The design and development of Branch Bot: a branch-crawling,caterpillar-inspired,soft robot

1.1. Why is soft important

Moving in complex 3D environments requires many degrees of freedom (DOFs). Although high-DOF robots can be built using rigid components linked by joints, these joints are difficult to design and are prone to failure as the number increases. An alternative approach is to fabricate climbing robots from soft materials that can deform in all dimensions. This offers significant advantages over rigid or flexible counterparts because the robot can conform to uneven terrain and squeeze through narrow gaps or change shape to access complex structures (Kovac, 2013). Soft robots can also interact with the environment without causing damage, and they are extremely resistant to impacts.

For commercial purposes, soft robots are expected to be cheap to manufacture and can be fabricated as shock-resistant monolithic structures with low part counts and few exposed parts. Projected applications include search-and-rescue robots in urban disasters and any situation in which a robot must interact with living or delicate surroundings such as agricultural work, environmental monitoring, and space-based activities. Soft robots can be constructed from environmentally friendly or biodegradable materials for scenarios in which the device cannot be retrieved or for medical and biosafety applications (Trimmer, 2013).

1.2. The biological inspiration

One approach to making robots that are effective in complex environments is to adapt mechanisms and locomotion strategies used by animals in similar surroundings. Caterpillars are the most prevalent macroscopic soft-bodied climbing animal. They crawl on leaves and branches in any orientation and can traverse surfaces of different stiffness and roughness while navigating over obstacles (Griethuijsen and Trimmer, 2014; van Griethuijsen and Trimmer, 2010). Although caterpillars are pressurized they are not particularly stiff (Lin et al., 2011), but instead conform to the surface curvature. Another factor that helps them maintain stability and maneuverability in 3D structures is their passive gripping appendages called prolegs. These have been studied in detail in the tobacco hornworm, Manduca sexta (Figure 2) (Mukherjee et al., 2018). At the tip of each proleg is an array of small hook-like structures known as crochets embedded in a soft membrane. The crochets dig into the surface or snag on very small asperities. Because the crochets act as grappling hooks, they produce passive grip that is proportional to their loading. The grip is so effective that M. sexta can support its own weight with just one proleg (Trimmer and Issberner, 2007), and in other species it allows the use of an inching gait with a single attachment point during each step. Grip release is accomplished by rotating and retracting the crochets away from the surface using a single muscle. The retraction system is self-adjusting and very robust, producing no detectable negative ground reaction force normal to the surface (Lin and Trimmer, 2010b).

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Fig. 2.

The tobacco hornworm, Manduca sexta, is a soft-bodied larval insect that lives on the stems and leaves of its host plant and serves as a biological inspiration for Branch Bot. The body is soft and elastic with longitudinal muscles in each segment working as tension actuators. Five body segments have paired prolegs, which are the primary gripping appendages. The tips attach to the substrate passively and detach though active contraction retractor muscles in each proleg.

1.3. Background and related work

Most of the research on scansorial robots has focused on robots that can climb walls or other relatively smooth surfaces (Brown et al., 2016; Liu et al., 2016; Xu et al., 2016; Yoshida and Ma, 2010), but little work has been done on robots capable of maneuvering in complex 3D environments. One rare example is the snake robot from Carnegie Mellon University (Wright et al., 2012, 2007). This robot has impressive capabilities, but it uses many joints and motors that are potential points of mechanical failure. This makes it heavy, complicated, and expensive.

Another robot that does a good job maneuvering in a complex 3D environment is Tree Bot (Lam and Xu, 2011a,b). Tree Bot has a pinion gear to drive axial movements along three rod-like springs that serve as a backbone and a pair of two-bar articulated legs each with linear actuators to control gripping. The backbone is a flexible continuum system similar to a manipulator arm that allows the robot to conform to the curvature of the substrate. The leg actuators are used to open and release the grippers and preloaded springs maintain grip in the closed position. Tree Bot can climb tree trunks at 22.4 cm/min and transition onto branches, but aside from its flexible backbone, it is constructed entirely from stiff materials and all its movements are actively controlled. These design features could limit its use in more complex or delicate environments.

