Running With Symmetry

Raibert, Marc H.

doi:10.1177/027836498600500401

Cited by 101 publications

(31 citation statements)

References 14 publications

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“…A convenient model for this form of locomotion is the Spring-loaded Inverted Pendulum (SLIP), which models the motion by assuming a single point mass connected to a sprung leg [15]. It is extended to quadrupeds via the use of "virtual legs" [4]; however, this is only applicable for symmetric gaits. Further, SLIP has no provision for capturing leg interactions.…”

Section: Related Workmentioning

confidence: 99%

“…This implies that the forward speeds and attitudes changes between strides. The consequence on modeling is that body accelerations are no longer odd functions that integrate to zero over symmetric limits [4], which prevents the use of simpler control strategies, especially those that simulate the motion as a bouncing ball [10]. [23]).…”

Section: Related Workmentioning

confidence: 99%

“…[4], [15], and [18] respectively. Approximate models are used to simplify the calculations and later linearizations needed by the EKF.…”

Section: A Modelmentioning

confidence: 99%

“…A flight phase disconnects this chain. Making the assumption that these intervals are completely ballistic, gives an approximate solution for forward position [4]. Therefore, to determine attitude it is necessary to measure the motion in a selfcontained manner with respect to an inertial frame.…”

Section: Introductionmentioning

confidence: 99%

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A Hybrid Motion Model for Aiding State Estimation in Dynamic Quadrupedal Locomotion

Singh

Waldron

2007

Proceedings 2007 IEEE International Conference on Robotics and Automation

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Abstract-Trotting and galloping allow a quadruped to rapidly traverse rough terrain. Modeling this motion, which is only dynamically stable, is of importance for legged robot operation and for quadrupedal animal motion estimation. Derived from an eight-step galloping cycle, this study presents a kinetic hybrid model in which the states vary based on the principal forces present. As compared to foot contact, or kinematic, hybrid quadruped models this reduces the maximum number of possible states from 120 to 6 and provides an alternative to foot contact monitoring. This approach was tested on a trotting quadruped robot equipped with an inertial sensor aided by video. This was processed using an EKF estimator framework to give attitude estimates at rates of up to 250 Hz with 5• error.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…[4], [15], and [18] respectively. Approximate models are used to simplify the calculations and later linearizations needed by the EKF.…”

Section: A Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Hybrid Motion Model for Aiding State Estimation in Dynamic Quadrupedal Locomotion

Singh

Waldron

2007

Proceedings 2007 IEEE International Conference on Robotics and Automation

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“…In contrast to the trot, bound and pace [3], which are paired foot gaits that have some form of symmetry, the gallop is a highly asymmetric single foot gait [4].…”

Section: Introductionmentioning

confidence: 99%

System Design of a Quadrupedal Galloping Machine

Nichol¹,

Singh

Waldron

et al. 2004

The International Journal of Robotics Research

104

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Abstract-Ohio State and Stanford Universities are cooperating to construct and artificial quadruped. This quadruped has a rest leg length of 0.68m and weighs 70kg. The body is made of four single-leg modules. Each module houses an articulated 3-dof leg. The articulated leg structure uses a set of mechanical springs to store energy. The stiffness of the leg, from hip to foot, is highly nonlinear. The leg initially stiffens as the leg is compressed the first 1/3 of its range, then remains roughly constant for the remainder. This stiffening allows the leg to maintain a relatively constant working length. A cable is used to flex the knee of the quadruped. As the cable is pulled, the knee bends, tensioning the energy storage springs. This cable makes about a ¼ turn over a pulley which is concentric with the hip axis, ½ turn around a pulley at the ankle and then ¾ turn back around a second hip pulley in a direction opposite the first hip pulley. This arrangement decouples cable tension and hip torque. The non-anchored end of the cable is tensioned by a capstan. This capstan uses unique geometry to decrease holding torque and to release the cable instantly. The current top speed of this leg in a 2-dimensional test is 4.15m/s. This leg has been controlled using two control systems, both implemented on an embedded controller attached to the leg. An articulated leg presents control challenges not seen when trying to control a prismatic leg. The first controller tested is a heuristic algorithm whose parameters are updated in real time by the LevenbergMarquardt learning method. This controller is similar to the controllers used by Raibert[24], with modifications to allow for leg asymmetry. The second controller tested is a direct adaptive fuzzy controller. The fuzzy controller consists of a rule base, inference mechanism, fuzzification interface, and defuzzification interface. Fuzzification starts by mapping an input (body velocity, desired change in velocity, height) into one or more membership functions.The inference mechanism then determines the applicability of each rule to the current inputs. Defuzzification combines the recommendations of each rule in an output based upon rule certainties. The adaptation mechanism modifies the rule output centers to correct velocity errors. The adaptation mechanism gains are experimentally tuned. Once tuned, the controller quickly adapts to leg changes. Both control systems were tested with and without adaptation. Both systems more accurately tracked desired velocity with adaptation. Accurate, high resolution, high speed body attitude sensing is essential for successful quadruped operation.No existing solutions meet the project requirements. An adequate sensor system is being developed in cooperation with a commercial vendor. Initial results show that accurate position tracking is possible with currently available MEMS inertial sensors.

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Entwurf eines nichtlinearen Laufmustergenerators

Frik¹,

Ahanikamangar²

1990

Z Angew Math Mech

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Es wird eine Methode zum Entwurf eines Laufmustergenerators vorgestellt, der bei Gehmaschinen zur Realisierung von Gehbewegungen verwendet werden kann. Der Laufmustergenerator wird modular aus gekoppelten Van der Pol Schwingern aufgebaut, deren Schwingungen den Bewegungen der einzelnen Glieder des Gehapparates entsprechen. Die Parameter und Koppelkoeffizienten werden so bestimmt, daß die rhythmischen, synchronisierten Bewegungen, die der gewünschten Gangart entsprechen, entstehen.

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Running With Symmetry

Cited by 101 publications

References 14 publications

A Hybrid Motion Model for Aiding State Estimation in Dynamic Quadrupedal Locomotion

A Hybrid Motion Model for Aiding State Estimation in Dynamic Quadrupedal Locomotion

System Design of a Quadrupedal Galloping Machine

Entwurf eines nichtlinearen Laufmustergenerators

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