Robots performing complex contact tasks (e.g., grinding) require a balance between compliance and motion precision. Model Predictive Control (MPC) achieves high-accuracy trajectory tracking by incorporating multi-objective constraints but suffers from high computational load and model sensitivity. In contrast, Impedance Control (IC) enables low-cost force interaction with tunable compliance but lacks inherent mechanisms for enforcing physical constraints, resulting in motion inaccuracies under force regulation. This paper proposes a nonlinear Model Predictive Impedance Control (MPIC) framework that synergizes MPC’s predictive optimization with IC’s compliance adaptability. MPIC solves a joint cost function to balance trajectory tracking and force regulation, enabling tasks like constant-force polishing and precise tangential velocity control. A hierarchical architecture that integrates end-effector impedance control with model predictive control converts Cartesian-space motion and force trajectories into joint-space torque commands for real-time implementation. The framework demonstrates effective coupling of compliance and precision in dynamically interacting scenarios.