Tails used as inertial appendages induce body rotations of animals and robots, a phenomenon that is governed largely by the ratio of the body and tail moments of inertia. However, vertebrate tails have more degrees of freedom (e.g., number of joints, rotational axes) than most current theoretical models and robotic tails. To understand how morphology affects inertial appendage function, we developed an optimization-based approach that finds the maximally effective tail trajectory and measures error from a target trajectory. For tails of equal total length and mass, increasing the number of equal-length joints increased the complexity of maximally effective tail motions. When we optimized the relative lengths of tail bones while keeping the total tail length, mass, and number of joints the same, this optimization-based approach found that the lengths match the pattern found in the tail bones of mammals specialized for inertial maneuvering. In both experiments, adding joints enhanced the performance of the inertial appendage, but with diminishing returns, largely due to the total control effort constraint. This optimization-based simulation can compare the maximum performance of diverse inertial appendages that dynamically vary in moment of inertia in 3D space, predict inertial capabilities from skeletal data, and inform the design of robotic inertial appendages.

翻译：作为惯性附肢的尾部可引发动物及机器人的躯体旋转，这一现象主要受躯体与尾部转动惯量比值的调控。然而，脊椎动物尾部比当前大多数理论模型与机器人尾部具有更多自由度（如关节数量、旋转轴）。为理解形态结构如何影响惯性附肢功能，我们开发了一种基于优化的方法，该方法能寻找最大化有效的尾部运动轨迹，并测量其与目标轨迹的误差。对于总长度和质量均相等的尾部，增加等长关节数量会提升最大化有效尾部运动的复杂度。当我们在保持尾部总长度、质量及关节数不变的情况下优化尾骨相对长度时，此基于优化的方法发现其长度分布模式与专精于惯性机动的哺乳动物尾骨形态相符。两项实验均表明，增加关节可提升惯性附肢性能，但存在收益递减现象，这主要受限于总控制能耗约束。该基于优化的仿真方法能够比较三维空间中转动惯量动态变化的多种惯性附肢的最大性能，根据骨骼数据预测惯性运动能力，并为机器人惯性附肢的设计提供理论依据。