This paper develops a comparative framework for the design of actuated inertial appendages for planar aerial reorientation. We define the inertial reorientation template, the simplest model of this behavior, and leverage its linear dynamics to reveal the design constraints linking a task with the body designs capable of completing it. As practicable inertial appendage designs lead to morphology that is generally more complex, we advance a notion of “anchoring,” whereby a judicious choice of physical design in concert with an appropriate control policy yields a system whose closed-loop dynamics are sufficiently captured by the template to permit all further designs to take place in its far simpler parameter space. This approach is effective and accurate over the diverse design spaces afforded by existing platforms, enabling a performance comparison through the shared task space. We analyze examples from the literature and find advantages to each body type, but conclude that tails provide the highest potential performance for reasonable designs. Thus motivated, we build a physical example by retrofitting a tail to a RHex robot and present empirical evidence of its efficacy.

In this work, we propose a control scheme for attitude control of a falling, two link active tailed robot with only two degrees of freedom of actuation. We derive a simplified expression for the robot's angular momentum and invert this expression to solve for the shape velocities that drive the body's angular momentum to a desired value. By choosing a body angular velocity vector parallel to the axis of error rotation, the controller steers the robot towards its desired orientation. The proposed scheme is accomplished through feedback laws as opposed to feedforward trajectory generation, is fairly robust to model uncertainties, and is simple enough to implement on a miniature microcontroller. We verify our approach by implementing the controller on a small (175 g) robot platform, enabling rapid maneuvers approaching the spectacular capability of animals.

We present a novel approach to stabilizing rapid locomotion in mobile terrestrial robots inspired by the tail function of lizards.We built a 177 (g) robot with inertial sensors and a single degree-of-freedom active tail. By utilizing both contact forces and zero net angular momentum maneuvering, our tailed robot can rapidly right itself in a fall, avoid flipping over after a large perturbation, and smoothly transition between surfaces of different slopes. We also use a modeling approach to show that a tail-like design offers significant advantages to other alternatives, including reaction wheels, when the speed of response is important.

Complementary filtering (CF) is a well known method that can effectively fuse a gyroscope and accelerometer measurement in order to robustly estimate the attitude of a rigid body in a planar single degree of freedom (DOF) setting. The attitude can be estimated individually by either integrating the gyroscope measurement or by calculating the inverse tangent of the components of a 2-axis accelerometer. The gyroscope can adequately estimate the angle in the higher frequency region, but suffers from drift issues at low frequency, whereas the accelerometer can accurately measure the acceleration and thus direction of gravity, but loses this accuracy when faced with motion accelerations. CF traditionally uses linear time invariant filters, however, this paper presents an extension to the CF method by proposing time-varying parameters. A fuzzy logic method is developed to adjust the parameters. Stability analysis as well as experimental results are presented to verify the proposed method.