Analysis and planning of planar manipulation tasks

This thesis addresses the problem of producing reliable solutions to manipulation tasks. Such tasks are strongly influenced by the task geometry, mechanics, and uncertainty. This thesis addresses these issues by applying the techniques of classical mechanics, and extends these techniques to include task geometry and uncertainty. In particular, the thesis addresses manipulation tasks that involve two rigid polygonal objects interacting in a plane; examples include linear pushing, compliant motion, and placing-by-dropping tasks. For this class of tasks, the thesis defines a collection of generic algorithms that analyze the kinematic, static, dynamic, and motion-specification aspects of a given task. These algorithms identify a continuous bounded set of actions that will retiably achieve the task goal, despite uncertainty in every physical parameter except object shape. The algorithms perform a kinematic analysis to construct the set of reachable ($x$, $y$, $\theta$) task configurations, a static analysis to identify the configurations where equilibrium is possible, a dynamic analysis to identify a set of initial configurations that converge to the goal, and a coordinate transformation to identify a set of commanded motions that will achieve the goal. The kinematic and static analysis algorithms have been fully implemented, and the dynamic analysis algorithms have been partially implemented. These programs were used to synthesize linear pushing actions, to analyze a part interacting with an orienting fixture, and to synthesize placing-by-dropping actions. A series of physical experiments were performed to test the validity of the programs' physical predictions; no failures were observed in these experiments, some of which included over 1200 trials. This thesis represents a step toward the application of classical mechanics to general manipulation problems; many open problems remain. The thesis presents a discussion of possible extensions of this work to enhance its generality, as well as a discussion of task domains that appear to require a completely different approach.