Control of quadruped walking behavior through an embedding of spring loaded inverted pendulum template

Yılmaz, Mert Kaan
Legged robots require complex dynamical behaviours in order to achieve stable, sustainable and efficient locomotion. Due to their mobile nature, they can neither afford to provide extensive computational power, nor use anything but the most energy efficient structural designs and algorithms to achieve stability and speed. Consequently, simple and efficient ways to solve the complex set of problems is one of the key points of focus in legged robot locomotion research. This thesis offers a novel method that uses an active embedding of the Spring-Loaded Inverted Pendulum (SLIP) dynamical model within a planar quadruped model in order to reduce the complexity of the control problem while also keeping the overall locomotion as efficient as possible. In particular, we hypothesize that the embedding of the SLIP model is particularly effective when used in conjunction with legs that incorporate compliance in parallel with the traditionally fully-actuated leg structures in most modern quadruped platforms. We first show in simulation, using a planar quadruped model with fully actuated 2DOF legs, how the embedding of the SLIP model is performed, and compare the locomotion performance with other contemporary methods. Subsequently, we show that the leg force profiles that arise from this embedding can largely be generated passively with the incorporation of parallel leg compliance during steady-state running, with only a small amount of energy expenditure necessary during stance to achieve stability and compensation of losses. We also provide comparative results to illustrate the efficiency of this approach for potential platforms with parallel compliance incorporated into the leg structure.


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Autonomous use of legged robots in unstructured, outdoor settings requires dynamically dexterous behaviors to achieve sufficient speed and agility without overly complex and fragile mechanics and actuation. Among such behaviors is the relatively under-studied pronking (aka. stotting), a dynamic gait in which all legs are used in synchrony, usually resulting in relatively slow speeds but long flight phases and large jumping heights. Instantiations of this gait for robotic systems have been mostly limited to ...
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Existing research on dynamically capable legged robots, particularly those based on spring-mass models, generally considers improving in isolation either the stability and control accuracy on the rough terrain, or the energetic efficiency in steady state. In this paper, we propose a new method to address both, based on the hierarchical embedding of a simple spring-loaded inverted pendulum (SLIP) template model with a tunable radial damping coefficient into a realistic leg structure with series-elastic actua...
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KERIMOGLU, Deniz; MORGUL, Omer; Saranlı, Uluç (2017-03-01)
Passive dynamic walking models are capable of capturing basic properties of walking behaviours and can generate stable human-like walking without any actuation on inclined surfaces. The passive compass gait model is among the simplest of such models, consisting of a planar point mass and two stick legs. A number of different actuation methods have been proposed both for this model and its more complex extensions to eliminate the need for a sloped ground, balancing collision losses using gravitational potent...
Stability of Planar Compass Gait Walking with Series Elastic Ankle Actuation
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Passive dynamic walking models capture the natural dynamics of stable human-like walking. The passive compass gait (PCG) model, consisting of a point mass and two rigid legs, is among the simplest of such models. The fully passive nature of these models, however, necessitates a sloped ground to recover the energy lost during the ground collisions [1]. A variety of methods have been proposed to eliminate this requirement through different actuation methods. Among these are impulsive energy injection after fo...
Citation Formats
M. K. Yılmaz, “Control of quadruped walking behavior through an embedding of spring loaded inverted pendulum template,” M.S. - Master of Science, Middle East Technical University, 2022.