Branching Vine Robots for Unmapped Environments

While exploring complex unmapped spaces is a persistent challenge for robots, plants are able to reliably accomplish this task. In this work we develop branching robots that deploy through an eversion process that mimics key features of plant growth (i.e., apical extension, branching). We show that by optimizing the design of these robots, we can successfully traverse complex terrain even in unseen instances of an environment. By simulating robot growth through a set of known training maps and evaluating performance with a reward heuristic specific to the intended application (i.e., exploration, anchoring), we optimized robot designs with a particle swarm algorithm. We show these optimization efforts transfer from training on known maps to performance on unseen maps in the same type of environment, and that the resulting designs are specialized to the environment used in training. Furthermore, we fabricated several optimized branching everting robot designs and demonstrated key aspects of their performance in hardware. Our branching designs replicated three properties found in nature: anchoring, coverage, and reachability. The branching designs were able to reach 25% more of a given space than non-branching robots, improved anchoring forces by 12.55×, and were able to hold greater than 100× their own mass (i.e., a device weighing 5 g held 575 g). We also demonstrated anchoring with a robot that held a load of over 66.7 N at an internal pressure of 50 kPa. These results show the promise of using branching vine robots for traversing complex and unmapped terrain.


B. Search Performance
Below ( Fig. S.1.) is the data used to generate the results in Fig. 3-A. We performed 10 runs to 400 generations each. We ran each experiment in both the Cave and Grid type environments. The small variance and quick climb of fitness in the Grid environment suggests that it was a smoother fitness landscape than the Cave environment. We also show the output of the best performing individual from generations 1, 10, 100, and 400 from one run of optimization in Fig. S.2. This is a single, representative example to illustrate the overall improvements in efficiency and coverage of the area.

C. Search Method Comparison
To verify that a given search method was finding quality solutions, we used a simplified task that did not rely on obstacle interactions or introduce randomness into the fitness evaluation. For this task, we initialized the given design in an open space with no obstacles present. We rewarded the unique area covered and penalized the total length of the design (f itness = 6 * area − covered − 0.02 * total − length). To improve understanding of the fitness, we set the penalty for length to be an order of magnitude smaller than the area for reward. This meant that an optimal design should have maximized the number of sensors with no overlap between the sensed areas. Any designs that met these criteria could then be compared through the total length used to maximize this sensor area (where a shorter length is better). While analogous to a circle packing problem, the parameterized design of the robot added additional constraints which made the optimized solutions less dense. A comparison of the results from a genetic algorithm and particle swarm algorithm are seen in Fig. S.2. The resulting design shown in (Fig. S.3-A) was generated by the custom evolutionary algorithm and those shown in (Fig.  S.3-B) was generated by a commercially available particle swarm search (Matlab). The total length of the design in Fig.  S.3-A was 2303.1, and the total length of the design in Fig. S.3-B was 2303, a difference in length of .005%. To test the reliability of the results, we ran five trials of the evolutionary algorithm, and only two of the five solutions were within 5% of the optimal length found by the particle swarm search. The fact that three of the five random seeds produced sub-optimal designs demonstrates the risk of getting stuck in a local optimum. Finally, the two optimized designs in Fig. S.2 have nearly the same fitness but with distinct morphologies, showing that there may be multiple fit design solutions for a certain task with this type of robot. For the evolutionary algorithm we used a (µ+λ) method with an elite pool of six in a population of 54 to preserve promising candidates since each fitness evaluation only provides an approximate estimate of true fitness. , and a commercially available particle swarm search (B) were qualitatively different, the fitnesses of the two designs were within 0.005%..

Sensor Coverage Heuristic
Area Factor (AF ) was based on measured area covered as a percentage of the total possible area. Area Efficiency (AE) and Length Efficiency (LE) were intended to penalize overlapping area i.e. promote unique coverage and were split up to allow for different costs based on design or fabrication constraints. Length Penalty (LP ) was used based on total length of the design to promote shorter designs where coverage or efficiency were equal. Each of these variables had a scalar of +1 added which was a legacy from older heuristic tests.

D. Laser Settings and TPU properties
We used a laser welding process for repeatable fabrication of the branching vine robots. This fabrication method allowed us to simultaneously cut and seal the actuator to remove excess material from the contractile section of the actuator which can restrict motion. We used a thermoplastic polyurethane (Stretchlon, Fibreglast) which can stretch up to 400-500% its original length. We performed tensile tests on five samples to test the elasticity and strain of the TPU material. The samples were strained at 0.05 mm/mm/s until failure. We ultimately did not use this relationship in our models, but have provided it as a reference.
This material was robust, making it a good material choice for a collapsible robot. Laser welding the TPU required fine tuning of the laser cutter settings until the pouch successfully sealed. To laser weld the TPU layers, we used the following procedure: Steps for TPU Laser Sealing 1) Place the TPU layers on heat press and roll out any bubbles.
2) Press both layers of tpu at 77 o F for 2 minutes 3) Let the TPU cool on the heat press for 5 minutes To laser weld the actuator, we used a commercial, digitally controlled C0 2 laser machining system (PLS6MW, Universal Laser Systems). We used two sets of settings to cut and seal the actuator. The first set of settings cut and sealed the the actuator simultaneously. Those settings were 80 % power, 100 % speed, and 500 pulses per inch at a bed height at 0 mm. We also tested settings that just sealed the top TPU layer to the bottom layer. These settings were 20 % power, 100 % speed, and 500 pulses per inch at a bed height at 0 mm.