There are numerous climbing robots composed of rigid modules connected by joints (Chen et al., 2014; Wang et al., 2009; Wang and Wu, 2016; Wei and Dawei, 2012; Wei and Long-chao, 2012; Zhang et al., 2009; Zhu et al., 2014). Many use gaits that mimic the kinematics of caterpillar crawling and inching, but they do not use the underlying mechanical phenomenon that makes caterpillars such successful climbers (Lin and Trimmer, 2010a,b; Simon et al., 2010). In particular, caterpillars rely on their soft elastomeric bodies to conform to the substrate, and deformability is a critical feature of their interactions with the environment. Current climbing robots must minimize their interactions with the environment or risk damaging it or themselves. One example of a soft, caterpillar-inspired robot that attempts to mimic kinematics of a caterpillar is PISRob (Xie et al., 2018). PISRob is a pneumatic robot that uses an inching gait. It has one pincer like gripper on each end. When crawling on the ground it uses the gripper to lift the end up off the ground, reducing the friction on that end. When crawling on top of a square rod, the grippers grab onto either side of the rod. PISRob moves forward by bending its body into a Ω shape. It is tethered and cannot climb vertically. Although the gait of PISRob is bio-inspired, the pneumatics do not imitate the behavior of muscles. In addition, unlike caterpillars, the grippers are active-grip, passive-release rather than passive-grip, active-release. PISRob crawls at a speed 36 m/h. In addition to these caterpillar-inspired robots, there is one example of a caterpillar-inspired gripper in the literature (Jung et al., 2013). This gripper uses flexure buckling to attach to rugged and uneven surfaces. The gripper is made mainly from glass fiber and is thus mostly rigid with a few soft sections acting as joints.

Given the limitations of current rigid-material robots, we have developed a family of soft robots whose locomotion depends on the body being highly deformable. These are either cast from silicone elastomers or directly 3D printed in soft materials such as Tango Plus©. Current models are electrically actuated with on-board shape-memory alloy coils or motor-tendons, and they are able to crawl on flat surfaces using an intrinsic friction switching system (Umedachi et al., 2016). Although these robots have been useful for testing different control schemes, they are unable to operate in complex environments and they cannot climb. Therefore, we have developed Branch Bot as a new robotic platform for climbing in 3D structures such as tree canopies or antennal arrays.

2.1. Body design

The robot consists of three grippers and two spring-like body segments (Figures 3 and 4). The body segments connect the grippers together. Each gripper and body segment is actuated independently. The spring-like body segments consist of two parallel hollow bellows connected by rigid ribs (see Figure 4 for a cross-section of the bellows). This structure is designed to compress and store energy. The bellows are made out of silicone, and the ribs are made out of 3D-printed ABS. The tendon that actuates the body segment passes through the middle of the ribs. This tendon compresses the segment, and the elastic energy stored in the deformation of the material extends the segment when the tendon relaxes. The bellows in each segment is divided into symmetrical left and right structures, which allow the tendons to be placed along the midline of the body for easy assembly and access. This arrangement also enables the robot to align itself along the substrate by creating a concave surface for the dowel to sit in. In addition, this arrangement of bellows provides sufficient area moment of inertia to minimize buckling without increasing the total cross-sectional area and height of the robot.

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Fig. 3.

An annotated CAD render of Branch Bot. The green material is soft and the yellow material is hard. The robot consists of two body segments and three grippers (see Figure 5a for more details). Each body segment is independently actuated and compressed by tendons that are controlled by Bowden cables at the front and rear of the robot. Similarly, each gripper is controlled by a Bowden cable attached to the top of the gripper assembly.

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Fig. 4.

An annotated CAD render of Branch Bot. The green material is soft and the yellow material is hard. The robot consists of two body segments and three grippers (see Figure 5a for more details). The body segments are two parallel bellows. The hatched section in the lower figure is a sagittal plane cross-section of the bellows. Each body segment is actuated by one tendon (marked in red), which controls the compression of that segment. The elastic energy stored in the body segments extends the segments when the tendon relaxes.

The motors were off-board so we could focus on studying the dynamics of the soft body. A 3D-printed pulley was connected to each motor shaft to wind a nylon tendon running through a stiff plastic sheath. The sheath and tendon system functioned as a Bowden cable actuator.

2.2. Gripper design

Branch Bot uses three passive grippers that are actively released by three independent motors (Figure 5a). The grippers are primarily silicone rubber with a few rigid 3D-printed inserts to control the routing of the tendons, the anchoring of the Bowden cables, and the anchoring of the tendons. The grippers consist of a base that is mostly stiff to anchor the Bowden cables and route the tendons and two flexible fingers. The tendons wrap around the outside of each finger and control the release of the fingers. The gripping surfaces of the fingers are made more conformable using the Fin Ray^® Effect (Crooks et al., 2016).

