SGER: Path Invariance for Optimal and Adaptive Maneuvering

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SGER: PATH INVARIANCE FOR OPTIMAL AND ADAPTIVEMANEUVERINGPrincipal InvestigatorPetar V. Kokotovic, ECE, UCSBSanta Barbara, CA 93106petar@ece.ucsb.eduPROPOSAL SUMMARYThis exploratory proposal pursues several promising new ideas which emerged from the final year of the research under the NSF Grant ECS-0228846 entitled "Nonlinear and adaptive control with unmodeled dynamics". The main results of this research are first briefly reviewed. They demonstrate major advantages achieved when a tracking problem is reformulated as a less restrictive path following problem in which the time variable is replaced by a free parameter to be used as an additional control. Path following formulations are more suitable for most common applications. At the same time they avoid some classical limitations in systems with unstable zero dynamics ("nonminimum phase systems".) This has been reported in our recent conference papers and journal publications which have appeared or are about to appear. Intellectual MeritWe will explore some less certain but highly promising new possibilities to exploit the design freedom provided by path following formulations. The proposed research will attempt to characterize the class of paths for which these possibilities exist. It will then focus on their applicability to an important class of problems in optimal and adaptive maneuvering for autonomous and operator assisted vehicles. The key dynamical property guaranteed by a path following controller is that a selected or optimized path becomes an invariant set, or an invariant manifold, of the vehiclecontroller feedback system. Methods are to be developed for design of such feedback controllers. The additional design freedom is then used to achieve desirable (optimal, adaptive) dynamical properties in the invariant set and thus guarantee the performance ofthe motion along the path. This proposals intellectual merit lies on clarifying further possibilities of separating geometric and dynamic tasks in nonlinear designs and thus making this more accessible to this and other areas of engineering.Broader impactsOn its applied side, this proposal aims at classifying most commonly used vehicular paths - orbits, turns, swerves, - and making them optimal with respect to practically important criteria: effort, energy, safety. An illustrative application of this kind will be a comparative study of advantages of four-wheel steering over the more common frontwheel steering. The expected broader impact of this research is its contribution to saferand more efficient ground vehicles. This proposal will also help educationally by providing funds to employ one graduate student.