The field of soft robotics is experiencing a transformative phase with the emergence of self-supporting modular soft robot arms, inspired by design principles drawn from climbing plants, which are gaining recognition as a rich source of bio-inspiration. The vision to deploy these systems in highly unstructured environments, qualifies the need to investigate model-free algorithms that facilitate motion capabilities based solely on data regarding system-environment interactions. This paper delves into the development of model-free controllers to enable tracking capabilities in these systems. While the trajectory tracking task is already recognized as challenging in the context of redundant continuum/soft arms, the difficulty is compounded when aiming to generate control policies solely from sequential feedback from the environment. The novelty of this work lies in the development of both learning-based and learning-free model-free computational frameworks to address this task. Both controllers are validated on a 9-DoF modular cable-driven plant-inspired soft arm for moving through multiple trajectories in 3D space. The comparison of these controllers holds significant insights to future directions for the practical applicability of these systems in real-world scenarios, and are promising to pave way for novel application scenarios.