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Fig. 5.

A side-by-side comparison of Branch Bot’s gripper with the proleg of M. sexta. (a) An annotated CAD render of Branch Bot’s gripper. The green material is soft and the yellow material is hard. The hatched section at the base of the gripper is a broken-out section showing the rigid part embedded in the soft structure. The gripper is released by a tendon running around the outside of the gripper (path shown in red). The gripper attaches when the tendon is relaxed and the elastic energy stored in the gripper causes the material to return to its initial shape. The Fin Ray® Effect (see Figure 6 for more details) allows the grippers to better conform to the substrate. (b) A view of the prolegs in the transverse-ventral plane showing them in the gripping position. An array of curved hooks (crochets) are embedded in a soft membrane (the planta) at the tip of each proleg. Elasticity and internal pressure maintain the prolegs in the gripping position passively. The prolegs can be pulled away from the surface by retractor muscles that insert at the planta tip and originate high on the body wall (approximate path shown by red arrows).

The fingers of the gripper are constructed as a triangular frame with cross braces parallel to the base. When fabricated from elastic material this shape deforms towards a force applied to the long edges thereby conforming around an applied object (Figure 6). This is called the Fin Ray^® Effect (Pfaff et al., 2011), and it helps to maximize the contact surface area of a soft gripper (Crooks et al., 2016). Elastic energy stored in the material restores the gripper to its undeformed state when the force is removed.

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Fig. 6.

A demonstration of the Fin Ray® Effect. When a force is applied to the long side of the triangle, the triangle bends towards the force rather than away from the force. For Branch Bot’s grippers the bending force is the normal force from the substrate. This causes the fingers of the gripper to conform around the substrate.

2.3. Dynamic model and control architecture

The motor tendon system provides tension-based actuation that is similar to that of natural muscle. However, the tendon system also brings control challenges that are shared with soft animals such as Manduca. For example, in the absence of articulated joints or antagonistic actuators, movement of the body can become decoupled from that of the tendon and motor. This is particularly noticeable when the motor is unwinding faster than the body is re-extending, and the tendon becomes slack. We represent this phenomenon by modeling the actuated part of the robot (gripper or body segment) as a damped spring. We ignore the mass of the robot because the motions are quasi-static. When the tendon is in tension, the body segment or gripper is coupled to the motor (Figure 7 and Equations (1)–(5)). When the tendon is slack, the motor is decoupled from the gripper or body segment (Figure 8 and Equations (6)–(8)). These two states create an interesting control problem. (See Table 1 for a summary of the notation.)

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Fig. 7.

Schematic describing the dynamics of the motor tendon system when the tendon is in tension. The gripper is modeled as a damped spring. When the F T goes to zero, the dynamics switch to the decoupled dynamics. The equations of motion for this system are Equations (1)–(5).

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Fig. 8.

Schematic describing the dynamics of the motor tendon system when the tendon is slack. When the tendon is slack, the motor is decoupled from the gripper. The gripper is modeled as a damped spring. When slack is removed from the tendon, the dynamics switch to the coupled dynamics. The equations of motion for this system are in Equations (6)–(8).

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Table 1.

Symbol definitions.

Symbol	Brief description	Reference
b	Damping constant	Equation (2)
b θ	Effective rotational damping	Equation (1)
F	Force	Figure 6
F T	Force of tension in tendon	Equation (1)
i	Current through motor	Equation (1)
J	Effective rotational inertia of the motor	Equation (1)
K τ	Motor torque constant	Equation (1)
k	Spring constant	Equation (2)
N	Gear ratio of motor	Equation (1)
n	Number of data points	Section 4.1
p	Probability null hypothesis is true	Section 4.1
r	Radius of pulley	Equation (1)
x	Displacement of gripper/body	Equation (2)
θ	Rotation of motor before gearing	Equation (1)

The second-order ordinary differential equation representing the relationship between the motor shaft angle θ , the applied current, i, and the tension in the tendon, F T , when the system is coupled is

J θ ·· = − b θ θ · + i K τ − F T r N

(1)

where J is the motor rotational inertia, b θ is the rotational viscous friction constant, and N is the gear ratio.

