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This paper presents the complete development and analysis of a soft robotic platform that exhibits peristaltic locomotion. The design principle is based on the antagonistic arrangement of circular and longitudinal muscle groups of Oligochaetes. Sequential antagonistic motion is achieved in a flexible braided mesh-tube structure using a nickel titanium (NiTi) coil actuators wrapped in a spiral pattern around the circumference. An enhanced theoretical model of the NiTi coil spring describes the combination of martensite deformation and spring elasticity as a function of geometry. A numerical model of the mesh structures reveals how peristaltic actuation induces robust locomotion and details the deformation by the contraction of circumferential NiTi actuators. Several peristaltic locomotion modes are modeled, tested, and compared on the basis of speed. Utilizing additional NiTi coils placed longitudinally, steering capabilities are incorporated. Proprioceptive potentiometers sense segment contraction, which enables the development of closed-loop controllers. Several appropriate control algorithms are designed and experimentally compared based on locomotion speed and energy consumption. The entire mechanical structure is made of flexible mesh materials and can withstand significant external impact during operation. This approach allows a completely soft robotic platform by employing a flexible control unit and energy sources.