On fine motion in mechanical assembly in presence of uncertainty.

A solution to the fine motion planning problem is essential to automated assembly using robots. This thesis develops a new framework for the fine motion planning problem. Contact and uncertainty are inherent to the fine motion problem. Contact formation, a formal representation for contact among polyhedral objects in introduced. It is shown that configuration space is partitioned by contact formations and that the configuration space can be represented by a finite connected graph. It is shown that the fine motion planning problem can be decomposed into planning problems at two levels. The first level plan consists of a sequence of contact formations and the second level plan consists of moves between consecutive contact formations in that sequence. A fine motion system based on the concept of contact formations is proposed. The proposed system assumes a nominal motion plan and divides the execution of a comm and ed motion into three part cycles, move, verify and replan. Nominal motion planning, Verification, and Replanning are identified as three major components of a fine motion planning and execution system. This thesis primarily addresses the Verification problem. A two-phase verification algorithm based on the hypothesis and testing paradigm is developed. The passive verification phase is based on formulating mechanics models for various hypotheses and testing for consistency with the sensed data. It is shown that for passive verification of termination conditions it is necessary to determine the contact forces. An approximate method for determination of contact forces in real time for statically determinate as well as statically indeterminate systems is developed. The active verification phase involves generation of small test motions based on reasoning about compliant degrees of freedoms for the different hypotheses. The concept of separation cones is introduced to formalize the representation of directions of compliance and separation. It is shown that for arbitrary geometries of objects, it is not always possible to successfully verify a comm and ed motion in the presence of geometric uncertainties and sensing errors. It is argued that given the bounds on geometric uncertainties and , sensing and control errors, design constraints should be derived such that when these constraints are met, the verification and replanning can be guaranteed. Example design restrictions for verifiability are derived. An algorithm for verification under these design restrictions is developed. It is shown that some of the design constraints translate into simple design rules which can be easily incorporated at the design stage. The proposed system was successfully implemented and tested on a PUMA robot system.Ph.D.Mechanical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162178/1/8920523.pd