Assuming a quasi-static model for the body of the robot (inertial effects are negligible), the differential equation relationship between the extension of the body, x, the spring force, and damping force of the body is

F T = kx + b x ·

(2)

where k is the spring constant of the body and b is the viscous friction constant. The algebraic relationship between the extension of x and the rotation of the motor shaft is

x = θ r N

(3)

where r is the radius of the spool on which the tendon is wound. Substituting Equation (3) into Equation (2), substituting that relationship for F T into Equation (1), and combining terms results in Equation (4), the new second-order differential equation accounting for the coupling between the body dynamics and the motor dynamics is

J θ ·· = − ( b θ + b r 2 N 2 ) θ · + i K τ − k θ r 2 N 2

(4)

The dynamics switch to the dynamics of the decoupled system when

F T = 0

(5)

The dynamics of the decoupled system are

0 = kx + b x ·

(6)

J θ ·· = − b θ θ · + i K τ

(7)

Because the system is decoupled there is no relationship between x and θ The dynamics of the system switches to the coupled dynamics when

x = θ r N

(8)

Hence, as the gripper is opened or the body segment compressed, F T > 0 and the dynamics are coupled.

In contrast, as the gripper is closed or the body segment extended, the dynamics can be either coupled or decoupled, often switching between the two states over the course of the motion. In the decoupled state the slack tendon can become tangled leading to an interesting control problem. We minimized the impact of this issue, while keeping the controller simple, by using a proportional–integral–derivative (PID) loop to control the position of the motor. We kept the proportional and integral gains low ensuring stability when the states switch. The integral term was needed to compensate for the spring and to prevent steady-state error when the system was in the coupled state. If the integral or proportional term was set too high, the system would be unstable in the decoupled state. Other possible solutions to this problem, including changing the actuator, are discussed in Section 5.2. The input to the PID loop is the desired position of the motor. This value steps between high and low values over the course of a single step (Figure 9).

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Fig. 9.

The control input to the different PID loops controlling the position of the motors over the course of a single step. See Figure 11 for how the robot moves in response to this input.

A mbed LPC1768 microprocessor serves as the robot controller. A sequence of motor activations are programmed into the microprocessor to create a “gait” for the robot. Each motor is controlled by a PID control loop that ensures that the motor moves the shaft and tendon pulley through the desired number of rotations. The microprocessor controls the motors using three TB6612FNG Dual Motor Driver Carriers from Pololu. The motors for the grippers are Pololu 6 V 100:1 Micro Metal Gearmotor HPCB with a Hall effect encoder, and the motors for the body segments are Pololu 6 V 50:1 Micro Metal Gearmotor HPCB with a Hall effect encoder. The motors for the grippers have a higher gear ratio than the motors for the body because it takes more force to release the gripper than it takes to contract the body. A standard desktop power supply set to 6 V provides power to the robot.

4.1. Locomotion on wooden dowel

Through empirical testing, we determined that the best step frequency was 1/12 Hz. Higher frequencies resulted in unstable motor performance caused by the nonlinear properties of the motor-tendon system. (See Section 2.3 for more details.) In addition, the natural damping in the material limited how quickly the material would relax. Even at the optimal speeds, slack would form on the tendons as the motor finished unwinding before the material completely relaxed. This slack would occasionally get tangled with the pulley or other tendons. In addition, the ideal step length was 1 cm. This was limited by the stall torque of the motors and the stiffness of the body segments. With these limitations, the expected speed of the robot without any slippage is 5 cm/min or 0.45 body lengths/min.

The crawling gait used in both orientations was standardized by activating each gripper in succession from the rear forwards (Figure 11). Crawls were recorded at 30 fps and 1 , 024 × 768 pixels and movements of the body were tracked using Kinovea software (Charmant, 2017). The weight of the Bowden cables and motors was supported to minimize their effect on locomotion.

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Fig. 11.

Sequence of movements by the robot making one step. A, also denoted in green, means the gripper is attached. O, also denoted in blue, means the gripper is open. (A) All grippers are attached and none of the body segments are compressed. (B) The tail gripper releases. (C) The rear body segment contracts moving the tail gripper forward. (D) The tail gripper attaches. (E) The middle gripper releases. (F) The rear segment extends while the front segment contracts, moving the compression forward in the robot, and moving the middle gripper forward. (G) The middle gripper attaches. (H) The head gripper releases. (I) The front segment extends moving the head forward. (J) The head gripper attaches. All grippers are now attached and the body segments are not compressed. See Figure 9 for the control input that generates this gait.

