Nowadays almost all products used in our daily life are made in pursuit of streamline and good look, including mobiles, motorcycles, aerospace and 3C industry; therefore, how to shorten process time and enhance the smoothness of the product¡¦s surface has become one of the important issues. However, the process method of traditional CNC machines only can support line and circular interpolations but cannot accept motion along curve and circular paths. Therefore, the traditional CNC machines have to rely on CAM, a method to generate the NC code called G-code and M-code by approximating many tiny linear or circular segments, to plan the cutter paths. But this approximating method requires higher transmission speed; it also occupies huge memory capacity and makes the velocity of machine tool discontinuous, in order to difficultly meet the requirement of high speed and better precision. In order to solve the above problems, this thesis adopts the NC code created by CAD/CAM¡¦s NURBS curve which called NURBS-code, making CNC machines have the function of processing NURBS curve interpolations to improve the defect of the traditional processing and thus reach the goal of high speed and better precision. Furthermore, due to NURBS interpolators are always implemented by the controller. This always makes CNC machine become very expensive; meanwhile, adjusting parameters is very troublesome. Therefore this thesis also provides the intergrated method of NURBS and DDA real-time interpolator to make the application in the easy way without the consideration of controller design for AC driver.

This dissertation focuses on compliant motion planning designed for robotic assembly. A Discrete Complaint Motion Planner (DCMP) reacts to detected discrete contact state transitions and issues compliant motion command to the underlying continuous robot system. It consists of a Qualitative Contact Model, a Compliant Motion Strategy Planner (CMSP) and a Compliant Motion Command Planner (CMCP).How to model and characterize a contact state is a major issue. In this dissertation, contact states are described using the qualitative configuration representation called Feature Interaction Matrix (FIM). A FIM encodes not only the contact information but also the relative configuration between two polyhedral parts. This FIM-based qualitative contact state model has several contributions: 1) an optimization-based approach is developed to verify the hypothetical states in FIM; 2) penetration check for hypothetical contact states through constraint satisfaction is simple and fast; 3) spatial adjacency can be easily determined using convex cone techniques; 4) a generate-and-test method is proposed to expand qualitative states in FIM; 5) compliant motion parameters are derived by an optimization method.The qualitative contact states and how they are connected is modeled with an adjacency graph/sub-graph, where nodes represent qualitative contact states and spatially adjacent contact states are connected by arcs. Each arc represents a desired contact state transition. The CMSP receives contact state transition event from an on-line estimator, then computes/checks the assembly strategy and issues the next desired contact state transition to the CMCP. The compliant motion strategy is computed using graph-search techniques with the automatic construction of the adjacency graph/sub-graph. The CMSP integrate hypotheses generation, hypotheses verification, spatial adjacency and graph search algorithms.When the next desired contact state transition is received, the CMCP computes the compliant motion parameters that are issued to the underlying continues robot system to achieve the desired contact state transition. The generation of motion parameters is defined as an optimization problem and an algorithm is developed to solve it.The DCMP in this dissertation considers both 3D translational and 3D rotational motions. Experiments are carried out to demonstrate the feasibility of the approach for the automatic assembly of polyhedral parts.