Pitch then power: limitations to acceleration in quadrupeds

Williams, Sarah; Tan, Huiling; Usherwood, James R.; Wilson, Alan M.

doi:10.1098/rsbl.2009.0360

Cited by 55 publications

(73 citation statements)

References 21 publications

(25 reference statements)

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“…Although its effect could be partially compensated for by altering musculoskeletal transmissions, this fundamental difference in muscle contractile mechanics has unavoidable consequences. As is typical of cursorial mammals, most of a dog's limb muscle is composed of its proximal retractors and, to a lesser extent, protractors (Pasi and Carrier, 2003;Williams et al, 2009a;Williams et al, 2009b) that actuate the limbs as levers. Hence, it is predicted that the limbs will function more as levers during uphill than downhill trotting (prediction 1).…”

Section: Introductionmentioning

confidence: 99%

Effects of grade and mass distribution on the mechanics of trotting in dogs

Lee

2011

Journal of Experimental Biology

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SUMMARYQuadrupedal running on grades requires balancing of pitch moments about the center of mass (COM) while supplying sufficient impulse to maintain a steady uphill or downhill velocity. Here, trotting mechanics on a 15deg grade were characterized by the distribution of impulse between the limbs and the angle of resultant impulse at each limb. Anterior-posterior manipulation of COM position has previously been shown to influence limb mechanics during level trotting of dogs; hence, the combined effects of grade and COM manipulations were explored by adding 10% body mass at the COM, shoulder or pelvis. Whole body and individual limb ground reaction forces, as well as spatiotemporal step parameters, were measured during downhill and uphill trotting. Deviations from steady-speed locomotion were determined by the net impulse angle and accounted for in the statistical model. The limbs exerted only propulsive force during uphill trotting and, with the exception of slight hindlimb propulsion in late stance, only braking force during downhill trotting. Ratios of forelimb impulse to total impulse were computed for normal and shear components. Normal impulse ratios were more different from level values during uphill than downhill trotting, indicating that the limbs act more as levers on the incline. Differential limb function was evident in the extreme divergence of forelimb and hindlimb impulse angles, amplifying forelimb braking and hindlimb propulsive biases observed during level trotting. In both downhill and uphill trotting, added mass at the up-slope limb resulted in fore-hind distributions of normal impulse more similar to those of level trotting and more equal fore-hind distributions of shear impulse. The latter result suggests a functional trade-off in quadruped design: a COM closer to the hindlimbs would distribute downhill braking more equally, whereas a COM closer to the forelimbs would distribute uphill propulsion more equally. Because muscles exert less force when actively shortening than when lengthening, it would be advantageous for the forelimb and hindlimb muscles to share the propulsive burden more equally during uphill trotting. This functional advantage is consistent with the anterior COM position of most terrestrial quadrupeds. Supplementary material available online at

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Section: Introductionmentioning

confidence: 99%

Effects of grade and mass distribution on the mechanics of trotting in dogs

Lee

2011

Journal of Experimental Biology

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“…In biology also, several studies indicate that hip-torque plays a key role in generating leg-thrust (Tan and Wilson, 2011). Indeed, the coupling between energy-input and body-pitch can be the overriding constraint to acceleration (Williams et al, 2009). For the sake of simplicity, we group the two control objectives of hopping-height and forward-velocity into a single objective, that of energy-input.…”

Section: Hypothesismentioning

confidence: 99%

On designing an active tail for legged robots: simplifying control via decoupling of control objectives

Heim

Ajallooeian

Eckert

et al. 2016

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Abstract-This work explores the possible roles of active tails for steady-state legged-locomotion. A series of simple models are proposed which capture the dynamics of an idealized running system with an active tail. The models suggest that the control objectives of injecting energy into the system and stabilizing body-pitch can be effectively decoupled via proper tail design: a long, light tail. Thus the overall control problem can be simplified, using the tail exclusively to stabilize body-pitch: this effectively relaxes the constraints on the leg-actuators, allowing them to be recruited specifically for adding energy into the system. We show in simulation that models with long-light tails are better able to reject perturbations to body-pitch than short-heavy tails with the same moment of inertia. Further, we present the results of a one degree-of-freedom tail mounted on the open-loop controlled quadruped robot Cheetah-Cub. Our results show that an active tail can greatly improve both forward velocity and reduce body-pitch per stride, while adding minimal complexity. Further, the results validate the long-light tail design: shorter, heavier tails are much more sensitive to configuration and control parameter changes than longer and lighter tails with the same moment of inertia.

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“…The ratio between the lengths of the distal and proximal link (shown in Figure 3) was chosen from numerical study to approximately maximize vertical leaping height over a range of scaling factors. The scaling factor of the distal and proximal links for the shorter legs was chosen near the smallest that allowed for balancing on the isolated foothold (specifically, to yield a minimal but non-empty intersection of the front and rear leg workspaces without core bending, allowing both legs to "grasp" the same point), and for the longer legs was chosen to be 1.5 times the shorter legs-a large enough increase to reasonably expect a significant performance difference compared to the shorter legs while keeping the extended leg length less than the hip-to-hip length as we were wary of avoiding excessive pitching when accelerating from rest caused by long legs [18].…”

Section: Technical Approach: the Utility Of Core Actuationmentioning

confidence: 99%

Core Actuation Promotes Self-manipulability on a Direct-Drive Quadrupedal Robot

Duperret

Kramer

Koditschek

2017

Springer Proceedings in Advanced Robotics

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For direct-drive legged robots operating in unstructured environments, workspace volume and force generation are competing, scarce resources. In this paper we demonstrate that introducing geared core actuation (i.e., proximal to rather than distal from the mass center) increases workspace volume and can provide a disproportionate amount of work-producing force to the mass center without affecting leg linkage transparency. These effects are analytically quantifiable up to modest assumptions, and are demonstrated empirically on a spined quadruped performing a leap both on level ground and from an isolated foothold (an archetypal feature of unstructured terrain). Abstract. For direct-drive legged robots operating in unstructured environments, workspace volume and force generation are competing, scarce resources. Disciplines Electrical and Computer Engineering | Engineering | Systems EngineeringIn this paper we demonstrate that introducing geared core actuation (i.e., proximal to rather than distal from the mass center) increases workspace volume and can provide a disproportionate amount of work-producing-force to the mass center without affecting leg linkage transparency. These effects are analytically quantifiable up to modest assumptions, and are demonstrated empirically on a spined quadruped performing a leap both on level ground and from an isolated foothold (an archetypal feature of unstructured terrain).

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Pitch then power: limitations to acceleration in quadrupeds

Cited by 55 publications

References 21 publications

Effects of grade and mass distribution on the mechanics of trotting in dogs

Effects of grade and mass distribution on the mechanics of trotting in dogs

On designing an active tail for legged robots: simplifying control via decoupling of control objectives

Core Actuation Promotes Self-manipulability on a Direct-Drive Quadrupedal Robot

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