# Plant-Inspired Soft Growing Robots: A Control Approach Using Nonlinear Model Predictive Techniques
## 1 Introduction  
Harmless robotics exploration of confined spaces, such as the application of Minimally Invasive Surgeries (MIS) in human bodies [1], or inspection of archaeological sites [2], is challenging while considering the existing rigid robot designs. Thus, designing new materials and locomotion systems for robots is crucial to perform in such challenging environments. Inspired by biological systems such as elephant trunks, octopus tentacles, and snakes, designs of soft continuum robots with continuous bending backbones have alleviated the non-destructive navigation in congested environments [3, 4]. Nonetheless, the small lengths of continuum robots are limiting their applicability in the exploration of distant spaces [5]. Taking inspiration from plants, a novel type of mobility called growth mobility was recently introduced. Namely, growing robots can mimic the biological growth of plants by gradually extending their lengths, volumes, or knowledge: [6]. Due to their soft materials or flexible joints, growing robots can extend their lengths to reach distant spaces while showing compliance when working in confined environments. Earlier research has shown few attempts for designing long flexible robots that can work in tight spaces. For instance, a multiple-degrees of freedom growing robot called \"Active Hose\" is proposed by [PERSON] et al. [7] for search and rescue applications. The proposed robot design was based on stacking two degrees of freedom units in series to enable the robot to extend its length and achieve the required flexibility. [PERSON] et al. [8] have come up with a flexible thin and extended cable with an attached camera to explore narrow spaces. Moreover, a pneumatically driven expendable soft arm known as \"Slime Scope\" [9] was developed for rescue applications in rubble environments. Nevertheless, the locomotion of these developed growing robots requires the movement of the entire robot's body, which in turn causes significant friction between the robot and the environment. Recently, two designs of novel plant-inspired growing robots were proposed, each having the capability of extending their body lengths with the addition of materials at their distant tips. In particular, in [10; 11], a plant root-like growing robot is proposed, and a three-dimensional (3D) printer-like head is attached to its tip to deposit the circular body layers of the robot incrementally. The steering capability is achieved efficiently by varying the speed of material deposition along the robot circumference. However, the robot's growth speed of the robot is limited based on the environment. On the other hand, a vine-like growing robot has been developed by [PERSON] et al. [12] based on a novel mechanism called \"tip-eversion\" [13]. It is a pneumatically-driven robot made of thin-walled polyethylene tubing that can ever from inside to outside, enabling the robot to extend for tens of meters into slippery and sticky environments. The steering of vine robots was achieved by either utilizing the environment's obstacles to guide the robot's movements [4] or by placing three or four Series Pneumatic Artificial Muscles (SPAM) which are inflated along the circumference of the robot to establish the required steering moment at the robot's tip [14]. Thus, the lengthening capacity, the ratio of the length to the diameter, and the compliance body enable vine-like robots to navigate distant cluttered environments as demonstrated in [15], where three key applications could obtain the benefits of vine-growing robots, namely, showing the deploying and reconfiguring structures, navigating constrained environments, and applying forces on the environment. Thus far, however, there has been little discussion about the control of growing robots' movements in spatial environments. Feedback control is particularly crucial in vine robots because their nonlinear dynamics are coupled with the absence of effective methods to deploy sensors throughout their long bodies.