Existing trajectory-tracking approaches for redundant manipulators predominantly focus on end-effector positioning while neglecting orientation constraints, consequently restricting the feasible region through multi-level joint limit incorporation, as evidenced in Chaps. 2 through 6. To address these limitations, a model predictive tracking control of position and orientation (MPTCPO) scheme for redundant manipulators is developed, enabling concurrent end-effector position and orientation regulation. The proposed MPTCPO scheme achieves simultaneous minimization of the trajectory error, joint-velocity norm, and joint-acceleration norm. This scheme directly enforces three-tiered joint constraints (angle, velocity, and acceleration) while preserving the feasible region of decision variables and eliminating the need for conversion techniques. Furthermore, a finite-time dynamic neural network (FTDNN) model is developed to compute optimal solutions for the MPTCPO scheme. Both simulations and experiments validate the effectiveness and precision of the FTDNN-based control scheme.