  Incorporating both flexible and rigid components in robot designs offers a
unique solution to the limitations of traditional rigid robotics by enabling
both compliance and strength. This paper explores the challenges and solutions
for controlling soft-rigid hybrid robots, particularly addressing the issue of
self-contact. Conventional control methods prioritize precise state tracking,
inadvertently increasing the system's overall stiffness, which is not always
desirable in interactions with the environment or within the robot itself. To
address this, we investigate the application of Control Barrier Functions
(CBFs) and High Order CBFs to manage self-contact scenarios in serially
connected soft-rigid hybrid robots. Through an analysis based on Piecewise
Constant Curvature (PCC) kinematics, we establish CBFs within a classical
control framework for self-contact dynamics. Our methodology is rigorously
evaluated in both simulation environments and physical hardware systems. The
findings demonstrate that our proposed control strategy effectively regulates
self-contact in soft-rigid hybrid robotic systems, marking a significant
advancement in the field of robotics.
