this paper, we first give a very brief overview of control engineering. The goal of control engineering is to improve, or in some cases ena- ble, the performance of a system by the addition of sensors, which measure various signals in the system and external command signals, control processors, which process the measu red signals to drive actuators, which affect the behav- ior of the system. A schematic diagram of a general control system is shown in Fig. 1. The use of the sensed response of the system (and not just the command signals) in the computation of the actuator signals is called feedback control, an old idea which has been developed and applied with great success in this century [1], [2]. Control engineering involves 1. Modeling or identification. The designer develops mathematical models of the relevant aspects of system to be controlled. This can be done using knowl- edge of the system (for example by applying Newton 's equations of motion to a mechanical system), and experimentally by observing responses of the Manuscript received November 30,1988; revised August 4,1989. This work was supported in part by the National Science Foundation (NSF) under ECS-85-52465, the Air Force Office of Scientific Research (AFOSR) under 89-0228, Boeing Electronics Company under LF0937, and Bell Communications Research, and the National Science and Engineering Research Council (Canada) 1967 Science and Engineering Scholarship. The authors arewith the Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305, USA. IEEE Log Number 8933936. system to various excitations, a procedure known as s)zstem identification [3]. In some cases, several models are developed, varying in complexity and accu racy. 2. Control configuration: selection and placement of sensors an...

This paper presents a set of methods by which a learning agent can learn a sequence of increasingly abstract and powerful interfaces to control a robot whose sensorimotor apparatus and environment are initially unknown. The result of the learning is a rich hierarchical model of the robot's world (its sensorimotor apparatus and environment). The learning methods rely on generic properties of the robot's world such as almost-everywhere smooth e ects of motor control signals on sensory features. At thelowest level of the hierarchy, the learning agent analyzes the e ects of its motor control signals in order to de ne a new set of control signals, one for each of the robot's degrees of freedom. It uses a generate-and-test approach to de ne sensory features that capture important aspects of the environment. It uses linear regression to learn models that characterize context-dependent e ects of the control signals on the learned features. It uses these models to de ne high-level control laws for nding and following paths de ned using constraints on the learned features. The agent abstracts these control laws, which interact with the continuous environment, to a nite set of actions that implement discrete state transitions. At this point, the agent has abstracted the robot's continuous world to a nite-state world and can use existing methods to learn its structure. The learning agent's methods are evaluated on several simulated robots with di erent sensorimotor systems and environments.

We present a general theory of topological maps whereby sensory input, topological and local metrical information are combined to define the topological maps explaining such information. Topological maps correspond to the minimal models of an axiomatic theory describing the relationships between the different sources of information explained by a map. We use a circumscriptive theory to specify the minimal models associated with this representation.

We present a physics-based system for the guided animation of articulated figures. Based on an efficient forward dynamics simulator, we introduce a robust feedback control scheme and a fast two-stage collision response algorithm. A user of our system provides kinematic trajectories for those degrees of freedom (DOFs) of the figure they want direct control over. The output motion is fully generated using forward dynamics. The specified motion trajectories are the input to a control system which computes the forces and torques that should be exerted to achieve the desired motion. The dynamic controllers, designed based on the Model Reference Adaptive Control paradigm, continuously self-adjust for optimal performance in trajectory following. Moreover, the user is given a handle on the type and speed of reaction of the figure 's controlled DOFs to sudden changes in their desired motion. The overall goal of our system is to provide a platform for generating and studying realistic, user cont...

Using the methods demonstrated in this paper, a robot with an unknown sensorimotor system can learn sets of features and behaviors adequate to explore a continuous environment and abstract it to a finitestate automaton. The structure of this automaton can then be learned from experience, and constitutes a cognitive map of the environment. A generate-andtest method is used to define a hierarchy of features defined on the raw sense vector culminating in a set of continuously differentiable local state variables. Control laws based on these local state variables are defined for robustly following paths that implement repeatable state transitions. These state transitions are the basis for a finite-state automaton, a discrete abstraction of the robot's continuous world. A variety of existing methods can learn the structure of the automaton defined by the resulting states and transitions. A simple example of the performance of our implemented system is presented. Introduction Imagine that y...

This paper advocates that cache coherence protocols use a bandwidth adaptive approach to adjust to varied system configurations (e.g., number of processors) and workload behaviors. We propose Bandwidth Adaptive Snooping Hybrid (BASH), a hybrid protocol that ranges from behaving like snooping (by broadcasting requests) when excess bandwidth is available to behaving like a directory protocol (by unicasting requests) when bandwidth is limited. BASH adapts dynamically by probabilistically deciding to broadcast or unicast on a per request basis using a local estimate of recent interconnection network utilization. Simulations of a microbenchmark and commercial and scientific workloads show that BASH robustly performs as well or better than the best of snooping and directory protocols as available bandwidth is varied. By mixing broadcasts and unicasts, BASH outperforms both snooping and directory protocols in the mid-range where a static choice of either is inefficient.

The use of physically-based techniques for computer animation can result in realistic object motion. The price paid for physically-based motion synthesis lies in increased computation and information re-quirements. We introduce a new approach to realistic motion spec-ification based on state-space controllers. A user specifies a motion by defining a goal in terms of a set of destination states. A state-space controller is then constructed, which provides an optimal-control solution that guides the object from an arbitrary starting con-figuration to a goal. Motions are optimized with respect to time and control energy. Because controllers are specified in terms of desti-nation states only, it is easy to reuse the same controller to produce different motions (from different starting states), or to create a com-plex sequence of motions by concatenating several controllers. An implementation of state-space controllers is presented, in which re-alistic motions can be produced in real time. Several examples will be considered.

We introduce a new class of dynamical systems called "linear complementarity systems." The time evolution of these systems consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector. The occurrence of events is governed by certain inequalities similar to those appearing in the Linear Complementarity Problem of mathematical programming. The framework we describe is suitable for certain situations in which both differential equations and inequalities play a role, for instance in mechanics, electrical networks, piecewise linear systems, and dynamic optimization. We present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions. 1 Introduction In many technical and economic applications one encounters systems of differential equations and inequalities. For a quick roundup of examples, one may think of the following: ...

Refinement is reviewed in a partial correctness framework, highlighting in particular the distinction between its use as a specification constructor at a high level, and its use as an implementation mechanism at a low level. Some of its shortcomings as specification constructor at high levels of abstraction are pointed out, and these are used to motivate the adoption of retrenchment for certain high level development steps. Basic properties of retrenchment are described, including a justification of the operation PO, simple examples, simulation properties, and compositionality for both the basic retrenchment notion and enriched versions. The issue of framing retrenchment in the wide variety of correctness notions for refinement calculi that exist in the literature is tackled, culminating in guidelines on how to `brew your own retrenchment theory'. Two short case studies are presented. One is a simple digital redesign control theory problem, the other is a radiotherapy dos...

The Spatial Semantic Hierarchy (SSH) is a set of distinct representations for large scale space, each with its own ontology and each abstracted from the levels below it. At the control level, the agent and its environment are modeled as continuous dynamical systems whose equilibrium points are abstracted to a discrete set of distinctive states. The control laws whose execution defines trajectories linking these states are abstracted to actions, giving a discrete causal graph representation for the state space. The causal graph of states and actions is in turn abstracted to a topological network of places and paths (i.e. the topological map). Local metrical models of places and paths can be built within the framework of the control, causal and topological levels while avoiding problems of global consistency. ...