Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control

LISP based simulation generators for modeling complex space processes

The development of a simulation assistant for modeling discrete event processes is presented. Included are an overview of the system, a description of the simulation generators, and a sample process generated using the simulation assistant

Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.Comment: 22 pages; 8 figure

Correlated Topological Insulators and the Fractional Magnetoelectric Effect

Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk theta term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional theta/pi. We show that fractional theta/pi is only possible in a gapped time reversal invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically non-trivial spaces. We illustrate this result with a concrete example of a time reversal symmetric topological insulator of correlated bosons with theta = pi/4. Extensions to electronic fractional topological insulators are briefly described.Comment: 4 pages + ref

Gapless Fermions and Quantum Order

Using 2D quantum spin-1/2 model as a concrete example, we studied the relation between gapless fermionic excitations (spinons) and quantum orders in some spin liquid states. Using winding number, we find the projective symmetry group that characterizes the quantum order directly determines the pattern of Fermi points in the Brillouin zone. Thus quantum orders provide an origin for gapless fermionic excitations.Comment: 23 pages. LaTeX. Homepage http://dao.mit.edu/~we