John Baillieul

Control and Communication Challenges in Networked Real-Time Systems

A current survey of the emerging field of networked control systems is provided. The aim is to introduce the fundamental issues involved in designing successful networked control systems, to provide a snapshot assessment of the current state of research in the field, to suggest useful future research directions, and to provide a broad perspective on recent fundamental results. Reflecting the goals of the Special Issue itself, this paper surveys relevant work from the areas of systems and control, signal processing, detection and estimation, data fusion, and distributed systems. We discuss appropriate network architectures, topics such as coding for robustly stable control in the presence of time-varying channel capacity, channels with fixed versus adaptively variable data width, issues in data rate problems in nonlinear feedback problems, and problems in routing for stability and performance. In surveying current research on networked control systems, we find that recent theoretical advances and target applications are intimately intertwined. The common goal of papers in the Special Issue which follows is to describe key aspects of this relationship. We also aim to provide a bridge between networked control systems and closely related contemporary work dealing with sensor networks and wireless communication protocols

Kinematic programming alternatives for redundant manipulators

In the growing literature on redundant manipulator control, a number of techniques have been proposed for solving the inverse kinemetics problem. Some of these techniques are surveyed with a discussion of strengths and weaknesses of each. A new approach, called the extended Jacobian technique, is also presented. It is argued that because this technique may be expected to lift closed end effector paths to closed joint angle paths, it provides a promising approach for the control of kinematically redundant industrial manipulators. It is further shown that this technique may be implemented as a suitably parameterized generalized inverse method.

Adaptive control of nonlinear systems with a triangular structure

In this paper, we introduce two distinct types of nonlinear dynamical systems, /spl Tscr//sub 1/ and /spl Tscr//sub 2/, both of which possess a triangular structure. It is shown that all systems belonging to /spl Tscr//sub 1/ can be made stable and that if they belong to a subclass /spl Tscr//sub 1s/, the stability holds globally. A precise characterization of the general class of nonlinear systems transformable to /spl Tscr//sub 1/ is carried out. The second class, /spl Tscr//sub 2/, corresponds to a set of second-order nonlinear differential equations and is motivated by problems that occur in mechanical systems. It is shown that global tracking can be achieved for all systems in /spl Tscr//sub 2/. A constructive approach is used in all cases to develop the adaptive controller, and both stabilization and tracking are shown to be realizable. Simple examples are given to illustrate the different classes of nonlinear systems as well as the idea behind the approach used to stabilize them. >

Avoiding obstacles and resolving kinematic redundancy

While obstacles in a robot workspace can effectively reduce the number of degrees of freedom, there need not be a corresponding loss of functionality for kinematically redundant mechanisms. In this paper, disk-like obstacles for a planar three-bar mechanism are classified. The extended Jacobian technique is used to implement an obstacle avoidance technique based on optimizing a distance criterion. The feasibility of applying multiple constraints or optimality criteria for resolving redundancy is investigated.

Programming and control of kinematically redundant manipulators

Because kinematically redundant robot manipulators have extra degrees of freedom with which to move and orient end effectors in the workspace, they offer a number of advantages over nonredundant designs. In this paper we show how extra degrees of freedom may be used to mitigate the problem of kinematically singular configurations. Programming and control techniques for resolution of redundancy are presented.

Information patterns and Hedging Brockett's theorem in controlling vehicle formations

Efforts to apply computer vision and various optical and acoustic proximity sensors for distributed/ coordinated motion control of a small group of autonomous vehicles has led us to consider a number of natural feedback control laws which utilize realtime measurements of relative distances between the vehicles. Unfortunately, none of the feedback laws satisfies Brocketts necessary conditions for asymptotic stabilization. They do appear to provide a basis for practical solutions to a number of interesting vehicle control problems, however. Part of the rationale for proposing feedback laws which are not asymptotically stabilizing is that in a number of cases of practical interest, one may show that the set of initial conditions which are not driven to the prescribed rest point is either small (in some sense) or uninteresting (in the problem context) or both. In some cases, one can also show that by choosing feedback gains in terms of the problems initial conditions-using say a table look-up-it is possible to steer from any given initial state into an arbitrarily small neighborhood of the desired goal state. The aim of the research here is to develop a large catalogue of simple controlled motions which in appropriate sequential combinations permit autonomous nonholonomic vehicles to assemble themselves and execute coordinated motions in highly structured formations.

Resolution of kinematic redundancy using optimization techniques

Recent work has shown that while one can resolve kinematic redundancy by the strategy of using the additional degrees of freedom to instantaneously minimize a cost criterion, one cannot do this in a singularity-free way. This motivates the research reported below regarding path planning based on optimization of integral cost criteria. For a wide variety of such criteria, optimal paths are shown to satisfy a system of differential equations. The analysis exploits ideas from the classical calculus of variations, and it is therefore not surprising that multiplicities of extremal solutions exist. Numerical examples are given where extremal solutions fall into distinct homotopy classes, not all of which are optimal.

Feedback coding for information-based control: operating near the data-rate limit

The paper begins with a restatement and proof of a tight bound on the data capacity a feedback channel must provide in order to stabilize a tight half-plane pole. This sets the stage for a treatment of some of the issues arising in the source coding of signals between controllers and plants in systems where feedback loops are closed using bandwidth limited communication links. In particular, we are interested in the qualitative dynamics of LTI feedback systems operating near the data-rate limit.

Chaotic motion in nonlinear feedback systems

New criteria are found which imply the existence of chaos in R^n . These differ significantly from criteria previously reported in the mathematics literature, and in fact our methods apply to a class of systems which do not satisfy the hypotheses of the usual theorems on chaos in R^n . The results are stated in such a way as to preserve the flavor of many well-known frequency-domain stability techniques. The results provide easily verifiable criteria for the existence of chaos in systems which are of dimension greater than one.

Stabilizability and stabilization of a rotating body-beam system with torque control

The stabilizability and stabilization of a rotating body-beam system with torque control are discussed. This system has a linear inertial manifold. An operator-theoretic argument is used to provide an alternative proof of this fact. By taking into account the effect of damping (structural or viscous), the stability result of J. Baillieul and M. Levi (1987) is proved using the LaSalle principle (1968). It is shown that there exists a critical angular velocity for the use of torque control to stabilize the system in the neutral configuration with constant angular velocity. For any constant angular velocity smaller than the critical one a feedback torque control law is given which exponentially strongly stabilizes the system in the neutral configuration with the system rotating at the given constant angular velocity. >