Across kingdoms and length scales, certain cells and organisms navigate their environments not through locomotion but through growth. This pattern of movement is found in fungal hyphae, developing neurons, and trailing plants, and is characterized by extension from the tip of the body, length change of hundreds of percent, and active control of growth direction. This results in the abilities to move through tightly constrained environments and form useful three-dimensional structures from the body. We report a class of soft pneumatic robot that is capable of a basic form of this behavior, growing substantially in length from the tip while actively controlling direction using onboard sensing of environmental stimuli; further, the peak rate of lengthening is comparable to rates of animal and robot locomotion. This is enabled by two principles: Pressurization of an inverted thin-walled vessel allows rapid and substantial lengthening of the tip of the robot body, and controlled asymmetric lengthening of the tip allows directional control. Further, we demonstrate the abilities to lengthen through constrained environments by exploiting passive deformations and form three-dimensional structures by lengthening the body of the robot along a path. Our study helps lay the foundation for engineered systems that grow to navigate the environment.

We describe two principles that help enable a basic recreation of this behavior in an artificial system. First, an inverted, compliant, thin-walled vessel will lengthen from the tip by everting when pressurized. We present our implementation of this principle, and report results showing lengthening at the tip with length change of thousands of percent, and speeds comparable to animal locomotion. Second, the tip of the vessel steers along a path when the relative lengths of the sides of the vessel are controlled while everting. We present our implementation of this principle and show results of a soft robot lengthening toward a light, autonomously controlling direction with feedback from an onboard camera at the tip. Last, we show examples of the abilities of this type of robot body, demonstrating navigation through constrained environments and the formation of structures from the lengthening body.

Although roboticists have successfully recreated movement through the environment using locomotion, defined as the translation of the body from one location to another ( 8 )—flying ( 9 ), running ( 10 ), swimming ( 11 , 12 ), cytoplasmic streaming ( 13 ), slithering ( 14 ), and leaping ( 15 )—navigating the environment through growth is challenging in artificial systems. The work on soft continuum manipulators ( 16 – 20 ) and tendril-like robots ( 21 , 22 ) has laid a foundation that has been built upon by the recent development of root-inspired robots and endoscopes that either enter a new part of the environment without changing length ( 23 , 24 ) or extend one to five body lengths by adding material at rates of 1 to 10 mm/min to move through granular media ( 25 , 26 ). However, tip-based length change on the order of thousands of percent with directional control at rates comparable to those of animal locomotion is still an open challenge.

( A ) A body lengthens from its tip toward a target. Because only the tip moves, there is no relative movement of the body with respect to the environment (colored bands do not move). This results in the capability to move with no sliding friction through a constrained environment. As the tip moves, the body forms into a structure in the shape of the tip’s path. ( B ) Examples of biological systems that grow to navigate their environments. Neurons grow through constrained tissue to create structures that act as signal pathways. Pollen tubes lengthen through pistil tissue to build conduits to deliver sperm to the ovary. Sclerenchyma cells grow within the xylem and phloem to create supporting structures.

Growth as a method for navigating the environment is found in fungal hyphae with diameters as small as a few micrometers ( 1 ) as well as in vines with girths as large as a meter ( 2 – 4 ). These organisms grow from their tips, increase length hundreds of times, and continually control growth direction based on environmental stimuli. Because lengthening from the tip, or apical extension, involves no relative movement of the body with respect to the environment, the body can lengthen along constrained paths without friction from sliding against the environment ( Fig. 1A ). Further, because each movement of the tip results in a directionally controlled lengthening of the body, the body forms into a three-dimensional (3D) structure along the path of the tip. These capabilities enable natural cells and organisms to grow through tightly packed tissue or abiotic materials and form structures with functions ranging from signal pathways to conduits for delivery ( Fig. 1B ) ( 5 – 7 ).

