Robots are now working not only in human environments but also interacting with humans, e.g., service robots or assistive robots. A 7DoFs robotic exoskeleton MARSE-7 (motion assistive robotic-exoskeleton for superior extremity) was developed as an assistive robot to provide movement assistance and/or ease daily upper-limb motion. In this paper, we highlight the nonlinear control of MARSE-7 using the modified sliding mode exponential reaching law (mSMERL). Conventional sliding control produces chattering which is undesired for this kind of robotic application as it causes damage to the mechanical structure. Compared to conventional sliding control, our approach significantly reduces chattering and delivers a high dynamic tracking performance. The control architecture was implemented on a field-programmable gate array (FPGA) in conjunction with a RT-PC. In experiments, trajectory tracking that corresponds to typical passive arm movement exercises for single and multi joint movements were performed to evaluate the performance of the developed robot and the controller. Experimental results demonstrate that the MARSE-7 can effectively track the desired trajectories.