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A novel kinematics analysis method using quaternion interpolation–a case study in frog jumping

Richards, CT; Porro, LB; (2018) A novel kinematics analysis method using quaternion interpolation–a case study in frog jumping. Journal of Theoretical Biology , 454 pp. 410-424. 10.1016/j.jtbi.2018.06.010. Green open access

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Abstract

Spherical Linear Interpolation (SLERP) has long been used in computer animation to interpolate movements between two 3D orientations. We developed a forward kinematics (FK) approach using quaternions and SLERP to predict how frogs modulate jump kinematics between start posture and takeoff. Frog limb kinematics have been studied during various activities, yet the causal link between differences in joint kinematics and locomotor variation remains unknown. We varied 1) takeoff angle from 8 to 60°; 2) turn angle from 0 to 18°; and 3) initial body pitch from 0 to 70°. Simulations were similar to experimentally observed frog kinematics. Findings suggest a fundamental mechanism whereby limb elevation is modulated by thigh and shank adduction. Forward thrust is produced by thigh and proximal foot retraction with little contribution from the shank except to induce asymmetries for turning. Kinematic shifts causing turns were subtle, marked only by slight counter-rotation of the left versus right shank as well as a 10% timing offset in proximal foot adduction. Additionally, inclining initial body tilt influenced the centre of mass trajectory to determine direction of travel at takeoff. Most importantly, our theory suggests firstly that the convergence of leg segment rotation axes toward a common orientation is crucial both for limb extension and for coordinating jump direction; and, secondly, the challenge of simulating 3D kinematics is simplified using SLERP because frog limbs approximately follow linear paths in unit quaternion space. Our methodology can be applied more broadly to study living and fossil frog taxa as well as to inspire new control algorithms for robotic limbs.

Type: Article
Title: A novel kinematics analysis method using quaternion interpolation–a case study in frog jumping
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jtbi.2018.06.010
Publisher version: https://doi.org/10.1016/j.jtbi.2018.06.010
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Frogs, Jumping, Kinematics, Simulation, Forward kinematics, Quaternions, Spherical linear interpolation
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences > Cell and Developmental Biology
URI: https://discovery.ucl.ac.uk/id/eprint/10074277
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