Hexapod Robot

Characterization of Dynamic Behaviors in a Hexapod Robot

Stride-to-stride energy regulation for robust self-stability of a torque-actuated dissipative spring-mass hopper

Analysis and Control of a Dissipative Spring-Mass Hopper with Torque Actuation

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