RESULTS

The first principle, which is based on the eversion of a thin membrane driven by internal pressure, enables lengthening at the tip with substantial elongation and at a relatively high speed. The internal pressure forces the inverted material to evert at the tip while pulling more material from the base through the core of the body (Fig. 2A). This principle is used to deploy invaginated appendages by a variety of invertebrates such as the Sipunculus nudus, which everts a proboscis for defense (27). An analog of this method of lengthening, continuous eversion as found in cytoplasmic streaming, is the inspiration for robotic whole-skin locomotion (13). In our system, we implement the principle with a thin membrane of polyethylene driven by a pneumatic pump that pressurizes the interior of the soft robot body (Fig. 2, A and B, and movie S1). The design is scalable; wall stresses remain constant during geometric scaling of a thin-walled vessel, meaning that the ratio of wall thickness to diameter can be maintained. We have tested diameters ranging from 1.8 mm to 36 cm (some shown in movies S3 and S4). The thin-walled, pressurized design enables not only lengthening at the tip but also substantial length change: Very little volume of precursor wall material results in a very large volume of pressurized body. Further, unlike lengthening invertebrates, we store the precursor material in a spool, allowing length change to be much greater than the 100% length change seen in these creatures. Although the number of turns that the soft robot body makes affects the maximum length (Supplementary Text and fig. S2), on paths with only a few turns, our system, initially 28 cm, has extended to a length of 72 m, limited by the amount of the plastic membrane on the spool (movie S1).

Fig. 2 Principle of pressure-driven eversion enables lengthening from the tip at rates much higher than those found in plant cell growth. (A) Implementation of principle in a soft robot. A pump pressurizes the body, which lengthens as the material everts at the tip. This material, which is compacted and stored on a reel in the base, passes through the core of the body to the tip; the rotation of the reel controls the length of the robot body. (B) Images of the lengthening body. The body diameter is 2.5 cm. (C) The relationship between lengthening rate (r) and internal pressure (P) shows a characteristic viscoplastic behavior: no extension below a yield pressure (Y) followed by a monotonic relationship between rate and pressure with a power term (n) close to 1. (D) Data show the relationship between rate and pressure above yield for the soft robot, worms with an everting proboscis (S. nudus), and a plant cell (Nitella mucronata). The extensibility φ (inverse viscosity) of a soft robot body is roughly seven orders of magnitude higher than that of the plant cell, resulting in a lengthening rate that is roughly five orders of magnitude higher. The extensibility of the soft robot body is slightly higher than the worm, which uses the same principle for lengthening.

This principle of lengthening based on pressure-driven eversion also results in relatively fast lengthening, especially when compared to organisms that use growth to navigate their environments, such as certain fungi and plants. To understand the behavior of the rate of lengthening in our system, we measured the rate as we varied the internal pressure (Fig. 3C). Because of the energy losses caused by everting the membrane, we see a behavior characteristic of a Bingham plastic, in which there is a minimum required pressure before yield, and a monotonic relationship between the rate of lengthening and pressure (28). This is the same behavior observed in growing plant cells, which soften and then stretch because of internal pressure before new material is added to rethicken the walls (29–32). In plants, the relationship between rate and pressure is described using an inverse viscosity, termed “extensibility,” φ (fig. S5; see Supplementary Text for discussion) (33, 34). Our system has an extensibility that is seven orders of magnitude higher than in plants and only one order of magnitude higher than in invertebrates that use the same mechanism of lengthening (Fig. 3, C and D). Our peak bursting pressure is lower than that in a plant cell, resulting in a maximum rate of lengthening roughly five orders of magnitude higher than that in plant cells, with a maximum speed over short distances of 10 m/s. Although our implementation allows for considerably faster tip movement than that of natural cells, real-time branching, as seen in fungal hyphae in a mycelium (1, 35), is not currently possible. However, a handful of preset branches are possible (fig. S4), and because the robot body is inexpensive and disposable, many parallel bodies, like a single branched body, could cover large areas for search and rescue applications (see Materials and Methods for manufacturing details).

