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Dynamical Resolution of Redundancy for Robot Manipulators
Abstract: A large class of work in the robot manipulator literature deals with the kinematical resolution of redundancy based on the pseudo-inverse of the manipulator Jacobian. In this paper an alternative dynamical approach to redundancy resolution is devel¬oped which utilizes the mapping between the actuator torques and the acceleration of the end-effector, at a given dynamic state of the manipulator. The potential advantages of the approach are discussed and an example of a planar 3R manipulator following a circular end-effector trajectory is used to illustrate the proposed approach as well as to compare it with the more well-known approach based on the pseudo-inverse.
Abstract: To plan safe, reliable walker motions, it is important to assess the stability of a walker. In this article, two basic modes of walker stability are defined and .developed: stance stability and walker stability. For slowly moving, statically stable walkers, it is convenient to use the magnitude of the amount of the work required to destabilize a walker as a measure of the stability of that walker. Furthermore, as shown in this article, the com¬pliance of the walker and/or terrain can significantly affect the work necessary to destabilize the walker. Consideration of compliance and the two modes of walker stability leads to the definition and development of .four energy-based stability mea¬sures: the rigid stance stability measure, the compliant stance stability measure, the rigid walker stability measure, and the compliant walker stability measure. (The rigid stance stability measure is identical to the energy stability margin reported in Messuri and Klein [1985).) Several examples are used to demonstrate the application and use of these stability measures in type selection. gait planning, and control of the walker. The outcome of the present work is a more complete approach to using stability measures to ensure reliable walker gait planning and control.
"Chaos" by Design in Mobile Robots
Abstract: A large class of tasks for mobile robots require the robot to cover an enclosed space that might contain several objects (obstacles). The usual approach to this problem is to design a sensor-intensive, computer-controlled robot that usually has a relatively simple kinematic form (type). The control of such a robot is difficult, expensive, and frequently unreliable. This paper demonstrates how the complexity in sensing and control can be circumvented by synthesizing a "chaotic" kinematic motion that, when appropriately embodied by a kinematic form, covers the space and easily deals with obstacles. The evolution of the "chaotic", sensorless, mechanical mobile robot from concept, through analysis, numerical simulation and form embodiment, to realization is described. The testing of the prototype clearly demonstrates how, for the present task, complex "chaotic" motions do considerably simplify the control of the robot. A computer controlled prototype capable of mimicking the behavior of its mechanical counterpart is also described.
The Definition, and Characterization of Acceleration Sets for Spatial Manipulators
Abstract: In this article. rhe approach developed by the authors for systematicallv studving rhe acceleration capabiliry and properties of rhe end effector of a planar manipulator is extended to the general. serial, spatial manipulator possessing three degrees of freedom. The acceleration of the end effector at a given configuration of the manipulator is a linearfunction of the actuator rorques and a (nonlinear) quadratic function of the joint velocities. By decomposing the functional relationships benveen the inputs (actuator toques and joint velocities) and the output (acceleration of the end effector) into nvo fundamental mappings-~ linear mapping benveen the actuator toques and the acceleration space of the end effector and a quadratic (nonlinear) mapping benveen the joint velocities and the acceleration space of the end effector-and by deriving the properties of these two mappings, it is possible to determine the properties of all acceleration sets that are the images of the appropriate input sers under rhe two fundamental mappings. A central feature of rhis article is the determination of the properties of the qundraric mapping, which then makes ir possible to obtain analytic expressions for most acceleration properties of interest. We show rhar a fundamental way of studving these quadratic mappings is in t e r n of the mapping of (input) line congruences into (output) line congruences. The article concludes with the application of the analytical results to the computation of the various acceleration properties of an actual spatial manipulator:
The Development of Virtual Concurrent Engineering and its Application to Design for Producibility
Abstract: It is well known that so-called concurrent engineering is a desirable alternative to the largely sequential methods which tend to dominate most product-development methods. However, the proper implementation of a concurrent engineering method is still relatively rare, due in part to unreliable guesswork, poor knowledge structuring and utilization, and the lack of integrated, global decision making. Thus, to remedy the current shortcomings, we propose an initial, straightforward theory for product development, which is based on properly-defined concurrent engineering principles. After establishing the overall goal for product development, we formulate an objective that a product-development method must meet. This objective then leads to three fundamental criteria, which basically govern where concurrent engineering must be implemented, how consistent communication between different domains must be carried out, and how to structure and network the vast amount of expert knowledge in an effective, feasible manner. The product-development objective and the three criteria guide the establishment of a feasible computer-based implementation of concurrent engineering, called virtual concurrent engineering (VCE). The effectiveness of VCE is demonstrated by applying it to refine a method, called design for producibility (DFP), that integrates the design and manufacturing stages of product development. Two elements that are crucial to the success of DFP are the producibility cost function network, and the software package AUTOPROD (Automated Producibility). The refined DFP method has been successfully applied to concurrent product and process design in three domains: stamping, forming, and machining.
