302 research outputs found
The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates
We have built a 12DOF, passive-compliant legged, tailed biped actuated by
four brushless DC motors. We anticipate that this machine will achieve varied
modes of quasistatic and dynamic balance, enabling a broad range of locomotion
tasks including sitting, standing, walking, hopping, running, turning, leaping,
and more. Achieving this diversity of behavior with a single under-actuated
body, requires a correspondingly diverse array of controllers, motivating our
interest in compositional techniques that promote mixing and reuse of a
relatively few base constituents to achieve a combinatorially growing array of
available choices. Here we report on the development of one important example
of such a behavioral programming method, the construction of a novel monopedal
sagittal plane hopping gait through parallel composition of four decoupled 1DOF
base controllers.
For this example behavior, the legs are locked in phase and the body is
fastened to a boom to restrict motion to the sagittal plane. The platform's
locomotion is powered by the hip motor that adjusts leg touchdown angle in
flight and balance in stance, along with a tail motor that adjusts body shape
in flight and drives energy into the passive leg shank spring during stance.
The motor control signals arise from the application in parallel of four
simple, completely decoupled 1DOF feedback laws that provably stabilize in
isolation four corresponding 1DOF abstract reference plants. Each of these
abstract 1DOF closed loop dynamics represents some simple but crucial specific
component of the locomotion task at hand. We present a partial proof of
correctness for this parallel composition of template reference systems along
with data from the physical platform suggesting these templates are anchored as
evidenced by the correspondence of their characteristic motions with a suitably
transformed image of traces from the physical platform.Comment: Technical Report to Accompany: A. De and D. Koditschek, "Parallel
composition of templates for tail-energized planar hopping," in 2015 IEEE
International Conference on Robotics and Automation (ICRA), May 2015. v2:
Used plain latex article, correct gap radius and specific force/torque
number
Frontal plane stabilization and hopping with a 2DOF tail
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
Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics
Properly designing a system to exhibit favorable natural dynamics can greatly
simplify designing or learning the control policy. However, it is still unclear
what constitutes favorable natural dynamics and how to quantify its effect.
Most studies of simple walking and running models have focused on the basins of
attraction of passive limit-cycles and the notion of self-stability. We instead
emphasize the importance of stepping beyond basins of attraction. We show an
approach based on viability theory to quantify robust sets in state-action
space. These sets are valid for the family of all robust control policies,
which allows us to quantify the robustness inherent to the natural dynamics
before designing the control policy or specifying a control objective. We
illustrate our formulation using spring-mass models, simple low dimensional
models of running systems. We then show an example application by optimizing
robustness of a simulated planar monoped, using a gradient-free optimization
scheme. Both case studies result in a nonlinear effective stiffness providing
more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on
Robotics (2019
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