Path-following: An alternative to reference tracking

Path-following is a relaxation of standard reference tracking in which the main objective is to steer a physical object to converge to a geometric path. A secondary objective is to ensure that object's motion along the path satisfies a given dynamic specification. In a path-following problem, the time dependance of the motion is suppressed by parameterizing the path with an auxiliary variable. The problem is first solved with respect to this auxiliary variable, leaving the choice of a timing law for it as an additional degree of freedom.; Reference tracking can be viewed as path-following in which the timing law along the path is prespecified. Our goal is to provide constructive procedures for exploiting the freedom obtained by recasting a reference tracking problem into the path-following framework. Specifically, we design timing laws that stabilize zero dynamics and reduce control effort.; In the first part of this thesis we develop several designs in which the timing law is constructed to stabilize the unstable zero dynamics. These designs confirm that path-following avoids the obstacle on tracking accuracy imposed by the unstable zero dynamics in a variety of situations. Applicability of our designs is illustrated on several practical examples including a PVTOL aircraft and, a two-mass mechanical system.; In the second part of this thesis we design the timing law to reduce the control effort. Maintaining the desired convergence to the path, our design provides a tradeoff between the dynamic performance along the path and the control effort. It is applicable to a class of nonlinear systems with stable zero dynamics and all sufficiently smooth paths. The effectiveness of our design in reducing control effort is shown on a realistic model of a hovercraft system.