Screw image space and its application to robotic grasping

This thesis is devoted to the study and extension of screw image space and its application to kinematic restraint and robotic grasping. In the study of restraint and robotic grasping, problems arise in relation to how to map the conditions and requirements of restraint in a special representational space, and how to map an object in the same space, so that all analysis and synthesis can be performed and further developed in such a space. Meanwhile, it is desirable that such a space would allow us to establish a relationship between equilibrium and geometry of a restraint circumstance, and also a relationship between geometry and algebra. The study is to introduce the restraint mapping in a newly extended screw image space. With the help of a new look at the properties of screws and screw systems, the screw image space is extended with its relevant spaces, the relationship among them is clarified together with a set of definitions. The screw image space is further completed with the study of its entities including hyperplanes, simplexes and polytopes, and further with the partition of the space. A framework is thus established and associated to restraint mapping and the extension of screw image space, and a set of theories is developed to study the entities in screw image space and to apply them to the restraint mapping. The study is based on the linear dependence of screws with detailed algebraic reasoning, which puts forward new properties of zero pitch screw combinations and theory of linear dependence of reciprocal screw systems together with algebraic and geometric reasoning. The study is successfully applied to kinematic restraint and robotic grasping with a set of theorems and methodologies, not only by mapping the restraint of an object, but also by mapping a set of restraint screws along the surface of an object. The graspability of an arbitrary object can thus be determined, the planning and optimisation can be carried out in the screw image space, together with three new invariant quality measures. An optimal grasp is hence achieved with isotropic resistance to arbitrary externally applied forces. The mapping and entities in screw image space are further weighted to account for the stiffness of contacts in dealing with frictional restraint, and planning is thus based on a stiffness weighted mapping. The planning and optimisation are further given in the concept of normal related restraint, and are achieved in the relevant screw image spaces. An augmented space is then established with the introduction of an affine condition. The relationship between the affine solution and the volumetric ratios of sub-simplexes to an n-simplex reconciles the quality measures with the optimisation. With the further introduction of elastic compatibility, frictional grasps are decomposed, and the force equation of equilibrium is augmented. The approach makes it possible to plan grasps in screw image space and to solve them in augmented space. The approach is further used to predict the failure of a specific case of grasping, and gives a satisfactory result, when compared with an experimental result. The final phase of the study is applied to the unknown grasping of unknown objects. By aggregating contact normals and their position vectors of an unknown object by means of newly developed tactile fingertip detectors, and by mapping them into screw image space, the description of an unknown object is completed. The planning and optimisation can thus operate in screw image space, giving a sufficient prediction of a grasp to be applied on the object. Examples and case studies are given through the thesis. Experiments are quoted to demonstrate the implementation of the new system of theories and methodologies in this Thesis. Further, a set of strategies and their methodology is given and incorporated into a package in C++ with a general application to the study of restraint in screw image space. The thesis ends with a concluding chapter reviewing the contents of the thesis and the main achievements of the study, proposing suggestions for further work .