Date: 22 May 2024

Dataset Title: Jointed tails enhance control of three-dimensional body rotation (dataset and code)
Dataset Creators: Xun Fu, Bohao Zhang, Ceri J. Weber, Kimberly L. Cooper, Ram Vasudevan, Talia Y. Moore

Dataset Contact: Talia Moore taliaym@umich.edu

Research Overview:
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.

Methodology:
We measured the maximal performance of a tail by using its actuation to make the torso follow a target "trajectory" of torso orientations. The target torso trajectories involve large accelerations within a short time, resulting in pitch, roll, and yaw rotations similar to those animals experience when banking for a turn or preparing for a leap. The task was formulated as a trajectory optimization problem. By solving the problem, we evaluated the performance of tails with different configurations. Performance of the tail was then quantified by assessing how well the torso tracked the target trajectories through the actuation of the tail under certain constraints. To quantify the tracking performance of a model, we used the integral of squared error between the target trajectory and the realized trajectory output by the optimization.

Detailed specifications of the optimization and models, including mass, size, joint torques, and other relevant parameters used for this study, are presented in the paper.

Instrument and/or Software specifications:
R software (no packages required)
Matlab

Files contained here:
-"Specimendata.csv" is a list of all the museum specimens with identifying information used in the study

-The "simulations" folder includes two subfolders. All files are in Matlab format.
--The "optimization outputs" folder includes the tail trajectories output by the optimization for both uniform (1-6 links) and variable length (2-4) models. Each specific configuration includes results from 100 iterations.
--The "target trajectories" folder includes 100 torso trajectories that act as goals for the optimization. Note that the target trajectories are not randomized, so each row in the output data (below) represents a specific target trajectory fit in each column by a different tail configuration.

Output data are all in csv format.
-The "t.tests" folder includes the data required to make the figures in the paper.
--"tailtest.R" is an R script that accesses all the other files in this directory to construct figures and compute significance values
--"alltailsCB.pdf" is generated by tailtest.R
--tipvel_uniform_1-6_link.csv contains the maximum tip velocity (magnitude) for each optimization trial for the uniform length tails. Each column represents the number of links in the tail. Each row represents a distinct trial. 
--tipvel_uniform_2-4link.csv is the columns 2-4 of the tipvel_uniform_1-6_link.csv file, for comparison with the variable length tails.
--tipvel_varied_2-4_link.csv contains the maximum tip velocity (magnitude) for each optimization trial for the variable length tails.  Each column represents the number of links in the tail, from 2-4. Each row represents a distinct trial.
--"uniform_1-6_link.csv" contains the total error for each trial in the uniform link length tails. Each column represents the number of links in the tail. Each row represents a distinct trial. This is used to create the anova table for uniform links (Figure 3a, Table 2a).
--"uniform_vs_varied_x_link.csv," where x is 2, 3, or 4 contains the total error for each trial in the variable link length tails, to generate Figure 6a. The columns are labeled with uniform or variable, and the rows represent the same target trajectories in the same order as above.
--"vertbyc1.csv" contains the length of caudal vertebrae normalized by the first caudal vertebra (Cd1). Each column represents a different species. Each row represents the caudal vertebral number, as labeled. This is used to create Figure 5b.
--The "joint_ctrl_effort_comp" folder includes subfolders for the two, three, and four link tails. In each folder, there is a .csv file that contains the control effort for each joint.

Related publication(s):
Xun Fu, Bohao Zhang, Ceri J. Weber, Kimberly L. Cooper, Ram Vasudevan, Talia Y. Moore. (in review) Jointed tails enhance control of three-dimensional body rotation.

Use and Access:
Attribution - NonCommercial 4.0 International (CC BY-NC 4.0)

To Cite Data:
Fu, Zhang, Weber, Cooper, Vasudevan, Moore (2024) Jointed tails enhance control of three-dimensional body rotation (dataset and code).