Tail Design for Maneuverability


The Biomimetic Robotics Lab investigates the way of using a tail to improve maneuverability of the MIT Cheetah. The research was initiated with the inspiration from videos, showing that the cheetah’s turn is accompanied by a movement of its tail, and some researches in biology, describing that cats or dogs are moving their tail during locomotion. We end up with hypothesizing that a tail may enhance balance of the legged robot. This hypothesis is investigated with three examples.


External disturbance rejection using a tail

A robotic tail is designed and implemented on the MIT Cheetah to verify its effect on balance when external disturbance exist. The mass of the tail is 0.74 kg and the moment of inertia about the motor rotation axis is 0.160 kg m^2. The figure below depicts the experimental setup; the MIT cheetah is set to stand while the clay wrecking ball is swung into the impact site on the rear pelvis.

The video below shows that a large disturbance, which is enough to fell down the MIT Cheetah, is applied and the tail effectively stabilizes the body after the disturbance.

The plot below compares the horizontal position of the hip with/ without tail actuation. Green dash-dotted line indicates the horizontal position of the hips with the activated tail, while Blue solid line indicates that with the tail held fixed. Red dotted line represents the difference between two lines.

Comparison of a reaction wheel and a tail

A reaction wheel, a well known engineering technology, and a tail are compared, in terms of their effectiveness of reorienting the body in cases when space, power, and time are limited. A reaction wheel is designed to fit within a volume so that it can rotate continuously, whereas a tail is allowed to have greater dimensions and greater effective moment of inertia, but it cannot rotate continuously without collision. Given different geometric constraints and with the assumption that either tool is operated while cheetah is in the air, maximum impulse, or average torque, is computed for each, within a time of interest. The figure below shows that a tail is appropriate when space is available for a high moment of inertia and the time of interest is very short.

Attitude Maneuvers using a tail

We proposed a simple feedback controller for three-axis spatial maneuvers using a straight, narrow tail to provide reaction moments. Control law is designed and followed by optimization to reorient the body from arbitrary orientation to a desired one (zero roll, pitch and yaw). At each instant, the controller finds the orientation and angular velocity of the body, computes the desired axis of rotation and angular momentum difference to achieve a desired orientation. Desired torque is calculated and projected onto the space of achievable torques. If it is allowed to optimize the initial tail orientation as if it was a planned maneuver, the performance becomes much better. The figure below shows that the controller successfully achieves a desired landing orientation during a limited flight time in simulation.

Further goal

The advantage and usefulness of tail in case of mid-air usage with single operation is well shown in the above results. More careful strategy is required to operate a tail continuously, considering characteristics of legged robots. To address this issue, one of ideas we have is that tail can be used as to help legs by ‘earning  short time’ in between leg sequence so that a body stays in the stable region when a correcting foot placement can be made. The idea is being verified via simulation with more detailed model.

Further reading

R. Briggs, J. Lee, M. Haberland, S. Kim,  ”Tails in Biomimetic Design: Analysis, Simulation, and Experiment”, In Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1473 – 1480, Oct 2012, Vilamoura, Portugal.