A Discrete Event Controller Using Petri Nets Applied To Assembly

Abstract

paper takes a new approach to robotic assembly, treating assembly as a discrete event system. A discrete event in assembly is defined as a change in contact state reflecting a change in a ge- ometric constraint. The discrete event modelling is ac~complished using Petri nets. The problems of task-level planning .and syn- thesis are addressed. Using the Petri net modelling, a discrete event controller (DEC) is developed. The DEC is a task-level controller that directs the assembly process to the desired end state. The DEC outputs both a desired velocity and it desired force command. The desired velocity commands insure consis- tency with geometric constraints while simultaneouslly directing the system toward the next desired discrete state. The desired force commands attempt to maintain the current state of contact. Task-level planning is accomplished using dynamic programming to deterimine the optimal sequence of discrete states for success- ful assembly. This desired sequence of discrete states is then used as a reference input to the DEC. 1 Iintroduction In discrete automation, assembly is one of the most error-prone, unreliablle processes. There is an increasing need for efficient methods of increased robustness and reliability in :the face of tolerancing errors and uncertainties in the workpieces and the environment. The control of assembly, including task level tra- jectories and on-line task level control, is a key component to improving the success of robotic assembly. The goal of this paper is to present a new approach to the control of robotic assembly tasks, treating assembly as a discrete event dynamic system. The abstraction to discrete event modelling highlights the necessary transitions for successful assembly. Additionally, the abstraction allows for planning on a task level rather than the cumbersome process of exact trajectory planning. Various methods have been proposed for the control of assem- bly processes. (Whitney, 19821 derives quasi-static con.dit,ions for a successful insertion operations. (Mason, 19821 (Raibert and Craig, 19811 describe a hybrid position/force control for various tasks. Other work has included using force feedback as a source of task preformance information (Hannaford, 19871. However, unlike most force-feedback applications, the state of contact changes during an assembly process. These discrete changes in state should be the focal point of the control procedure In order t,o incorporate the state changes, we will model assembly as a discrete event dynamic system. The discrete state vector will be the discrete states of contact in the assembhly process. The discrete events (occurring at discrete instances in time) are the since they indicate significant changes in the system dynamics. changes in contact state. Typically, discrete event dynamic sys- tem models arise from certain aspects of manufacturing systems and data network protocols. In contrast to these applications, this paper presents the discrete event modelling and control of robotic assembly. The difficulty of modelling and designing discrete event control systems has long been recognized in the literature. Moreover, there is apparently no unifying theory for the control of discrete event systems. Numerous methods have been proposed for the modelling and analysis of discrete event systems, each having different characteristics. Some of these include formal languages (Ramadge, 19891, finite state machines (Tadmor and Maimon, 19891, and Petri nets (Peterson, 19811. The goal of this paper is to present a new approach to robotic assembly, treating assembly as a discrete event dynamic system. The discrete event modelling is accomplished using Petri nets. The abstraction of assembly to Petri net modelling highlights the key transitions necessary for successful insertion. Additionally, the abstraction allows for planning on a task level rather than the cumbersome process of exact trajectory planning. Using the Petri net modelling, a discrete event controller (DEC) is developed. The DEC is a task-level controller that directs the assembly process to the desired end state. Two condi- tions are derived that perform this function. First, a closed form solution is given for the desired velocity commands. Desired ve- locity commands insure consistency with geometric constraints while simultaneously directing the system toward the next de- sired discrete state. Second, an equation is derived the specifies the desired force commands, The desired force commands are the forces that attempt to maintain the current state of contact. Lastly, an optimal sequence of discrete events (changes of con- tact) leading to successful insertion is determined using dynamic programming, thus completing the specificaiions for the DEC.