Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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1994 - 19983

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Author: search.filters.author.Manikonda, VikramSubject: search.filters.subject.geometric control

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    Control and Stabilization of a Class of Nonlinear Systems with Symmetry
    (1998) Manikonda, Vikram; Krishnaprasad, P.S.; ISR; CDCSS
    The focus of this dissertation is to study issues related to controllability and stabilization of a class of underactuated mechanical systems with symmetry. In particular we look at systems whose configuration can be identified with a Lie group and the reduced equations are of the Lie-Poisson type. Examples of such systems include hovercraft, spacecraft and autonomous underwater vehicles. We present sufficient conditions for the controllability of affine nonlinear control systems where the drift vector field is a Lie-Poisson reduced Hamiltonian vector field. In this setting we show that depending on the existence of a radially unbounded Lyapunov type function, the drift vector field of the reduced system is weakly positively Poisson stable. The weak positive Poisson stability along with the Lie algebra rank condition is used to show controllability. These controllability results are then extended to the unreduced dynamics. Sufficient conditions for controllability are presented in both cases where the symmetry group is compact and noncompact. We also present a constructive approach to design feedback laws to stabilize relative equilibria of these systems. The approach is based on the observation that, under certain hypotheses the fixed points of the Lie-Poisson dynamics belong to an immersed equilibrium submanifold. The existence of such equilibrium manifolds, along with the center manifold theory is used to design stabilizing feedback laws.
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    Control Problems of Hydrodynamic Type
    (1998) Krishnaprasad, Perinkulam S.; Manikonda, Vikram; ISR; CDCSS
    It has been known for some time that the classical work of Kirchhoff, Love,and Birkhoff on rigid bodies in incompressible, irrotational flows provideseffective models for treating control problems for underwater vehicles.This has also led to a better appreciation of the dynamics of suchsystems. In this paper, we develop results based on geometric mechanics andcenter manifold theory to solve controllability and stabilization questionsfor a class of under-actuated left invariant mechanical systems on Liegroups that include approximate models of underwater vehicles and surfacevehicles. We also provide numerical evidence to capture the globalproperties of certain interesting feedback laws.

    (This work appears as an invited paper in the Proc. IFAC Sympo. on NonlinearControl Systems Design (NOLCOS'98), (1998), 1:139-144)

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    A Hybrid Control Strategy for Path Planning and Obstacle Avoidance with Nonholonomic robots
    (1994) Manikonda, Vikram; Krishnaprasad, P.S.; ISR
    The primary focus is on providing a formal basis for behavior- based robotics using techniques that have been successful in control-based approaches for steering and stabilizing robots that are subject to nonholonomic constraints. In particular, behaviors for robots are formalized in terms of kinetic state machines, a motion description language and the interaction of the kinetic state machine with information coming in from (limited range) sensors. This allows us to create a mathematical basis for discussing these systems, including techniques for integrating sets of behaviors. In addition we suggest optimality criteria for comparing both atomic and compound behaviors in various environments. A hybrid architecture for the implementation of path planners that use the motion description language is presented. The design and implementation of a planner for path planning and examples of obstacle avoidance with nonholonomic robots are discussed.