Ian A. Gravagne

Manipulability, force, and compliance analysis for planar continuum manipulators

Continuum manipulators, inspired by the natural capabilities of elephant trunks and octopus tentacles, may find niche applications in areas like human-robot interaction, multiarm manipulation, and unknown environment exploration. However, their true capabilities will remain largely inaccessible without proper analytical tools to evaluate their unique properties. Ellipsoids have long served as one of the foremost analytical tools available to the robotics researcher, and the purpose of this paper is to first formulate, and then to examine, three types of ellipsoids for continuum robots: manipulability, force, and compliance.

Nonregressivity in switched linear circuits and mechanical systems

We analyze several examples of switched linear circuits and a switched spring-mass system to illustrate the physical manifestations of regressivity and nonregressivity for discrete and continuous time systems as well as hybrid discrete/continuous systems from a time scales perspective. These examples highlight the role that nonregressivity plays in modeling and applications, and they point out a fascinating dichotomy between purely continuous systems and discrete, continuous, or hybrid systems. We conclude with a physically realizable null space criterion for inducing nonregressivity.

Bandwidth reduction for controller area networks using adaptive sampling

This paper presents a method by which controllers operating on real-time networks such as the Controller Area Network (CAN) can reduce their bandwidth requirements in response to periods of high network traffic from sporadic sources. The method derives from advances in the theory of dynamic systems on time scales.

Goldfinger: a non-anthropomorphic, dextrous robot hand

In this paper, we describe the hardware and control architecture of a novel four-fingered dextrous robot hand. The benefits of the unusual arrangement of the fingers (which resembles that in raptors and other birds) in the hand are discussed. Kinematic models for the fingers and transmission system are presented. A simulation and real-time control environment has been developed for the hand, and is discussed in the paper. Experiments in dextrous and dynamic manipulation using the hand are also detailed.

Manipulability and force ellipsoids for continuum robot manipulators

Manipulability and force ellipsoids have long been a useful tool for analyzing the relative capabilities of robotic, manipulators to move in, or to exert forces in, certain directions. The purpose of this paper is to first formulate, and then to examine, the manipulability and force ellipsoids for continuum robots. Continuum robots have continuously flexible backbones; consequently, their infinite-dimensional kinematics present special challenges in the formulation and interpretation of ellipsoids.

A Unified Approach to High-Gain Adaptive Controllers

It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales.

How deterministic must a real-time controller be?

Real-time computing platforms are ubiquitous in the fields of automation, robotics and control. These are often based on a real-time operating system that offers a high level of determinism to support processes such as discrete-event and feedback control. Using methods derived the theory of dynamic systems on time scales, this paper discusses through modeling and simulation the effects of non-determinism. The papers conclusion supports the hypothesis that strict determinism is not always required to obtain adequate overall system performance.

Emergent Behaviors of Protector, Refugee, and Aggressor Swarms

Simple rules, when executed by individual agents in a large group, or swarm, can lead to complex behaviors that are often difficult or impossible to predict knowing only the rules. However, aggregate behavior is not always unpredictable-even for swarm models said to be beyond analysis. For the class of swarming algorithms examined herein, we analytically identify several possible emergent behaviors and their underlying causes: clustering, drifting, and explosion. They also analyze the likelihood of these behaviors emerging from randomly selected swarm configurations and present a few examples. The analytic results are illustrated via simulation

Algebraic and dynamic Lyapunov equations on time scales

We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov-based stability arguments. The goal is to generalize and extend these types of equations and subsequent analysis to dynamical systems on domains other than R or Z, called “time scales”, e.g. nonuniform discrete domains or domains consisting of a mixture of discrete and continuous components. In particular, we compare and contrast a generalization of the algebraic Lyapunov equation and the dynamic Lyapunov equation in this time scales setting.

Linear state feedback stabilisation on time scales

For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly exponentially stable with a prescribed rate. The methods here generalise and extend Gramian-based linear state feedback control to much more general time domains, e.g., nonuniform discrete or a combination of continuous and discrete time. In conclusion, we discuss an experimental implementation of this theory.