Kinematic reducibility of multiple model systems

This paper considers the relationship between second order multiple model systems and first order multiple model systems. Such a relationship is important to, among other things, studying path planning for mechanical control systems. This is largely due to the fact that the computational complexity of a path planning problem rapidly increases with the dimension of the state space, implying that being able to reduce a path planning problem from TQ to Q can be helpful. Not surprisingly, the necessary and sufficient condition for such a reduction is that each model constituting a multiple model control system be reducible. We present an extensive example in order to illustrate how these results can provide insight into the control of some specific physical systems

Smooth feedback control algorithms for distributed manipulators

This paper introduces a smooth control algorithm for controlling fully actuated distributed manipulation systems that operate by frictional contact. The control law scales linearly with the number of actuators and is simple to implement. Moreover, we prove that control law has desirable robustness properties in the presence of the nonsmooth mechanics inherent in distributed manipulation systems that rely upon frictional contact. This algorithm has been implemented on an experimental distributed manipulation test-bed, whose structure is briefly reviewed. The experimental results confirm the validity and performance of the algorithm

Global stability for distributed systems with changing contact states

Analyzes the global stability of distributed manipulation control schemes. The "programmable vector field" approach, which assumes that the system's control actions can be approximated by a continuous vector force field, is a commonly proposed scheme for distributed manipulation control. In practical implementations, the continuous control force field idealization must then be adapted to the specifics of the discrete physical actuator array. However, in Murphey and Burdick (2001) it was shown that when one takes into account the discreteness of actuator arrays and realistic models of the actuator/object contact mechanics, the controls designed by the continuous approximation approach can be unstable at the desired equilibrium configuration. We introduced a discontinuous feedback law that locally stabilizes the manipulated object at the equilibrium. However, the stability of this feedback law only holds in a neighborhood of the equilibrium. In this paper we show how to combine the programmable vector field approach and our local feedback stabilization law to achieve a globally stable distributed manipulation control system. Simulations illustrate the method

Nonsmooth controllability theory and an example

Extends results in local controllability analysis for multiple model driftless affine (MMDA) control systems. Such controllability results can be interpreted as non-smooth extensions of Chow's theorem, and use a set-valued Lie bracket. In particular, we formulate controllability in terms of generalized differential quotients. Additionally, we present an extensive example in order to illustrate how these results can provide insight into the control of some specific physical systems. Moreover, the paper indicates that a multiple model system consisting of individually controllable models is not necessarily controllable

On the stability and design of distributed manipulation control systems

Analyzes the stability of distributed manipulation control schemes. A commonly proposed method for designing a distributed actuator array control scheme assumes that the system's control action can be approximated by a continuous vector force field. The continuous control vector field idealization must then be adapted to the physical actuator array. However, we show that when one takes into account the discreteness of actuator arrays and realistic models of the actuator/object contact mechanics, the controls designed by the continuous approximation approach can be unstable. For this analysis we introduce and use a "power dissipation" method that captures the contact mechanics in a general but tractable way. We show that the quasi-static contact equations have the form of a switched hybrid system. We introduce a discontinuous feedback law that can produce stability which is robust with respect to variations in contact state

Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints

We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton-Jacobi equation as the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton-Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to non-degenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with non-closed two-forms. Accordingly, the Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac-Hamilton-Jacobi equation can be used to exactly integrate the equations of motion.Comment: 44 pages, 3 figure

Quantitative Characterization of the Filiform Mechanosensory Hair Array on the Cricket Cercus

Crickets and other orthopteran insects sense air currents with a pair of abdominal appendages resembling antennae, called cerci. Each cercus in the common house cricket Acheta domesticus is approximately 1 cm long, and is covered with 500 to 750 filiform mechanosensory hairs. The distribution of the hairs on the cerci, as well as the global patterns of their movement vectors, have been characterized semi-quantitatively in studies over the last 40 years, and have been shown to be very stereotypical across different animals in this species. Although the cercal sensory system has been the focus of many studies in the areas of neuroethology, development, biomechanics, sensory function and neural coding, there has not yet been a quantitative study of the functional morphology of the receptor array of this important model system.We present a quantitative characterization of the structural characteristics and functional morphology of the cercal filiform hair array. We demonstrate that the excitatory direction along each hair's movement plane can be identified by features of its socket that are visible at the light-microscopic level, and that the length of the hair associated with each socket can also be estimated accurately from a structural parameter of the socket. We characterize the length and directionality of all hairs on the basal half of a sample of three cerci, and present statistical analyses of the distributions.The inter-animal variation of several global organizational features is low, consistent with constraints imposed by functional effectiveness and/or developmental processes. Contrary to previous reports, however, we show that the filiform hairs are not re-identifiable in the strict sense