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Soft robots have shown great potential to enable safe interactions with unknown environments due to their inherent compliance and variable stiffness. However, without knowledge of potential contacts, a soft robot could exhibit rigid behaviors in a goal-reaching task and collide into obstacles. In this paper, we introduce a Sliding Mode Augmented by Reactive Transitioning (SMART) controller to detect the contact events, adjust the robot’s desired trajectory, and reject estimated disturbances in a goal reaching task. We employ a sliding mode controller to track the desired trajectory with a nonlinear disturbance observer (NDOB) to estimate the lumped disturbance, and a switching algorithm to adjust the desired robot trajectories. The proposed controller is validated on a pneumatic-driven fabric soft robot whose dynamics is described by a new extended rigid-arm model to fit the actuator design. A stability analysis of the proposed controller is also presented. Experimental results show that, despite modeling uncertainties, the robot can detect obstacles, adjust the reference trajectories to maintain compliance, and recover to track the original desired path once the obstacle is removed. Without force sensors, the proposed model-based controller can adjust the robot’s stiffness based on the estimated disturbance to achieve goal reaching and compliant interaction with unknown obstacles.