The location of the grippers was tracked over time for both horizontal and vertical locomotion (Figure 12 and Extension 1). We measured the step length by taking the difference in the position of the gripper at the start of one step and the start of the next step. This measure of step length included the distance lost due to slippage. We also calculated the velocity of the robot by multiplying the step length by step frequency. The average step length was 0.9±0.1 cm ( n = 40 ) during horizontal locomotion and 0.9±0.13 cm ( n = 11 ) during vertical locomotion. The average speed during horizontal locomotion was 4.5±0.5 cm/min or 0.4±0.04 body lengths/min. The average speed during vertical locomotion was 4.5±0.7 cm/min or 0.4±0.06 body lengths/min. These speeds are not significantly different ( p = 0 . 86 ), which is also true for the crawling and climbing of M. sexta. This suggests that Branch Bot is not significantly effected by the direction of gravity. The experimental speed is only slightly slower than the expected speed.

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Fig. 12.

Example plots of the trajectory of the robot crawling on a (a) horizontal and (b) vertical wooden dowel. (See Extension 1 for the video these plots come from). The dashed lines are the displacements based on the ideal step length and step frequency for the robot. The solid lines are the experimental displacements. During both horizontal and vertical locomotion, the tail experiences an extra step when the middle moves. In addition, during vertical locomotion, when the head releases, it falls down and off the dowel a bit because of unintended forces from the body segment buckling when compressed.

During both horizontal and vertical locomotion the tail gripper moved slightly forwards after starting its stance phase (“secondary steps" in Figure 12). This motion was very small (1 mm horizontal, 2.5 mm vertical) and corresponded to the start of the middle gripper swing phase. Interestingly, this behavior is also present in the terminal proleg of M. sexta (Trimmer and Issberner, 2007). On Branch Bot it is caused by force transmitted through the rear body segment causing the tail gripper to rotate backwards. As the middle gripper switched from being pushed by the rear body segment to being pulled forward by the front body segment, the tail was rotated forwards. During vertical locomotion the added force of the extra weight from the middle gripper caused the tail to rotate backwards even further.

During horizontal locomotion the head, middle, and tail of Branch Bot slowly pulled together over the course of multiple steps. This is visible in Figure 12a as the three lines slowly drifting apart with each step. This was likely caused by friction with the dowel when the middle and head extended. This effect was more pronounced on the head than the middle because the middle both pulled and pushed forwards in each step. During vertical locomotion, the middle segment took slightly longer steps than either the head or the tail. Presumably this occurred because the middle section moves while supported on both sides. In contrast the tail and head are only supported by the adjacent segment while they are moving and either rotate backwards (tail) or do not extend the full distance forwards (head). The overall effect is for the body segments to change length disproportionately over a series of steps. The deformation is relatively small and does not affect the performance of the robot appreciably.

The robot was very consistent at horizontal locomotion. It could crawl until the dowel ended, or until there was an error with one of the pulleys (i.e. the tendon gets tangled). The robot was less consistent during vertical locomotion but could still climb for nine successive steps. The most common failure occurred when the head gripper released while the front body segment was compressed. During compression the body segments tend to buckle away. This buckling results in unintended forces on the grippers. Although this did not cause a problem for horizontal crawling, it did cause the front gripper to rotate away from the substrate when climbing and sometimes led to the robot toppling backwards (Figure 12b). This effect could be minimized by shortening the segments to reduce the toppling moment or by reshaping the anterior segments to minimize backwards buckling. Both of these changes would more closely resemble the anatomy of M. sexta.

4.2. Locomotion on branch

Branch Bot was tested on a variety of branches. Each was approximately 0.8 cm in diameter. The smallest diameter section was 0.48 cm and the largest was 1.27 cm. These sections were knots and stubs of broken off branches where the diameter of the branch sharply increased or decreased. The branches were oriented so that the robot was mostly moving horizontally, but the orientation varied appreciably along the length.

