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.