Tail Assisted Dynamic Self Righting

Abstract

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.

Parallel composition of templates for tail-energized planar hopping

“…1 center) forgoes Raibert's prismatic shank actuator, and instead places that actuator in an inertial appendage. This motivates us to explore how tails can be "recycled" from their transitional agility duties [11], [12], now repurposed to substitute for Raibert's shank actuator and play the role of steady-state running energizer in the sagittal plane. Apart from their use in transitional maneuvers (inertial control in free-falling lizards [14] and robots [11], [12] or in turning lizards [15] and robots [16]) it has recently been discovered that kanagaroos do positive work with their tails Hybrid mode, where 1 is stance, 2 is flight…”

“…Shape reorientation [12] g sh 2 pa 2 , 9 a 2 q "´kgka 2´kg 9 a 2 (15) in a quasistatic pentapedal gait [17]. In our implementation, the tail contributes the reorientation function in flight, and the energetic "pump" function in stance (albeit in a dynamic fashion).…”

“…1. At the leaves of this hierarchy tree, we introduce four different 1DOF templates that emerge from the decades old bioinspired running literature [3], [10], joined by a new arrival from recent work on bioinspired tails [11], [12]. We apply the four decoupled 1DOF control laws associated with these isolated "leaf" templates directly to the (highly dynamically coupled) physical platform and demonstrate empirically steady sagittal plane running (on a circular boom) whose body motions reveal, when viewed in the appropriate coordinates, Fig.…”

Precise dynamic turning of a 10 cm legged robot on a low friction surface using a tail

“…Analysis of tail-body dynamics while a robot is in free fall has been explored by [9] [27]. The analysis presented below is similar but incorporates friction from the legs, a piecewise linear motor model, and compares turning with the tail to legged steering, also modeled here.…”

“…Aquatic robots have used tails for turning based on hydrodynamic forces [5]. Tails have also been used on robots to control pitch and orientation [27] while airborne, ensuring the robot lands on its feet [9][4] [18]. Here we explore the use of the tail for yaw turning using angular momentum exchange, but also with complex ground interaction and friction, not previously examined.…”