Branch Bot could move along all of the branches using the same gait that it used for crawling along the wooden dowels (Figures 13 and 14). This result demonstrated an important advantage of the soft body design; despite the changing direction and diameter of the branch, a single pre-configured motor program produced effective crawling. Because it can passively conform to changes in the substrate, the robot is able to interact with its environment and move past obstacles. The morphological computation of the body allowed it to crawl on a complicated substrate without a complicated control algorithm. For example, when the robot encountered large knots, forward progression would slow or cease, and the body and grippers would deform thereby altering the direction of the applied forces. In many cases this was sufficient for the gripper to release after several actuation cycles. In more extreme cases this strategy is insufficient, and we expect that feedback control and added controlled DOFs will be necessary to avoid getting stuck. Adding additional sensors to the control system would significantly improve adaptability. For example, by detecting that forward progress has been impeded, Branch Bot could reverse its stepping pattern, back away from the obstruction, and then advance forward; slight changes in the body posture and gripping position might be sufficient to overcome the obstacle. Another strategy would be to use an extra controlled DOF to arch the body so that the leading gripper can be maneuvered around knots and other irregularities.

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Fig. 13.

The path of the head, middle, and tail of Branch Bot while it crawls along the branch. The robot is using a simple gait that does not control for the curvature and changing diameter of the branch. Instead the conformability of the body compensates for the curvature and changing diameter of the branch.

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Fig. 14.

The path of the head, middle, and tail of Branch Bot while it crawls along the branch that curves to the side. The video is taken from the top pointing down. The robot is using a simple gait that does not control for the curvature and changing diameter of the branch. Instead the conformability of the body compensates for the curvature and changing diameter of the branch.

4.3. Gripper performance

The performance of the gripper was quantified on a 0.8 cm diameter uniform wooden dowel by pulling a string attached to the gripper and measuring the applied force. The force was measured using a Harvard Apparatus Isometric Force Transducer (No. 60-2996). When the gripper was attached, the force sensor was set to the 500 g range; when the gripper was released, the force sensor was set to the 50 g range. The string was attached to the base of gripper using a square knot. The force was slowly increased until the gripper lost its grip and fell off. The peak measured force in each trial was recorded in four configurations: with the gripper in the released or attached state and with the force applied along the axis of the dowel (axial) or pulling away from the dowel (normal) (Figure 15).

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Fig. 15.

The experimental setup for testing the effectiveness of the gripper. The isometric force transducer is connected to the gripper using a string. The isometric force transducer is then slowly pulled on with an increasing force until the gripper comes off the dowel. We tested the gripper with the force applied along the dowel, or axial, and pulling the gripper off the dowel, or normal.

In the axial direction the gripper supported 1.39±0.1 N ( n = 20 ) when gripping and 0.207±0.1 N ( n = 20 ) when released. In the normal direction the gripper supported 1.34±0.15 N ( n = 20 ) when gripping and 0.097±0.04 N ( n = 20 ) when released. The performance of the grip in the axial direction is particularly important for the robot. Most of the forces acting on the gripper during horizontal and vertical locomotion are in the axial direction. During horizontal locomotion, the forces from the body segments act on the gripper in the axial direction. During vertical locomotion, the grippers also have the weight of the robot acting on it in the axial direction.

Branch Bot’s grippers can support up to five times the weight of the robot (25.8 g). We know that the grippers can support the forces encountered during horizontal and vertical locomotion because the robot crawls at the same speed during both.

Although we only quantified the performance of the grippers on 0.8 cm diameter dowel, we have done some trials on larger diameter dowels. Attachment forces in both the gripping and released states increase with substrate diameter. This is simply a function of the elasticity of the gripper which produces more force at larger displacements. The geometry of this gripper limits the maximum releasable substrate to around 15 mm and the smallest grippable dowel to approximately 3 mm.

5.1. Comparison of Branch Bot with other caterpillar-inspired robots

Table 2 is a comparison of the speeds of various caterpillar-inspired robots to Branch Bot. All these robots use grippers to attach to the substrate. We compared Branch Bot with robots that use a crawling gait, defined as a gait using more than two grippers, and robots that use an inching gait, defined as a gait using two grippers. Not all robots are capable of climbing. Branch Bot is the fastest robot that uses a crawling gait, but it is slower than the robots that use an inching gait. When speed is expressed in body lengths per minute, Branch Bot is still the fastest crawling robot and also faster than one of the inching robots. One reason that the inching robots are generally faster than the crawling robots is that a crawling step consists of more actions than an inching step. For example, a step of Branch Bot’s crawling gait is 10 actions. If Branch Bot used an inching gait, a step would only be 7 actions. This difference would be more extreme with more grippers. The advantage of crawling, and the reason that so many caterpillars use it over inching, is that the increased number of attachment points reduce the risk of falling and increases the weight the robot/animal can carry.

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Table 2.