Abstract: In this paper, we establish the Design for Producibility Design Development Meth¬odology for stamped products which integrates both the design and manufacture of the stamped product. The general concept of considering manufacturing tech¬niques at the initial design stages, often termed Design for Manufacturability, is certainly not novel. However, the proper implementation of this concept is not so widely understood. Our proposed method permits the product designer to control both product functionality ( which he has incorporated into an initial design) and subsequent manufacturing costs through an iterative re-design process. The key step in this method is the mapping scheme from the final product design domain to the manufacturing domain; this scheme captures the cause-effect relations between de-sign ( and thus functional) specifications and manufacturing requirements and costs. We also describe the implementation of the design methodology in a knowledge-based computer environment called the Producibility Evaluation Package (P.E.P. ) that, as a result of the design methodology, also automatically generates much of the process plan.
An Optimization-Based Framework for Simultaneous Plant-Controller Redesign
Abstract: In this paper we develop a framework for the redesign of computer-controlled, closed-loop, mechanical systems for improved dynamic performance. A central notion which underlies the redesign framework is that, in order to achieve the best possible performance from a constrained closed-loop system, the plant and controller should be designed simultaneously. The framework is presented as the formulation and solution of a progression of optimization problems which establish the limits of performance of the dynamic system under various conditions of interest, thereby enabling the engineer to systematically establish the various redesign possibilities. Using a second order linear dynamic system and a nonlinear controller as an example, we demonstrate the application of the framework and substantiate the idea that in order to achieve the best possible performance from a constrained closed-loop system, the plant and controller should be redesigned simultaneously. We then show how the redesign framework can be used to select the best control strategy for a robotic manipulator from a dynamic performance standpoint. Finally, in order to demonstrate that the redesign framework yields solutions which the engineer can implement with confidence, we present the experimental verification of the numerical solution of a manipulator redesign optimization problem.
Reactor-scale models for rf diode sputtering of metal thin films
Abstract: This article describes the development of an integrated physical model for the rf diode sputtering of metal thin films. The model consists of: (1) a computational fluid dynamic finite element model for the velocity and pressure distribution of the working gas Ar flow in the chamber, (2) a steady-state plasma model for the flux and energy of Ar ions striking the target and the substrate, (3) a molecular dynamics sputtering model for the energy distribution, angle distribution, and yield of the sputtered atoms (Cu) from the target, and (4) a direct simulation Monte Carlo (DSMC) model for the transport of Cu atoms through the low-pressure argon gas to the deposition substrate. The individual models for gas flow, plasma discharge, Cu sputtering, and DSMC-based Cu atom transport are then integrated to create a detailed, steady-state, input–output model capable of predicting thin-film deposition rate and uniformity as a function of the process input variables: power, pressure, gas temperature, and electrode spacing. Deposition rate and uniformity in turn define the characteristics of thin films exploited in applications, for example, the saturation magnetic field for a giant magnetoresistive multilayer. This article also describes the development of an approximate input–output model whose CPU time is several orders-of-magnitude faster than that of the detailed model. Both models were refined and validated against experimental data obtained from rf diode sputtering experiments.
