Mechanics and Planning of Workpiece Fixturing and Robotic Grasping

• Main Author: Lin, Qiao
• Format: Others
• Language: en
• Published: 1998
• Online Access: https://thesis.library.caltech.edu/411/1/Lin_q_1998.pdf; Lin, Qiao (1998) Mechanics and Planning of Workpiece Fixturing and Robotic Grasping. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1d4m-j065. https://resolver.caltech.edu/CaltechETD:etd-01302008-111854 <https://resolver.caltech.edu/CaltechETD:etd-01302008-111854>

<p>This thesis addresses several key issues in mechanics and automated planning of workpiece fixturing and robotic grasping, including accurate and efficient modelling of compliance, well-defined and practically useful quality measures, and well-defined kinematic metric functions for rigid bodies.</p> <p>The accurate and efficient modelling of compliant fixtures and grasps is considered. A stiffness matrix formula is derived using the overlap compliance representation for quasi-rigid bodies. In contrast to existing approaches using the linear contact model, this formula is well-suited to automated planning algorithms since it can incorporate realistic nonlinear contact models (e.g., the classical Hertz model), and can be directly computed from CAD data on basic geometric and material properties of the bodies. The formula is then used as a basis for a systematic analysis of local curvature effects on fixture stability. This analysis shows that destabilizing effects of local curvatures are practically negligible, and that curvature effects can be used to stabilize, sometimes significantly, an otherwise unstable fixture. The stiffness matrix formula is also used to show that stability analysis in general depends on the choice of contact models, which offers additional evidence for the importance of using realistic contact models.</p> <p>The stiffness and deflection quality measures are defined for compliant fixtures and grasps, and are applied to optimal planning. Unlike existing quality measures that rely on heuristic rules or depend on reference frame choices, the stiffness and deflection quality measures are theoretically sound. Equally important is that these quality measures accurately characterize functional performances which are important to practical fixturing applications, such as fixture stiffness and workpiece deflections. The stiffness and deflection quality measures are applied to optimal fixture and grasp planning, resulting in maximum-stiffness and minimum-deflection fixtures and grasps. The qualitative properties of optimal fixtures are characterized with respect to each quality measure, and efficient techniques are developed for finding such optimal fixtures.</p> <p>The final key issue is concerned with formal well-definedness conditions and practical development methods for rigid body kinematic metric functions, such as norms, inner products, and distance metrics. Based on an intrinsic definition of the configuration space of a rigid body, the notion of objectivity is proposed to formalize the natural requirement that metric measurements be indifferent to the observers who perform the measurements. This notion is then used to clarify the fundamental physical implications of left, right and bi-invariant functions on SE(3), and is further shown to be equivalent to the notion of frame-invariance. Based on these clarifications, several frame-invariant norms of rigid body velocities and wrenches, which have interesting physical interpretations, are defined.</p>