The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper

In this paper, we aim to realize compliant biped walking on uneven terrain with point feet. A control system is designed for a 5-link planar biped walker. According to the role that each leg plays, the control system is decomposed into two parts: the swing leg control and the support leg control. The trajectory of the swing foot is generated in realtime to regulate the walking speed. By considering the reaction torque of the swing leg's hip joint as disturbance, a sliding model controller is implemented at the support leg's hip joint to control the torso's posture angle. In order to make sure the landing foot does not rebound after impact, the vertical contact force control is set as the internal loop of the hip's height control. In simulation, the control system is tested on a virtual 5-link planar biped walker in Matlab. Finally, stable biped walking is realized on uneven terrain with roughness up to 2cm.

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“…A variation of Raibert's speed controller is employed to regulate the hip's horizontal velocity at the MSM [28,29]: …”

Section: Swing Foot Trajectory Generationmentioning

confidence: 99%

Compliant Biped Walking on Uneven Terrain with Point Feet

Hou

Zhang

Chen

et al. 2016

International Journal of Advanced Robotic Systems

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“…6 It can stand for most kinds of robots in a hopping motion, thus the ASLIP model tends to possess some universal properties to some extent.…”

Section: Ioannis Poulakakismentioning

confidence: 99%

Height control for a two-mass hopping robot based on stable limit cycle

Zhang

Wei

et al. 2016

International Journal of Advanced Robotic Systems

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Differing from the commonly used spring loaded inverted pendulum model, this paper makes use of a two-mass spring model considering impact between the foot and ground which is closer to the real hopping robot. The height of upper mass which includes the upper leg and body is the main control objective. Then we develop a new kind of control algorithm acting on two levels: The upper level aims to achieve the desired velocity of the upper mass based on a stable limit cycle, where three different controllers are used to regulate the limit cycle; the target of the lower level is to drive the system to converge to the desired state and control the contact force between the foot and ground within an appropriate range based on the inner force control at the same time. Simulation results presented in this paper confirm the efficiency of this control algorithm.

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“…3͑c͒ illustrates a human-like legged morphology with an upright body posture, 23 the most difficult scenario for which the TD-SLIP morphology would be relevant. Unlike the previous example, body dynamics are close to those of an inverted pendulum and are naturally unstable.…”

Section: B Relevance and Feasibility Of Hip Torque Actuationmentioning

confidence: 99%

“…[13][14][15][16][17] This led to the development of the simple yet accurate SLIP model to describe such behaviors. 18,19 Significant research effort was devoted to both the use of this model as a basis for the design of fast and efficient legged robots 1,2,20,21 and associated control strategies 22,23 as well as its analysis to reveal fundamental aspects of legged locomotory behaviors. 11 The present paper falls into the latter category and contributes by investigating the previously unaddressed question of how the presence of passive damping and actuation through a controllable hip torque affects the behavioral characteristics of running.…”

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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The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper

Cited by 243 publications

References 48 publications

Compliant Biped Walking on Uneven Terrain with Point Feet

Compliant Biped Walking on Uneven Terrain with Point Feet

Height control for a two-mass hopping robot based on stable limit cycle

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

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