Snake robotics is an important research topic with a wide range of applications, including inspection in confined spaces, search-and-rescue, and disaster response. Snake robots are well-suited to these applications because of their versatility and adaptability to unstructured and constrained environments. In this paper, we introduce a soft pneumatic robotic snake that can imitate the capabilities of biological snakes, its soft body can provide flexibility and adaptability to the environment. This paper combines soft mobile robot modeling, proprioceptive feedback control, and motion planning to pave the way for functional soft robotic snake autonomy. We propose a pressure-operated soft robotic snake with a high degree of modularity that makes use of customized embedded flexible curvature sensing. On this platform, we introduce the use of iterative learning control using feedback from the on-board curvature sensors to enable the snake to automatically correct its gait for superior locomotion. We also present a motion planning and trajectory tracking algorithm using an adaptive bounding box, which allows for efficient motion planning that still takes into account the kinematic state of the soft robotic snake. We test this algorithm experimentally, and demonstrate its performance in obstacle avoidance scenarios.