Backlash
Impactive dynamic systems
Understanding human walking as well
as machines with backlash
This work is done with Marco Mata and Bernard Brogliato
from LAG-ENSIEG, Grenoble, France.
It is known that impacts can profoundly alter the behavior
of dynamic
systems. Impacts may occur in a broad class of systems.
At every heel touchdown during human walking, the swinging
leg comes to a complete stop which gives rise to a large
foot/ground force. This can be considered as an impact and
has a fundamental importance on the human gait. It is
thought that the evolution of the human leg structure
and the associated kinematics and dynamics has been
driven, among other objectives, to minimize the detrimental
effects of impact on the human body. Our initial efforts
involve the modeling and control of interaction between
simple non-linear compliant systems with and without friction.
Impacts involving much larger force spikes and much sharper
velocity discontinuities may take place in mechanical systems.
The clearance between two moving machine parts, due such
effects as gear backlash, machining imprecision
(however small) and thermal effects, favors the
occurrence of impacts in these systems. Impacts
are known to be responsible for chattering and
instability problems in machines and is extremely
difficult to control.
We use the so-called impact damper model in order to study
the phenomenon of dynamic backlash including its
inherent non-linearities. We propose a PD control
scheme to generate periodic trajectories in this
system. We show that appropriate gains in the PD
control scheme can be selected such that the
closed-loop system is locally stable around a desired symmetric
periodic orbit. We use the impact Poincare map to
demonstrate the local
stability of the motion induced by the controller.
In order to enlarge the basin of attraction of this
orbit we propose the use of a hybrid control in
addition to the PD control.
A list of my papers on this topic:
- On the control of
mechanical systems with dynamic backlash
- M. Mata-Jimenez, B. Brogliato, and A. Goswami
- CDC Conf, San Diego, CA, December 1997.
- Analysis of PD
control of mechanical systems with dynamic backlash
- M. Mata-Jimenez, B. Brogliato, and A. Goswami
- 2nd Int. Symp. MV2 on Active Control in Mechanical Engineering,
Lyon, France, October 1997.
- Periodic stabilization of a 1-dof hopping robot over nonlinear
compliant surface
- C. Canudas de Wit, L. Roussel, and A. Goswami
- IFAC Symp. on Robot Control (SyRoCo),
Nantes, France, September 1997.