The Fast Resource Evaluation Grid
Abstract: The success of product design, development and delivery in a technological enterprise crucially depends on the optimal integration of enterprise resources. The Fast Resource Evaluation Grid permits the comprehension of the strengths and importances of these resources as a rational basis for the allocation of effort to close resource gaps.
A Value-Centered Model of Product Design, Development and Delivery
Abstract: A value-centered model of product design, development and delivery (PD3) can enable the proper assessment and allocation of resources in order to maximize the value of the product. To develop such a model, a two-dimensional grid that unifies the function and process elements of PD3 is described. The grid leads to a rational definition of enterprise resources. Then, useful attributes –strength, importance, cost - of a resource are defined, and used to develop the notion of resource value. The determination of the resource attributes, including value, is illustrated by an elementary example.
Distributed Nonlinear Model Predictive Control for Dynamic Supply Chain Management (presented at the International Workshop on Assessment and Future Directions of Model Predictive Control, Freudenstadt-Lauterbad, Germany, August 26-30, 2005.)
Abstract: The purpose of this paper is to demonstrate the application of a new theory developed for distributed nonlinear model predictive control (NMPC) to a promising and exciting future domain for NMPC – that of dynamic management of supply chain networks. Recent work by the first author provides a distributed implementation of NMPC for application in large scale systems comprised of cooperative dynamic subsystems [1, 2]. The generic control objective is for the subsystems to cooperatively meet mutual objectives, e.g., a set of unmanned vehicles are required to realize a predefined formation while avoiding collisions. The nonlinear subsystems can be coupled through performance objectives and state constraints [1], as well as through their dynamics [2]. By the implementation, each subsystem optimizes locally for its own policy, and communicates the most recent policy to those subsystems to which it is coupled. Stabilization is guaranteed for arbitrary interconnection topologies, provided each subsystem not deviate too far from the previous policy (consistent with traditional control deviation penalties), and that the updates happen sufficiently fast. Simulations have demonstrated performance comparable to a centralized implementation [1]. A contribution of this paper will be to demonstrate the relevance and efficacy of the distributed NMPC approach in the venue of supply chain management. A supply chain can be defined as the interconnection (coupling) and evolution (dynamics) of a demand network. Example subsystems include raw materials, distributors of the raw materials, manufacturers, distributors of the manufactured products, retailers, and customers. Key elements to an efficient supply chain (performance) is accurate pinpointing of process flows and timing of supply needs at each subsystem, both of which enable subsystems to request items as they are needed, thereby reducing safety stock levels to free space and capital. Recently, Braun et al. [3] demonstrated the effectiveness of MPC in realizing these elements for management of a linear dynamic semiconductor chain, citing benefits over traditional approaches and robustness to model and demand forecast uncertainties. In this context, the chain is isolated from competition, and so a cooperative approach is appropriate. It turns out that Braun et al. employ a heuristic version of the distributed implementation in [1], with no theoretical justification, by sharing policies with down stream echelons in an acyclic single chain topology. Since there are no cycles, implemented policies can be shared in real-time (ignoring communication delay). When uncertainty is present, control deviation penalties are critical to yield stability, a fact consistent with the theory in [1]. Limitations of their approach are that it requires acyclic topologies and sequential updates from up to down stream, while realistic supply chains contain cycles and do not in general operate sequentially. The second main contribution of this paper will be to demonstrate the scalability, stability and robustness properties of our distributed implementation in a supply chain simulation example, permitting nonsequential updates and cycles in the interconnection network topology. We will also briefly examine the implications of incorporating game theoretic approaches so that the local management mechanisms can simultaneously handle cooperative and competitive objectives, as this occurs in more realistic settings.