Despite substantial evidence for the crucial role played by an active backbone or spine in animal locomotion, its adoption in legged robots remains limited because the added mechanical complexity and resulting dynamical challenges pose daunting obstacles to characterizing even a partial range of potential performance benefits. This paper takes a next step toward such a characterization by exploring the quasistatic terrestrial self-righting mechanics of a model system with coronal plane spine twisting (CPST). Reduction from a full 3D kinematic model of CPST to a two parameter, two degree of freedom coronal plane representation of body shape affordance predicts a substantial benefit to ground righting by lowering the barrier between stable potential energy basins. The reduced model predicts the most advantageous twist angle for several cross-sectional geometries, reducing the required righting torque by up to an order of magnitude depending on constituent shapes. Experiments with a three actuated degree of freedom physical mechanism corroborate the kinematic model predictions using two different quasistatic reorientation maneuvers for both elliptical and rectangular shaped bodies with a range of eccentricities or aspect ratios. More speculative experiments make intuitive use of the kinematic model in a highly dynamic maneuver to suggest still greater benefits of CPST achievable by coordinating kinetic as well as potential energy, for example as in a future multi-appendage system interacting with a contact-rich 3D environment.

We present the design, fabrication, and feedforward control of a insect-sized (142 mg) aerial robot that is equipped with a bio-inspired inertial tail. A tail allows the robot to perform rapid inertial reorientation as well as to shift weight to modulate aerodynamic torques on its body. Here we present the first analysis of inertial reorientation using a piezo actuator, departing from previous work to date that has focused exclusively on actuation by DC electric motor. The primary difference is that unlike a geared motor system, the piezo-tail system operates as a resonant system, exhibiting slowly-decaying oscillations. We present a dynamic model of piezo-driven inertial reorientation, along with an open-loop feedforward controller that reduces excitation of the resonant mode. We validate our approach on a tethered testbed as well as a flight-capable prototype. Our results indicate that incorporating a tail can allow for more rapid dynamic maneuvers and could stabilize the robot during flight.

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.