Frontal plane stabilization and hopping with a 2DOF tail

Abstract

The Jerboa, a tailed bipedal robot with two hip-actuated, passive-compliant legs and a doubly actuated tail, has been shown both formally and empirically to exhibit a variety of stable hopping and running gaits in the sagittal plane. In this paper we take the first steps toward operating Jerboa as a fully spatial machine by addressing the predominant mode of destabilization away from the sagittal plane: body roll. We develop a provably stable controller for underactuated aerial stabilization of the coupled body roll and tail angles, that uses just the tail torques. We show that this controller is successful at reliably reorienting the Jerboa body in roughly 150 ms of freefall from a large set of initial conditions. This controller also enables (and appears intuitively to be crucial for) sustained empirically stable hopping in the frontal plane by virtue of its substantial robustness against destabilizing perturbations and calibration errors. The controller as well as the analysis methods developed here are applicable to any robotic platform with a similar doubly-actuated spherical tail joint. Disciplines

Smooth extensions of feedback motion planners via reference governors

“…In general, smooth extensions of rather generic vector fields, with known Lyapunov functions, can be constructed using total energy, but the resulting policies can only ensure local stability and offer no assurance of collision avoidance [7]. In [8], instead of total energy, a similar approach based on angular momentum is utilized to design a locally stable reorientation controller for a second-order tailed biped robot that tracks reference dynamics constructed for a simplified kinematic model.…”

Analytically-Guided Design of a Tailed Bipedal Hopping Robot

“…This work was supported in part by AFRL grant FA865015D1845 (subcontract 669737-1) and in part by ONR grant #N00014- 16 during flight [9], stance [10], and for reorientation [11]. Bioinspired robot designs often introduce a tail (i.e.…”

“…Robotic tails have also been used to assist in leaping [5]. To the best of the authors' knowledge, the Penn Jerboa [1] is the first robot to have used its tail to energize hopping as well as for balance and attitude control [2,16]. These varied uses for tails suggest their broader value in affording many different behaviors with relatively few actuators, thereby allowing for high power density.…”

“…3) that measures the leg extension. This measurement is used to calculate ψ v for oscillatory tail energization (7), as well as for touchdown detection (formerly achieved using an IR distance sensor [16]). This measurement also allows for on-line calculation of the leg infinitesimal kinematics, which we can subsequently use to estimate the fore-aft body velocity.…”

“…The design of the leg (modeled as a prismatic passive spring, and actively-controlled revolute hip joint) plays an important role in decoupling the radial and tangential reaction forces in fore-aft hopping. Many designs were historically considered in the design of the Jerboa leg [1,16], but the analytical result of Sec. II motivates a new study in this area.…”