1,077 research outputs found
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
Input to State Stability of Bipedal Walking Robots: Application to DURUS
Bipedal robots are a prime example of systems which exhibit highly nonlinear
dynamics, underactuation, and undergo complex dissipative impacts. This paper
discusses methods used to overcome a wide variety of uncertainties, with the
end result being stable bipedal walking. The principal contribution of this
paper is to establish sufficiency conditions for yielding input to state stable
(ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and
phase-based uncertainties. In particular, it will be shown formally that
exponential input to state stabilization (e-ISS) of the continuous dynamics,
and hybrid invariance conditions are enough to realize stable walking in the
23-DOF bipedal robot DURUS. This main result will be supported through
successful and sustained walking of the bipedal robot DURUS in a laboratory
environment.Comment: 16 pages, 10 figure
An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion
We describe a whole-body dynamic walking controller implemented as a convex
quadratic program. The controller solves an optimal control problem using an
approximate value function derived from a simple walking model while respecting
the dynamic, input, and contact constraints of the full robot dynamics. By
exploiting sparsity and temporal structure in the optimization with a custom
active-set algorithm, we surpass the performance of the best available
off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We
describe applications to balancing and walking tasks using the simulated Atlas
robot in the DARPA Virtual Robotics Challenge.Comment: 6 pages, published at ICRA 201
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