Parts entropy methods for robotic assembly system design

Carncgie-Mellon University, Schenley Park, Pittsburgh, Pcnnsylvania 15213 Abstract Asscmhly tasks require thc fccding, acquisition. oricntation, and lnating of parts subject to contact forccs. Positional entropy providcs s n cfficicnt tool for dcscribing an asscmhly task and its ysteln impic~ncntation i n terms of the uncertainty in position and oricntation of parts as the assembly scqucncc progresses. A parts cntwpy mcasurc H ( X ) may he calculatcil from thc prOhahility distribution o f parts positions and oricn:ati~~s at a gibcn assembly stcp defined ovcr an cnsemblc of rcpcated asscmhly tasks. '[he part cntiopy may bc reduced mcchanicnlly by containcrization, flxturing, manipulation, or product rcdcsign. l'hc part entropy may also be rcduccd using scnsors (typically vision or tactile) by rcducing the col?ditional entropy IH (X/Y) duc to the scnsory mcasurcment. The information obtained %out part position may bc defined in tcrms of the liltitual information I(X;Y). I n tllcsc terms, thc goal of an asscmbly systcm is to reduce thc joint entropy among parts by mating them in stable configurations. 'I'hc positional entropy conccpt providcs a unifying tool for asscssing thc rcladvc cffcctivencss of systen~s designs which incorporate both mcchanical and scnsar-bascd :cchniqucs. The approach may hlso providc a useful ingrcciicnt for quantitative asscssmcnc of product designs. cornplcxity of asscmbly proccdurcs, and flexibility of assembly systems. An cxamplc of the usc of positional entropy for analysis of an electronic assembly task is given. Q . .