In this paper, a hierarchical hybrid motion/force control architecture for the manipulation and grasping of mobile manipulators is presented, where the systems are subject to varieties of physical constraints such as Coulomb friction cones, nonholonomic/holonomic constraints, and actuator saturation limits. The incorporation of a projection-based operation space control and an adaptive controller based on the neural networks used in this paper formulates a novel control scheme, so the system stability is further guaranteed and the uncertain dynamics is handled without redesigning the minimal-order dynamics model. Considering the effects of these constraints, the actuator saturation limits are handled by an auxiliary designed system, and the neural dynamics optimization is applied for the quadratically constrained programing problem of the optimal robotic grasping. The dynamic uncertainties can be estimated online by using the developed motion/force control strategy, and the application of a novel disturbance observer is explored to ensure the good tracking performance. The experimental results are presented to verify the performance and the efficiency of the proposed method. Note to Practitioners —This paper is motivated by the problems of robotic grasping, the trajectory tracking of mobile manipulation, which are with time-varying topology (e.g., actuator saturation limits, switching constraints). Traditional approaches tackling such problems mainly use multiple-models switching control architecture; however, these methods are not suitable for the switching conditions. Therefore, it is necessary to develop a novel control approach dealing with these issues together. In this paper, a unified hierarchical hybrid motion/force control architecture is proposed using the notion of projection operator, and the control inputs are decomposed into the null space, which produces the motion complement of the system and the orthogonal complement space constructing physical constraints, respectively. In addition, an auxiliary system is also designed to solve the limits from the actuator saturation. The feasibility of the system is demonstrated by the extensive experiment results including trajectory tracking and the switching constraints in the developed mobile manipulator.