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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Item REU Report: An Implementation of the MDLe Platform(1999) Cockrell, Jacqueline; Krishnaprasad, P.S.; ISRThe purpose of this project was to create an implementation of the MDLe (motion description language, extended)platform, a platform that has an interface of standard language (the C++ programminglanguage) serving as a protocol between the programmer and a specific robot'sdetails of implementation. A program ("The Mailman") was designed and createdto enable a robot to deliver mail form one room in the A.V. Williams buildingto another (Dr. Krishnaprasad's office) on its own. This paper offers anintroduction to the MDLe system, background information on the mathematics thatgovern the motion of the robot, and a detailed layout of "The Mailman" plan.Item Control and Stabilization of a Class of Nonlinear Systems with Symmetry(1998) Manikonda, Vikram; Krishnaprasad, P.S.; ISR; CDCSSThe 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.Item Motion Control for Nonholonomic Systems on Matrix Lie Groups(1998) Struemper, Herbert Karl; Krishnaprasad, P.S.; ISR; CDCSSIn this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coordinates and other mathematical tools provided by the Lie group setting. An approximate tracking control law is derived for so-called chained form systems which arise as local representations of systems on a certain nilpotent matrix group. After studying the technique of nilpotentization in the setting of systems on matrix Lie groups we show how motion control laws derived for nilpotent systems can be extended to nilpotentizable systems using feedback and state transformations. The proposed control laws exhibit highly oscillatory components both for tracking and feedback stabilization of local representations of nonholonomic systems on Lie groups. Applications to the control and analysis of the kinematics of mechanical systems are discussed and numerical simulations are presented.Item Control Problems of Hydrodynamic Type(1998) Krishnaprasad, Perinkulam S.; Manikonda, Vikram; ISR; CDCSSIt 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)
Item The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws(1998) Tsai, L. W.; Tsai, L. W.; ISRIn this paper, the theory of reciprocal screws is reviewed. Reciprocal screwsystems associated with some frequently used kinematic pairs and chains aredeveloped. Then, the application of reciprocal screw systems for theJacobian analysis of parallel manipulators is described. The Jacobian andsingular conditions of a six-degree-of-freedom parallel manipulator are analyzed.Item A Three Degree of Freedom Parallel Manipulator with Only Translational Degrees of Freedom(1997) Stamper, R. E.; Tsai, L-W.; ISRIn this dissertation, a novel parallel manipulator is investigated. The manipulator has three degrees of freedom and the moving platform is constrained to only translational motion. The main advantages of this parallel manipulator are that all of the actuators can be attached directly to the base, closed-form solutions are available for the forward kinematics, the moving platform maintains the same orientation throughout the entire workspace, and it can be constructed with only revolute joints. Closed-form solutions for both the forward and inverse kinematics problems are presented. It is shown that the inverse kinematics problem has up to four real solutions, and the forward kinematics problem has up to 16 real solutions. The Jacobian matrix for the manipulator is also developed, and used to identify singular poses of the manipulator, where the manipulator instantaneously gains or loses a degree of freedom. The manipulator workspace volume as a function of link lengths and leg orientation is determined using the Monte Carlo method. A procedure for characterizing the quality of the workspace is also developed. Using these results, optimization studies for maximum workspace volume and for well-conditioned workspace volume are conducted. The objective function for the well-conditioned optimization study is defined as the integration of the reciprocal of the condition number of the Jacobian matrix over the workspace volume, and named the global condition index. Three different models are developed for the manipulator dynamics, with numerical simulations presented for all three models. The first model is based upon the application of the Newton-Euler equations of motion used in conjunction with the Jacobian matrix to map the inertial and gravitational loadings of the moving platform to the actuators. The second model was developed to give a more complete characterization of the dynamics, and is based upon the Lagrangian multiplier approach. The third model neglects the highly coupled nature of the manipulator and models each input link individually. This model is developed for use with single- input single-output type controllers. A prototype was fabricated to demonstrate this manipulator. Three controllers are developed and tested on the prototype, where each type of control tested relied on different characterizations of the manipulator dynamics. The three controllers are a PID controller, a computed torque controller, and an iterative learning controller. The research presented in this dissertation establishes this parallel manipulator as a viable robotic device for three degree of freedom manipulation. The manipulator offers the advantages associated with other parallel manipulators, such as light weight construction; while avoiding some of the traditional