Underactuated Vehicle Control Research Summary Report Number 4 2 Papers Reviewed 2.1 Nonlinear Tracking of Underactuated Surface Vessels 2.2 Nonlinear Control Design for Slightly Non-minimum Phase Systems

1 Overview This brief report summarizes our recent research eeorts on the underactuated vehicle control problem. I will describe the papers and books I reviewed this week and comment on a new literature search. I will also summarize the steps we have taken toward solving the control problem for the vehicle and our current plans for the next few weeks. You will notice that the main title of this brief report has changed from \Planar Underwater Body" to \Underactuated Vehicle Control" to describe the general type of problem we are investigating. Note: I commented on this paper in Report 3. The following comments contain a summary of that information and also highlight a few aspects of the research that are signiicant for our work, but not mentioned earlier.] The conference paper by Godhavn 1] describes a controller to perform tracking for an underactuated vehicle. The paper develops a simple kinematic model for a surface vessel with nonlinear equations of motion and the primary assumption that the vehicle always has a positive forward velocity. One key diierence between Godhavn's problem and our problem is that we consider equations of motion that incorporate a non-minimum phase structure and Godhavn does not. He acknowledges this type of motion is possible, but does not analyze it. The author develops a motion planning algorithm for the system based on nding the shortest path connecting a sequence of points and satisfying orientation conditions along the way. The path is composed of arcs of circles and straight lines. The algorithm maintains the vehicle orientation by limiting the maximum curvature along a trajectory. The design section of the paper uses backstepping to derive the control law for the system. The system has two inputs and the controller attempts to track a reference trajectory, assuming the trajectory is composed of arcs and straight lines. The derivation using backstepping is abbreviated, but the resulting controller is relatively simple and we should be able to exploit some of these techniques to develop a controller for the non-minimum phase system. The paper by Hauser, Sastry and Meyer 2] looks at the problem of controlling an underactuated non-minimum phase system through exact linearization of the equations of motion. The key results in the paper show that if the system is only slightly non-minimum phase, (that is, the zero dynamics for the system are not asymptotically stable,) then designing a feedback controller based on …