Passive dynamic quadrupedal walking

Smith, Andrew C.; Berkemeier, M.D.

doi:10.1109/robot.1997.620012

Cited by 36 publications

(26 citation statements)

References 4 publications

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“…When extending the principles of passive dynamic walking to quadrupedal locomotion [8,9], a simple planar model is able to produce two distinct kinds of symmetric periodic gaits: two-beat gaits in which the front and back legs swing in phase, and four-beat gaits in which the leg pairs are acting 90º out of phase and the feet strike the ground in an evenly timed sequence (Fig. 1).…”

Section: Introductionmentioning

confidence: 99%

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Passive dynamic walking with quadrupeds - Extensions towards 3D

Remy¹,

Hutter²,

Siegwart³

2010

2010 IEEE International Conference on Robotics and Automation

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Abstract-In the present study, we applied the principles of passive dynamic walking onto the three dimensional motion of a simplified quadrupedal model. We extended the simulation framework of a planar system to include a rolling degree of freedom and searched for limit cycles that represent periodic gaits. Among the eight different gaits that we identified, were three kinds of trots and paces, as well as a lateral and diagonal single foot sequence. We could show that a distinct relation exists between the lateral spacing of the legs and the relative phase of the front and the back legs, and a certain trade-off between efficiency and dynamic stability. In agreement with established bipedal models, our results showed that the lateral rolling motion is invariably unstable.

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Section: Introductionmentioning

confidence: 99%

“…The graph therefore excludes gaits such as bounding, pronking, or galloping. Moreover, when mirrored at the saggital plane, the second half of the stride of a symmetrical gait is equal to the first half, which means that it is possible to limit the analysis to a half-stride; a technique that was employed in [8] and [9].…”

Section: Introductionmentioning

confidence: 99%

Passive dynamic walking with quadrupeds - Extensions towards 3D

Remy¹,

Hutter²,

Siegwart³

2010

2010 IEEE International Conference on Robotics and Automation

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“…There exists a class of walking machines for which walking is a natural dynamic mode. Once started on a shallow slope, a machine of this class will settle into a steady gait, without active control or energy input [2,3]. the capabilities of these machines are quite limited.…”

Section: Introductionmentioning

confidence: 99%

Complex-order dynamics in hexapod locomotion

2006

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This paper studies the dynamics of foot-ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear springdashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with footforce feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot-ground transfer function, which presents complex-order dynamics. r

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“…Thus, the magnitude of the largest eigenvalue of the return map, disregarding the eigenvalue corresponding to the orbit, is a suitable stability margin for a periodic system. Measuring the eigenvalues of Poincare return maps is commonly used for analyzing Passive Dynamic Walking robots [16,8,27,2,4,29] and was used by Miura and Shimoyama [17] to analyze their Biper robots. However, using eigenvalues of Poincare return maps assumes periodicity and is valid only for small deviations from a limit cycle.…”

Section: Eigenvalues Of Poincare Return Mapsmentioning

confidence: 99%

“…However, its utility has perhaps led to its overuse, resulting in the majority of bipedal robots relying heavily on prerecorded trajectories and stiff joint control to achieve those trajectories. Such stiff joint control of prerecorded trajectories typically leads to poor robustness to pushes and unknown rough terrain, relies on a flatfooted gait, and makes it difficult to incorporate natural dynamic mechanisms that have shown their utility in Passive Dynamic Walkers [16,8,27,2,4,29], and a growing number of powered bipeds [22,3,33].…”

Section: Zero Moment Point (Zmp) and Foot Rotation Indicator (Fri)mentioning

confidence: 99%

Velocity-Based Stability Margins for Fast Bipedal Walking

Pratt

Tedrake²

Lecture Notes in Control and Information Sciences

166

153

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We present velocity-based stability margins for fast bipedal walking that are sufficient conditions for stability, allow comparison between different walking algorithms, are measurable and computable, and are meaningful. While not completely necessary conditions, they are tighter necessary conditions than several previously proposed stability margins. The stability margins we present take into consideration a biped's Center of Mass position and velocity, the reachable region of its swing leg, the time required to swing its swing leg, and the amount of internal angular momentum available for capturing balance. They predict the opportunity for the biped to place its swing leg in such a way that it can continue walking without falling down. We present methods for estimating these stability margins by using simple models of walking such as an inverted pendulum model and the Linear Inverted Pendulum model. We show that by considering the Center of Mass location with respect to the Center of Pressure on the foot, these estimates are easily computable. Finally, we show through simulation experiments on a 12 degree-of-freedom distributed-mass lower-body biped that these estimates are useful for analyzing and controlling bipedal walking. Introduction"How stable is your robot?" is a fundamental yet challenging question to answer, particularly with fast moving legged robots, such as dynamically balanced bipedal walkers. With many traditional control systems, questions of stability and robustness can be answered by eigenvalues, phase margins, loop gain margins, and other stability margins. However, legged robots are nonlinear, under-actuated, combine continuous and discrete dynamics, and do not necessarily have periodic motions. These features make applying traditional stability margins difficult.

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Passive dynamic quadrupedal walking

Cited by 36 publications

References 4 publications

Passive dynamic walking with quadrupeds - Extensions towards 3D

Passive dynamic walking with quadrupeds - Extensions towards 3D

Complex-order dynamics in hexapod locomotion

Velocity-Based Stability Margins for Fast Bipedal Walking

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