Fig. 3 Principle of asymmetric lengthening of tip enables active steering. (A) Implementation in a soft robot uses small pneumatic control chambers and a camera mounted on the tip for visual feedback of the environment. The camera is held in place by a cable running through the body of the robot. (B) To queue an upward turn, the lower control chamber is inflated. (C) As the body grows in length, material on the inflated side lengthens as it everts, resulting in an upward turn (see Materials and Methods and Fig. 5 for details). (D) Once the chamber is deflated, the body again lengthens along a straight path, and the curved section remains. (E) A soft robot can navigate toward light using a tip-mounted camera. Inset: The view from the camera shows the target to the right. Electronically controlled solenoid valves inflate the control chamber on the left side of the robot body, resulting in the tip reorienting to the right and forming a right turn. (F) The target is straight ahead, and the robot steers straight. (G) The target is to the left, and the robot steers left. (H) The robot reaches the target. (I) Position of the target along the horizontal axis of the camera as the robot lengthens toward the target.

The second principle that we leverage in our design enables the active control of direction and is based on setting the relative lengths of either side of the body at the tip as the body grows in length. This principle of directional control is found in tip-growing cells such as pollen tubes (36), fungal hyphae (1), rhizoids of algae (37), and root hairs (7). In our system, we implement this principle by selectively allowing one side of the robot body to lengthen with respect to the other side as the body everts from the tip (Fig. 3, A to D). Small control chambers that run along the side of the robot body act as the control input; when one of these chambers is inflated, the section of the robot body that is everting from the tip on that side will be lengthened. For example, when the left channel is inflated, the left side of the tip lengthens, resulting in a right turn (see Materials and Methods and Fig. 5 for details). Thus, by controlling the relative pressures of these control chambers, steering is achieved (movie S2). This method of turning is efficient and simple; it requires neither the addition of energy (beyond the control signal) nor any bulky actuators to bend an existing segment. Rather, the turn is created at the same time as the segment, using the energy stored in the pressurized fluid of the main chamber. Each turn is permanent, thus control of direction is nonholonomic (38), like in a steering car or growing pollen tube. Our implementation results in much faster changes in direction than the chemical diffusion of natural cells [less than a second for our system in contrast to roughly a minute for pollen tubes (39)]. However, our implementation has closely packed discrete sections that can be lengthened (Fig. 5), resulting in a digital system, which sacrifices some resolution that an analog system affords. To demonstrate our implementation, a soft robot navigates to a light using an onboard tip-mounted camera with closed-loop active control (Fig. 3, E to H, and movie S2).

Fig. 5 Details of an implementation of a mechanism within the control chambers for selective lengthening of the sides of the soft robot. A series of latches are manufactured into the control chambers shown in Fig. 3 (A to D). Each latch crosses pinched material, such that when released, the side lengthens. There are four total states. State 1: When the control chamber is depressurized and the latch is on the side, the latch remains closed. State 2: When the control chamber is depressurized and the latch is at the tip, the latch remains closed. (When a control chamber is depressurized, the pressure from the main chamber keeps the latch closed regardless of whether the latch is on the side or at the tip.) State 3: When the control chamber is pressurized and the latch is on the side, the latch remains closed. State 4: When the control chamber is pressurized and the latch is at the tip, the latch opens. (When the control chamber is pressurized, the latch remains closed if it is along a side, due to the shape of the interlocking of the latch, but the latch opens if it is at the tip because the high curvature overcomes the interlocking.)

In addition to demonstrating tip growth, substantial length increase, high-speed tip motion, and directional control, the presented class of soft robot shows some of the capabilities of natural cells and organisms that navigate by growth: movement through tightly constrained environments and the creation of 3D structures with the lengthening body. We tested our system by lengthening a soft robot body through challenging constrained environments (Fig. 4A and movie S3) and demonstrated its insensitivity to surface characteristics (Fig. 4B): It takes no more pressure to grow between two adhesive surfaces than between two polytetrafluoroethylene (PTFE) surfaces. Its ability to passively deform aids in its ability to move through constrained spaces and adapt to the environment. We also demonstrated 3D structures created by lengthening a preformed body: an active hook, a fire hose, and a radio antenna (Fig. 4C and fig. S3), as well as a structure that lengthens across land and water and another that pulls a cable through a dropped ceiling (movie S4). Like the natural examples of structure creation (Fig. 1B), a variety of purposes are demonstrated: the fire hose demonstrates delivery (like pollen tubes), the structure of the antenna demonstrates support (like sclerenchyma cells), and the cable-pulling structure demonstrates connecting remote locations (like neurons).