Passive Control of Mechanical Systems and the
Application to Smart Exercise Machines
Perry Y. Li
Dept. of Mechanical Engineering
University of Minnesota
In many applications, a mechanical system has to interact with its
physical environment. The stability of this interaction is critical,
especially for machines that must interact safely with humans.
Interaction stability can be guaranteed by the passivity theorem for a
large class of physical environments if the closed loop control system
is rendered passive when the mechanical power is considered as the
supply rate. Closed loop mechanical systems are not generally passive in
this sense. In this talk, we shall discuss the design and properties of
a class of controllers that preserve the passivity properties of
mechanical systems in the closed loop.
The primary motivation is for the control of a class of novel smart
exercise machines. These machines have the following features: 1) they
can identify the biomechanic characteristic of the individual user
(specifically the force-velocity or Hill relationship of the muscles);
2) they are controlled such that the manner that the user exercises
tracks the (user specific) optimal velocity profile which enables the
user to exert maximum power; 3) the machines appears like a passive
system to the user so that they are safe to interact with. These
machines thus help users to accomplish a desired amount of exercise
quickly.
The Passive Velocity Field Control (PVFC) methodology has been developed
for this application in which the control objective is specified as a
velocity field on the configuration space of the system. The geometric
properties of the closed loop system can be described in terms of a
special affine connection which is compatible with a Riemannian metric
related to energy, and whose geodesics are the closed loop trajectories.
If time permitting, the robustness properties of the system will also be
discussed. Towards the end of the talk, I shall discuss several other
applications for which passive controllers have been or are currently
being developed and applied. These include contour following, robotic
deburring, and bilateral teleoperated manipulators.