Applications
of Hybrid Control to Robotics
University
of Illinois at Chicago
Department
of Electrical and Computer
Engineering
Emerging applications of control in areas such as transportation
and biology made hybrid control popular in the control community. However, many of the studies assume that the
process that is being controlled is continuous and the hybrid behavior is
imposed by the controller. In several robotics applications, most notably
walking and haptics, this assumption is too restrictive and the control
engineer needs to cope with a process that is inherently discontinuous. In this
talk we will describe two methods that address this shortcoming.
First, we will discuss passivity in the context of hybrid systems.
This work is motivated by problems in haptics and teleoperation where passivity
is often used for controller design. To account for time delays and to better
react to user actions it is desirable to design controllers that can switch
between different operating modes. A traditional passivity definition requires
that a
storage function exists that is common to all the modes. We show
that stability of the system can be guaranteed even if different storage
function is found for each of the modes, provided appropriate conditions are
satisfied when the system switches.
In the second part of the talk, we will describe a general method
for stabilization of periodic orbits for hybrid systems with impact effects.
Our primary motivation is controller synthesis for walking robots. Limit cycles
of hybrid systems are characterized by the fact that they span different
dynamic regimes. For smooth systems, dynamics of the system along the limit
cycle can be decomposed into the transverse and tangential components. We
demonstrate that this decomposition can be adapted to hybrid systems.
Furthermore, we show that when the transverse dynamics is linearized and
discretized, the resulting robust control synthesis problem can be cast as a
semidefinite program and thus efficiently solved.
3:30 – 4:30
p.m.