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.