2 research outputs found
Planar Symmetric Juggling of a Devil-Stick
Juggling a devil-stick can be described as a problem of non-prehensile
manipulation. Assuming that the devil-stick remains confined to the vertical
plane, the problem of juggling the stick between two symmetric configurations
is considered. Impulsive forces are applied to the stick intermittently and the
impulse of the force and its point of application are modeled as control inputs
to the system. The dynamics of the devil-stick due to the impulsive forces and
gravity is described by half-return maps between two Poincare sections; the
symmetric configurations are fixed points of these sections. A coordinate
transformation is used to convert the juggling problem to that of stabilization
of one of the fixed points. Inclusion of the coordinate transformation in the
dynamic model results in a nonlinear discrete-time system. A dead-beat design
for one of the inputs simplifies the control problem and results in a linear
time-invariant discrete-time system. Standard control techniques are used to
show that symmetric juggling can be achieved from arbitrary initial conditions
Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincare Maps
The problem of orbital stabilization of underactuated mechanical systems with
one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints
are enforced using a continuous controller; this results in a dense set of
closed orbits on a constraint manifold. A desired orbit is selected on the
manifold and a Poincare section is constructed at a fixed point on the orbit.
The corresponding Poincare map is linearized about the fixed point; this
results in a discrete linear time-invariant system. To stabilize the desired
orbit, impulsive inputs are applied when the system trajectory crosses the
Poincare section; these inputs can be designed using standard techniques such
as LQR. The Impulse Controlled Poincare Map (ICPM) based control design has
lower complexity and computational cost than control designs proposed earlier.
The generality of the ICPM approach is demonstrated using the 2-DOF
cart-pendulum and the 3-DOF tiptoebot.Comment: The paper is under review in Systems and Control Letter