33,793 research outputs found
Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers
Hybrid systems theory has become a powerful approach for designing feedback
controllers that achieve dynamically stable bipedal locomotion, both formally
and in practice. This paper presents an analytical framework 1) to address
multi-domain hybrid models of quadruped robots with high degrees of freedom,
and 2) to systematically design nonlinear controllers that asymptotically
stabilize periodic orbits of these sophisticated models. A family of
parameterized virtual constraint controllers is proposed for continuous-time
domains of quadruped locomotion to regulate holonomic and nonholonomic outputs.
The properties of the Poincare return map for the full-order and closed-loop
hybrid system are studied to investigate the asymptotic stabilization problem
of dynamic gaits. An iterative optimization algorithm involving linear and
bilinear matrix inequalities is then employed to choose stabilizing virtual
constraint parameters. The paper numerically evaluates the analytical results
on a simulation model of an advanced 3D quadruped robot, called GR Vision 60,
with 36 state variables and 12 control inputs. An optimal amble gait of the
robot is designed utilizing the FROST toolkit. The power of the analytical
framework is finally illustrated through designing a set of stabilizing virtual
constraint controllers with 180 controller parameters.Comment: American Control Conference 201
Discrete Mechanics and Optimal Control Applied to the Compass Gait Biped
This paper presents a methodology for generating locally optimal control policies for simple hybrid mechanical systems, and illustrates the method on the compass gait biped. Principles from discrete mechanics are utilized to generate optimal control policies as solutions of constrained nonlinear optimization problems. In the context of bipedal walking, this procedure provides a comparative measure of the suboptimality of existing control policies. Furthermore, our methodology can be used as a control design tool; to demonstrate this, we minimize the specific cost of transport of periodic orbits for the compass gait biped, both in the fully actuated and underactuated case
Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems
We provide explicit closed form expressions for strict Lyapunov functions for
time-varying discrete time systems. Our Lyapunov functions are expressed in
terms of known nonstrict Lyapunov functions for the dynamics and finite sums of
persistency of excitation parameters. This provides a discrete time analog of
our previous continuous time Lyapunov function constructions. We also construct
explicit strict Lyapunov functions for systems satisfying nonstrict discrete
time analogs of the conditions from Matrosov's Theorem. We use our methods to
build strict Lyapunov functions for time-varying hybrid systems that contain
mixtures of continuous and discrete time evolutions.Comment: 14 pages. Accepted for publication in Nonlinear Analysis: Hybrid
Systems and Applications on September 6, 200
Robust Stability Analysis of Nonlinear Hybrid Systems
We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems
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