7,487 research outputs found
Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems
Many modern nonlinear control methods aim to endow systems with guaranteed
properties, such as stability or safety, and have been successfully applied to
the domain of robotics. However, model uncertainty remains a persistent
challenge, weakening theoretical guarantees and causing implementation failures
on physical systems. This paper develops a machine learning framework centered
around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and
unmodeled dynamics in general robotic systems. Our proposed method proceeds by
iteratively updating estimates of Lyapunov function derivatives and improving
controllers, ultimately yielding a stabilizing quadratic program model-based
controller. We validate our approach on a planar Segway simulation,
demonstrating substantial performance improvements by iteratively refining on a
base model-free controller
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
A Separation Principle on Lie Groups
For linear time-invariant systems, a separation principle holds: stable
observer and stable state feedback can be designed for the time-invariant
system, and the combined observer and feedback will be stable. For non-linear
systems, a local separation principle holds around steady-states, as the
linearized system is time-invariant. This paper addresses the issue of a
non-linear separation principle on Lie groups. For invariant systems on Lie
groups, we prove there exists a large set of (time-varying) trajectories around
which the linearized observer-controler system is time-invariant, as soon as a
symmetry-preserving observer is used. Thus a separation principle holds around
those trajectories. The theory is illustrated by a mobile robot example, and
the developed ideas are then extended to a class of Lagrangian mechanical
systems on Lie groups described by Euler-Poincare equations.Comment: Submitted to IFAC 201
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