球形线性插值(SLERP)长期以来一直用于计算机动画中，以在两个3D方向之间插值运动。我们使用四元数和SLERP开发了一种前向运动学（FK）方法，以预测青蛙如何在开始姿势和起飞之间调节跳跃运动学。青蛙肢体运动学已经在各种活动中进行了研究，然而，关节运动学差异和运动变异之间的因果关系仍然未知。我们将1）起飞角度从8°变为60°；2）从0到18°的转角；3）初始车身俯仰从0到70°。模拟类似于实验观察到的青蛙运动学。研究结果表明，大腿和小腿内收调节肢体抬高的基本机制。向前推力是由大腿和近端脚的缩回产生的，除了引起转弯的不对称性外，小腿的贡献很小。导致转弯的运动学变化是微妙的，仅表现为左右小腿的轻微反向旋转以及近端足内收的10％定时偏移。此外,倾斜的初始身体倾斜影响质心轨迹，以确定起飞时的行进方向。最重要的是,我们的理论首先表明，腿段旋转轴向共同方向的收敛对于肢体伸展和协调跳跃方向都是至关重要的；并且，其次,使用SLERP简化了模拟3D运动学的挑战，因为青蛙四肢在单位四元数空间中近似遵循线性路径。我们的方法可以更广泛地应用于研究生物和化石青蛙类群，以及激发机器人肢体的新控制算法。
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.
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