A novel kinematics analysis method using quaternion interpolation–a case study in frog jumping. (7th October 2018)

• Record Type: Journal Article
• Authors: Richards, Christopher T.; Porro, Laura B.
• Is Part Of: Journal of theoretical biology. Volume 454(2018)
• Page Start: 410
• Page End: 424
• Publication Date: 2018-10-07
• Subjects: Frogs -- Jumping -- Kinematics -- Simulation -- Forward kinematics -- Quaternions -- Spherical linear interpolation; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2018.06.010
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: Frog leg segments follow paths that can be derived from quaternion spherical linear interpolation (SLERP) between the pre-jump posture and takeoff. Our model predicts that frogs jump by straightening their limb in a manner that minimises rotation. Limb segment adduction (rather than body pitch) is the key determinant of jump steepness. The orientation of the shank segment appears to be the primary steering mechanism in frog jumps to modulate pitch and turn angle. Our simple model may provide tools for simulating kinematics in a broad range of living and extant taxa. 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.