Speed of Branch Bot compared with other caterpillar-inspired robots. The robots in this table are all caterpillar-inspired robots in the literature that use grippers to crawl or climb. An inching gait is defined as a gait that uses two grippers. A crawling gait uses more than two grippers.

Robot name	Gait type	Speed (cm/min)	Speed (body lengths/min)
Branch Bot	Crawling	4.5	0.4
Tree Bot (Lam and Xu, 2011a,b)	Inching	22.4	0.34
PISRob (Xie et al., 2018)	Inching	61.2	2.87
Mini-modular climbing caterpillar robot (Wang et al., 2009)	Inching	16.67	1.06
Mini-modular climbing caterpillar robot (Wang et al., 2009)	Crawling	3.33	0.1
A caterpillar climbing robot (Wang and Wu, 2016)	Crawling	1.65	0.04

5.2. Limitations and future development

Although Branch Bot has too few grippers to effectively model all aspects of caterpillar locomotion, it is relatively straightforward to increase the number of grippers or to simply couple two robots together and coordinate their motor patterns to function as one unit. With more body segments the robot could be used to study various aspects of caterpillar locomotion such as visceral-pistoning (in which extension of the head is coupled to the initiation of a crawl) (Simon et al., 2010) and the environmental skeleton strategy (in which caterpillars stay in tension and apply compressive forces to the substrate) (Lin and Trimmer, 2010a).

A major limitation of the current Branch Bot is that it is driven by off-board motors. Moving the motors, power, and control hardware off the body was an intentional design choice that enabled us to study the performance of the robot without the added weight and rigidity of these components. Although we were careful to support the Bowden cables, it is possible that the dynamics of the robot are affected by the tethers so it is important to make an untethered version of Branch Bot. Placing actuators into any soft robot is a significant challenge because traditional motors and solenoids are rigid, heavy, and likely to compromise deformability. Although pneumatic systems such as PneuNets are conformable, these are mostly suitable for manipulators and grippers where the power source, compressors, and valving can be off-board. It is very difficult transfer this hardware onto a climbing machine.

As with our monolithic 3D printed robots (Umedachi et al., 2016), Branch Bot is electrically powered and uses tension-based actuators that best mimic natural muscle. It is therefore relatively straightforward to design and build a fully untethered version. This can be implemented using active materials (electroactive polymers, shape-memory alloys, etc.) or by placing motors and control circuitry where they do not interfere with the movements of the soft chassis. One approach is to place them in a posterior section that hangs like a tail. Not only does this reduce the backwards toppling moment during upwards climbing, but it can also stabilize horizontal climbing by keeping the robot’s center of mass below the centroid, a strategy that is common in climbing animals.

Although Branch Bot is faster than many other caterpillar-inspired crawling robots, it is still too slow for most practical applications. It makes up for its speed by being consistent. During horizontal locomotion, it only stops crawling due to errors rising from slack in the tendons (see Section 2.3 for details). There are a few ways to prevent the tendons from going slack. The simplest would be to use very slow speed motors so that elastic recovery of the body is always sufficient to maintain tendon tension. This is not guaranteed to work in all circumstances and it would slow the robot down even further. Another possible solution is to use a back-drivable actuator such as a direct drive motor or a clutch system. In this configuration disabling the power supply to the motor or clutch will allow the elasticity of the soft robot components to close the gripper or extend the body segments without slack forming in the tendon. In each of these cases it will be important to match the torque and speed requirements of the actuator to the mechanical properties of the robot components.

Another major limitation of Branch Bot is that buckling of the body segments can lead to inconsistent vertical locomotion. This could be resolved by redesigning the anterior body segments to promote buckling towards the substrate. It is worth noting that a similar bias is found in the mechanical properties of the body segments of M. sexta which are more easily bent ventrally than dorsally.

Another future step is to improve the biomimicry of the grippers. Caterpillars use crochets, small spines on the ends of their prolegs to grab onto substrates (Figure 5b). These spikes dig into the substrate like grappling hooks. The crochets are embedded in a very soft membrane that can be collapsed by the contraction of a retractor muscle to release the grip. Currently the grippers on Branch Bot rely on friction and adhesion. The addition of crochets to the gripper would reduce the amount of force needed to actuate the gripper while also improving the effectiveness of the gripper. Designing a soft gripper that uses crochets will require carefully interfacing of the stiff microspines with the compliant soft polymer of the robot gripper.