disadvantages of parallel manipulators such as the extensive use of spherical joints and coupling of the platform orientation and position.Item Enumeration and Selection of Clutching Sequences Associated with Epicyclic-type Transmission Mechanisms(1997) Hsieh, Hsin-I; Tsai, L. W.; ISRThis dissertation investigates the kinematics, the torque distributions, and the power losses of epicyclic gear mechanisms based upon the concepts of fundamental geared entities and fundamental circuits. The kinematic characteristics of fundamental geared entity are applied to the overall speed ratio analysis of epicyclic gear mechanisms. It is shown that the overall speed ratio of an epicyclic gear mechanism can be symbolically expressed in terms of the speed ratios of its fundamental geared entities by decomposing an epicyclic gear mechanism into two subsystems and each subsystem into two subsystems until the lowest level subsystem contains only one fundamental geared entity. The results are then used for the estimation and comparison of various speed ratios of an epicyclic gear mechanism, which leads to the development of a methodology for the enumeration of feasible clutching sequences for a given epicyclic gear mechanism. Finally, a systematic methodology for the torque and power loss analyses is described and a procedure for selecting a most efficient clutching sequence of an epicyclic gear mechanism is presented.Item A Parallel Manipulator with Only Translational Degrees of Freedom(1997) Tsai, Lung-Wen; Stamper, Richard E.; ISRThis report presents a novel three degree of freedom parallel manipulator that employs only revolute joints and constrains the manipulator output to translational motion. Closed-form solutions are developed for both the inverse and forward kinematics. It is shown that the inverse kinematics problem has up to four real solutions, and the forward kinematics problem has up to 16 real solutions.Item Optimization of a Three DOF Translational Platform for Well- Conditioned Workspace(1997) Stamper, Richard E.; Tsai, Lung-Wen; Walsh, Gregory C.; ISRTwo optimization studies on the design of a three degree of freedom translational parallel platform are conducted and the results are compared. The objective function of the first study maximizes total volume of the manipulator workspace without regard to the quality of the workspace. The second study optimizes the total volume of well conditioned workspace by maximizing a global condition index. The global condition index is a function of the condition number of the Jacobian matrix, providing a means of measuring the amplification error between the actuators and the end effector. Both objective functions involve an integration over the workspace of the manipulator. This integral is approximated using the Monte Carlo method.Item Design and Optimization of Planar Leg Mechanisms Featuring Symmetrical Foot-Point Paths(1996) Shieh, W-B.; Tsai, L-W.; ISRDesign and optimization of planar leg mechanisms featuring symmetrical foot-point paths are presented in this study. These leg mechanisms are designed in such a way that a corresponding walking machine has the flexibility required for walking on a rough terrain, while it can achieve fast locomotion, is easy to control, and requires minimal actuation for walking on a flat ground. In addition, such leg mechanisms are compact in size with respect to a specified horizontal stride.Based on a set of functional requirements, the concept generation of a set of leg mechanisms is accomplished via a systematic methodology. By temporarily excluding the degree-of-freedom (DOF) associated with the up-and-down motion of the leg, and based on a set of evaluation criteria, six admissible one-DOF planar four-, six-, and eight-bar leg mechanisms are found to have the desirable features to be used as a leg mechanism.
It is argued that a symmetrical foot-point path can be advantageous in reducing the maximum driving torque and making the motion control of the leg easier. While the four- and eight-bar compound mechanisms have been studied, a new class of six-bar linkages with an embedded (skew-) pantograph featuring a symmetrical foot-point path is introduced. Construction and design limitations for six-bar mechanisms are explored. The guidelines to prevent double point(s) are derived and the conditions to select between the propelling and non-propelling portions of the path are established.
For the dimensional synthesis, the admissible mechanisms with and without an adjustable pivot are investigated. For those mechanisms with an adjustable pivot, one DOF is used for normal walking to provide an ovoid path which emulated that of humans, while the other (the motion of the adjustable pivot) is used only when necessary to walk over obstacles. For those mechanisms without an adjustable pivot, the sole DOF provides a large D- shaped path, with which the leg mechanisms are capable of performing the up-and-down as well as the back-and-forth motions, To exploit these to the fullest, a multi-objective optimization-based design problem formulation is developed to minimize the following three design objectives: (i) peak crank torque, (ii) maximum actuating force, and (iii) leg size. Results from the optimization model show that an eight-bar compound mechanism with an adjustable pivot and a six-bar mechanism without an adjustable pivot are the two best leg designs among those studied here.
Finally, further reduction of the actuating force and crank torque is successfully demonstrated by placing tension spring elements onto an already optimized eight-bar leg mechanism.