Fig. 1 Contact states Fig. 2 Model-based approach to monitoring of process state

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1 A Model-Based Approach to the Interpretation of Force and Position Sensor Signals for the Process Monitoring of Assembly Operations Shinichi HIRAI*, Haruhiko ASADA** and Hidekatsu TOKUMARU* A model-based approach to the monitoring of assembly processes is presented. In assembly operations, efficient control strategies cannot be generated by single control laws because the task condition varies in the process. Robot manipulators must monitor the process state in order to modify task strategies depending on the state. In this paper, we develop a new method of generating procedures that identify the state of assembly processes. The procedure interprets displacement and force information acquired in the process in order to identify the process state. In particular, the system is capable of monitoring the contact state; at which surface or edge the assembly parts are contacting to each other. We first analyze kinematic and static behavior of assembly parts at each contact state by applying the theory of polyhedral convex cones. The theory enables us to treat constraints by mechanical contact in a systematic manner. Identification procedures that discriminate contact states are formulated with use of the polyhedral convex cones. We then develop a new method of generating the procedures automatically based on geometric models of assembly parts. To reduce real-time computations, the procedures are simplified to a minimum set by using reduction rules of polyhedral convex cones. Key Words: robot manipulator, manipulation, assembly process, signal interpretation, polyhedral **Center for Information-Driven Mechanical Systems, M.I.T., Cambridge, Massachusetts, U.S.A. *Faculty of Engineering, Kyoto University, Kyoto (Received June 21, 1989) (Revised October 2, 1989)

2 Fig. 1 Contact states Fig. 2 Model-based approach to monitoring of process state

3 Fig. 3 Polyhedral convex cone k X= c~ui ci>o, i-1,2,...~ (4) i=1 def X*={UyxEX,xTYGO} (6) N A(q) = U An(q) (8) n=1 Table 1 Procedure to identify contact state

4 S1= U F() geri =span {f S, fe} S(q)= s- dq drr~a(q) (ll) Si span {fi, f2, fl} N =F(ql) + F(q2) -F... + F(qL) S(q)= u S() (12) n=1 def ~~ ~~' EAn(q) Sn(q) = s=.p AEF() (13) N Si = U U Sn(q) n=1 ger2 U Sn~q) (15) geri Si= U S(q) (14) geri def L S i = S(Q)(16) l=1 N si = U S7 (17) n=1 Fig. 4 Estimation of observable signal sets

5 Fig. 5. Reduction of polyhedral convex cones Fig. 6 Reduction of unions of polyhedral convex cones

6 Fig. 7 Compact discriminant function

7 Table 2 Simplified identification procedure def X(S1, Sj ; k)- span {am(m ~ k), bn} (34) de{ P(S;, S)= face {ak 1akX(Sz, S; ; k)} (36) DS(NI, N;) = n D(S;, Sk) (47) NkETI,k~j N si = U Si n=1 L S; = U S; (37) l=1 L SE P(Si, S;) (39) l=1 def N L D(SI, S,) = U n P(S7, S;) (42) n=1 l=1

8 Table 3 Results of computing discriminant functions Fig. 8 Simple example of measured force 1) D.E. Whitney: Historical Perspective and State of the Art in Robot Force Control, Int. J. Robotics Research, 6-1, 3/14 (1987) 2) M.T. Mason: Compliant Motion, M. Brady, et al., eds., Robot Motion, 305/322, Cambridge, MIT Press (1982) 3) D.E. Whitney: Quasi-Static Assembly of Compliantly Supported Rigid Parts, ASME J. Dynamic Syst., Meas., Contr., 104, 65/77 (1982) 4) J. Rasmussen: Skills, Rules, and Knowledge; Signals, Signs, and Symbols, and Other Distinctions in Human Performance Models, IEEE Trans. Systems, Man, and, Cybernetics, SMC-13-3, 257/266 (1983) 5) T. Lozano-Perez, M.T. Mason and R.H. Taylor: Automatic Synthesis of Fine-Motion Strategies for Robots, Int. J. Robotics Research, 3-1, 3/24 (1984) 11) A.J. Goldman and A.W. Tucker: Polyhedral Con- Cones, H.W. Kuhn and A.W. Tucker eds., vex Linear Inequalities and Related Systems, Annals of Math. Studies, 38, 19/39, Princeton (1956)

MmUm+FopX m Mm+Mop F-Mm(Fop-Mopum)M m+mop MSuS+FX S M S+MOb Fs-Ms(Mobus-Fex)M s+mob Fig. 1 Particle model of single degree of freedom master/ slave sy

MmUm+FopX m Mm+Mop F-Mm(Fop-Mopum)M m+mop MSuS+FX S M S+MOb Fs-Ms(Mobus-Fex)M s+mob Fig. 1 Particle model of single degree of freedom master/ slave sy Analysis and Improvement of Digital Control Stability for Master-Slave Manipulator System Koichi YOSHIDA* and Tetsuro YABUTA* Some bilateral controls of master-slave system have been designed, which can