In 1969, a palaeontologist proposed that theropod dinosaurs used their tails as dynamic stabilizers during rapid or irregular movements, contributing to their depiction as active and agile predators. Since then the inertia of swinging appendages has been implicated in stabilizing human walking, aiding acrobatic manoeuvres by primates and rodents, and enabling cats to balance on branches. Recent studies on geckos suggest that active tail stabilization occurs during climbing, righting and gliding. By contrast, studies on the effect of lizard tail loss show evidence of a decrease, an increase or no change in performance. Application of a control-theoretic framework could advance our general understanding of inertial appendage use in locomotion. Here we report that lizards control the swing of their tails in a measured manner to redirect angular momentum from their bodies to their tails, stabilizing body attitude in the sagittal plane. We video-recorded Red-Headed Agama lizards (Agama agama) leaping towards a vertical surface by first vaulting onto an obstacle with variable traction to induce a range of perturbations in body angular momentum. To examine a known controlled tail response, we built a lizard-sized robot with an active tail that used sensory feedback to stabilize pitch as it drove off a ramp. Our dynamics model revealed that a body swinging its tail experienced less rotation than a body with a rigid tail, a passively compliant tail or no tail. To compare a range of tails, we calculated tail effectiveness as the amount of tailless body rotation a tail could stabilize. A model Velociraptor mongoliensis supported the initial tail stabilization hypothesis, showing as it did a greater tail effectiveness than the Agama lizards. Leaping lizards show that inertial control of body attitude can advance our understanding of appendage evolution and provide biological inspiration for the next generation of manoeuvrable search-and-rescue robots.
In this paper we explore the design space of tails intended for self-righting a robot's body during free fall. Conservation of total angular momentum imposes a dimensionless index of rotational efficacy upon the robot's kinematic and dynamical parameters whose selection insures that for a given tail rotation, the body rotation will be identical at any size scale. In contrast, the duration of such a body reorientation depends upon the acceleration of the tail relative to the body, and power density of the tail's actuator must increase with size in order to achieve the same maneuver in the same relative time. Assuming a simple controller and powerlimited actuator, we consider maneuverability constraints upon two different types of parametersmorphological and energetic-that can be used for design. We show how these constraints inform contrasting tail design on two robots separated by a four-fold length scale, the 177g Tailbot and the 8.1kg X-RHex Lite (XRL). We compare previously published empirical self-righting behavior of the Tailbot with new, tailed XRL experiments wherein we drop it nose first from a 2.7 body length height and also deliberately run it off an elevated cliff to land safely on its springy legs in both cases. This was supported primarily by the ARL/GDRS RCTA and the NSF CiBER-IGERT under Award DGE-0903711.
Ahstract-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 feed forward 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.
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 as to permit all further design 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 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.
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.
An innovative implementation of attitude estimation in 3 degrees of freedom (3-DOF) combining the TRIAD algorithm [1] and a time-varying nonlinear complementary filter (TVCF) is derived. This work is inspired by the good performance of the TVCF in 1-DOF [2] developed for applications limited to small mobile platforms with low computational power. To demonstrate robust 3-DOF estimation, information from vector and rate-gyroscope measurements are fused. Simulation and experimental results demonstrate comparable performance to the extended Kalman filter (EKF) and improved performance over alternative methods such as sole gyroscope rate-integration and the TRIAD algorithm without the TVCF as a pre-filter. NOMENCLATURE r i fixed vectors in reference frame b i measured vectors in body frame b gi vectors via integrating gyro fromb î b i best estimate of vectors in body frame A rotation matrix from reference to body frame F r reference frame F b body frame ω ω ω angular velocity β β β time-varying bias in gyroscope measurement ω c cutoff frequency for TVCF W a triad formed from {b 1 , b 2 } V a triad formed from {r 1 , r 2 }
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