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Control Problems in Robotics and Automation - B. Siciliano and K.P. Valavanis (Eds) Part 10

Tham khảo tài liệu 'control problems in robotics and automation - b. siciliano and k.p. valavanis (eds) part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 212 B.J. McCarragher Tk ip x t 2.9 Note that Eq. 2.9 does not imply that Tk changes continuously as x t changes. The state space of the plant is partitioned into contiguous regions. The function Ip generates a new plant event only when the state first enters one of these regions. The function Ip is usually well defined. However the state variable x t needs to be estimated according to 2.4 . Thus we have an estimator equation for the determination of the discrete plant events. Tk Ip x t 2.10 Note that f of Eq. 2.4 does not need to be close to the actual function f provided that Tk is a good estimate of Tk. 2.2 An Assembly Example It is important to note that the DES modelling of assembly is motivated by the key discrete event features of the process itself. The first key element is that for polygonal models of the workpiece and the environment the states of contact or constraints between the two parts are discrete. In modelling the manipulation process as a DES we define the state of contact to be the discrete state vector. The second key element is that the states of contact or constraints change at discrete and often unknown instances. It is an abrupt change where the dynamics change instantly. Moreover due to the uncertainty of location and speed the instant when the transition occurs is often unknown. A transition that results in a change of state either a loss of contact or a gain of contact is defined as a discrete event. The discrete events are key because at these points the geometric constraints on the workpiece dynamics change requiring a change in both the trajectory and the controller. DES modelling makes transitions one of the central control features of the model. Three dimensional polygonal objects can be fully described using three components surfaces edges and vertices as shown in Fig. 2.2. Each of these components is labeled surfaces with upper case letters edges with numbers and vertices with lower case letters. The labeling is done for both the .