Object grasping is a crucial aspect of performing activities of daily living, as it facilitates individuals to interact effectively with their environment. In elderly human subjects, this capability often becomes challenging due to factors such as reduced muscular strength, diminished motor coordination, and neurodegenerative disorders that impair hand functionality. Additionally, age-related declines in grasping strength and joint flexibility further complicate the ability to precisely and accurately grasp objects. Therefore, this study demonstrates the design and development of an assistive device aimed at improving object grasping performance and overall quality of life in the elderly population, which contributes to bridging the gap between mind and machine. This work focuses on improvement in grasping assistance tasks while developing a two-fingered hand exoskeleton along with a robust grasping force control strategy. Real-time force feedback, obtained through embedded FSR-402 sensors on fingertips, the proposed Sliding Mode Control (SMC)-based approach enables continuous regulation of actuator output, thereby maintaining precise and stable grasping force across different-sized objects. The effectiveness of the proposed system was evaluated based on three distinct groups of object grasping experiments (i. constant grasping force, ii. multi-step grasping force tracking, and iii. disturbance rejection) for three different-sized objects while involving two elderly human subjects. The promising findings indicate that the combination of the proposed robust SMC- based grasping force control with a developed two-fingered hand exoskeleton constitutes a significant advancement toward functional human-machine integration, particularly in the domain of rehabilitation, assistive technology, and activities of daily living.