Soft robotics has garnered attention for its substantial prospective in various domains, such as manipulation and interactions with humans, by offering competitive advantages against rigid robotic systems, including inherent compliance and variable stiffness. Despite these benefits, their theoretically infinite degrees of freedom and prominent nonlinearities pose significant challenges in developing dynamic models and guiding the robots along desired paths. Additionally, soft robots may exhibit rigid behaviors and potentially collide with their surroundings during path tracking tasks, particularly when possible contact points are unknown. In this dissertation, reduced-order models are used to describe the behaviors of three different soft robot designs, including both linear parameter varying (LPV) and augmented rigid robot (ARR) models. While the reduced-order model captures the majority of the soft robot's dynamics, modeling uncertainties notably remain. Non-repeated modeling uncertainties are addressed by categorizing them as a lumped disturbance, employing two methodologies, $H_\infty$ method and nonlinear disturbance observer (NDOB) based sliding mode control, for its rejection. For repeated disturbances, an iterative learning control (ILC) with a P-type learning function is implemented to enhance trajectory tracking efficacy. Furthermore,for non-repeated disturbances, the NDOB facilitates the contact estimation, and its results are jointly used with a switching algorithm to modify the robot trajectories. The stability proof of all controllers and corresponding simulation and experimental results are provided. For a path tracking task of a soft robot with multi-segments, a robust control strategy that combines a LPV model with an innovative improved nonlinear disturbance observer-based adaptive sliding mode control (INASMC). The control framework employs a first-order LPV model for dynamic representation, leverages an improved disturbance observer for accurate disturbance forecasting, and utilizes adaptive sliding mode control to effectively counteract uncertainties. The tracking error under the proposed controller is proven to be asymptotically stable, and the controller's effectiveness is is validated with simulation and experimental results. Ultimately, this research mitigates the inherent uncertainty in soft robot modeling, thereby enhancing their functionality in contact-intensive tasks.