A Discrete Event
Previous: Introduction
Hybrid systems, in which digital and analogue devices and sensors interact over time, is attracting the attention of researchers. Representation of states and the physical system condition includes continuous and discrete numerics, in addition to symbols and logical parameters. Most of the current vision and robotics problems, as well as problems in other domains, fall within the description of hybrid systems. There as many issues that need to be resolved, among them, definitions for observability, stability and stabilizability, controllability in general, uncertainty of state transitions and identification of the system. The general observation problem falls within the hybrid system domain, as there is a need to report, observe and control distinct and discrete system states. There is also a need for recognizing continuous 2-D and 3-D evolution of parameters. Also, there should be a symbolic description of the current state of the system, especially in the manipulation domain.
The underlying mathematical representation of complex computer-controlled systems is still insufficient to create a set of models which accurately captures the dynamics of the systems over the entire range of system operation. We remain in a situation where we must tradeoff the accuracy of our models with the manageability of the models. Closed-form solutions of mathematical models are almost exclusively limited to linear system models. Computer simulation of nonlinear and discrete-event models provide a means for off-line design of control systems. Guarantees of system performance are limited to those regions where the robustness conditions apply. These conditions may not apply during startup and shutdown or during periods of anomalous operation.
Recently, attempts have been made to model low and high-level system changes in automated and semi-automatic systems as discrete event dynamic systems (DEDS). Several attempts to improve the modeling capabilities are focused on mapping the continuous world into a discrete one. However, repeated results are available which indicate that large interactive systems evolve into states where minor events can lead to a catastrophe. Discrete event systems (DES) have been used in many domains to model and control system state changes within a process. Some of the domains include: Manufacturing, Robotics, Autonomous Agent Modeling, Control Theory, Assembly and Planning, Concurrency Control, Distributed Systems, Hierarchical Control, Highway Traffic Control, Autonomous Observation Under Uncertainty, Operating Systems, Communication Protocols, Real-Time Systems, Scheduling, and Simulation.
A number of tools and modeling techniques are being used to model and control discrete event systems in the above domains. Some of the modeling strategies include: Timed, untimed and stochastic Petri Nets and State Automata, Markovian, Stochastic, and Perturbation models, State Machines, Hierarchical State Machines, Hybrid Systems Modeling, Probabilistic Modeling (Uncertainty Recovery and Representation), Queueing Theory, and Recursive Functions.
We do not intend to give a solution for the problem of defining, monitoring or controlling such hybrid systems in general. What we intend to present in this work is a framework that works for the class of hybrid systems encountered within the robotic observation paradigm. The representation we advocate allows for the symbolic and numeric, continuous and discrete aspects of the observation task. We conjecture that the framework could be explored further as a possible basis for providing solutions for general hybrid systems representation and analysis problems.
We suggest the use of a representation of discrete event dynamic systems, which is augmented by the use of a concrete definition for the events that causes state transitions, within the observation domain. We also use some uncertainty modeling to achieve robustness and smoothness in asserting state and continuous event variations over time.
Dynamic systems are sometimes modeled by finite state automata with partially observable events together with a mechanism for enabling and disabling a subset of state transitions [11,13,14], the reader is referred to those references for more information about this class of DEDS representation. We propose that such a DEDS skeleton is a suitable high-level framework for many vision and robotics tasks, in particular, we use the DEDS model as a high-level structuring technique for a system to observe a robot hand manipulating an object.
A Discrete Event
Previous: Introduction