Compression-only arch structures are structurally highly efficient in force equilibrium. However, the material efficiency is offset by the traditional use of scaffolds ...
Robotic Equilibrium: Scaffold Free Arch Assemblies
Kaicong Wu Princeton University Axel Kilian Princeton University
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ABSTR ACT Compression-only arch structures are structurally highly efficient in force equilibrium. However, the material efficiency is offset by the traditional use of scaffolds to position materials and counter the out-of-equilibrium forces during assembly. We introduce a method of sequentially assembling compression-only structures without a scaffold by robotically maintaining the compression equilibrium in every step. A two-arm collaborative robotic setup was used to maintain force equilibrium throughout arch assembly. The arms took turns first hot-wire cutting and placing blocks then providing a temporary scaffold to support the arch end point. To test the approach, a single catenary arch was generated using form-finding techniques and sequentially built from foam blocks. Moving forward we show the relationship between the joint valence (largest number of joined branches) of a multi-branched structure and the minimum number of robotic arms required for assembly using our initial technique. With only two robotic arms available, the technique was further developed to reduce the required number of arms per arch branch from two to one by attaching caterpillar tracks at the block-supporting end effector. This allows a human to load the next block and the arm to move forward along the arch while maintaining equilibrium. Results show that robotic equilibrium scaffold-free arch assembly is possible and can reduce scaffold waste and maintain the material efficiency of compression-only structures. Future work will explore further applications of assistive robotics in construction, replacing static construction aids with dynamic sensory feedback of equilibrium forces.
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Partially constructed compression-only arch structures using a two-arm collaborative robotic setup to provide equilibrium forces during construction. In the early stage, the partially constructed arch end was maintained only by the weight of a new block, and no additional compression force was applied. Thus only a few blocks can be constructed without collapse.
INTRODUCTION The material efficiency of compression-only structures is partially offset by the need for precise custom scaffolds to support the incomplete structure during construction. Due to the irregular geometric forms, the scaffolds are often highly detailed and require custom fabrication using techniques such as CNC milling, thus increasing costs, energy use, transportation, and material waste (Davis et al. 2012; Block et al. 2017). Moreover, scaffolds must be manually assembled and demolished on-site, further increasing the efforts to maintain precision. Precedent research focused on reducing scaffold waste for compression-only structures using a number of different approaches. One conceptually similar approach explored the use of chains and specially designed sequences for maintaining equilibrium during vault assembly, where the number of trivial cable supports along the unfinished shell edge can be reduced substantially through structural analysis in the more complex case of shell structures (Deuss et al. 2014). However, a large anchoring framework must be designed to connect the chains and the structural elements. Another approach is inspired by the construction techniques of traditional Nubian and Catalan tile vaulting to reduce scaffold waste by relying on ribs for building surface geometries between them with minimal guidance (Block et al. 2014). However, the material waste and labor effort spent on constructing the ribs for large-scale compression-only structures still cannot be avoided with the approach. Meanwhile, advances in collaborative robotic fabrication and assembly have shown the potential of reducing the scaffold waste for compression-only structures. Substantial progress has been made in developing more materially sustainable scaffolds, such as collaboratively hot-blade cut foam molds (Rust et al. 2016; Søndergaard and Feringa 2017). Recent studies of collaborative robotic fabrication have shown the potential of achieving construction tasks that cannot be done with individual robots without additional scaffolds (Parascho et al. 2017). For instance, where one robotic arm stabilizes partially built parts, a second arm positions a to-be-assembled component at the same time. Thus in lightweight structures, collaborative robotic assembly is a possible alternative approach to static supports. We explored how collaborating robotic arms can support partially constructed structures, and this method was tested through two different approaches. For the first approach, two robotic arms alternate in first cutting and then adding a to-be-assembled block to the open end of
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an arch, which allows the other robotic arm previously holding the last block to release its block. This assembly sequence provides the necessary compression force just in time to maintain the force equilibrium in the assembled arch. Known limitations are the 40 kg payload limit of the chosen ABB IRB-4600 robotic arm. Therefore, their use for counteracting the arch compression forces is limited to the lightest of materials. The load limit can be potentially increased by replacing the two arms with other robot models that have a larger payload. The approach was tested by building a 3 m wide compression-only arch from expanded polystyrene (EPS) foam blocks. Further limitations arise when expanding the method to non-planar branching arches due to the relationship between the joint valence (largest number of joined branches) and the number of robotic arms required in the first approach. Thus our second approach is developed by attaching custom caterpillar tracks as end effectors for providing the equilibrium forces, allowing for a single arm to continuously support an arch segment as it lengthens. As a result, the number of arms required per branch can be reduced from two to one. It was tested by partially building a multibranched compression-only arch structure. Results show that scaffold waste can be avoided using this construction technique to maintain the material and structural efficiency of compression-only structures.
METHODS Fabrication and Assembly Setups
In a first test, one robotic arm counteracts the weights of the to-be-assembled blocks and the compression forces at the end of the partially assembled structures, and another arm loads a new fabricated component. Lightweight (16–45 kg/m3) expanded polystyrene (EPS46) foam blocks (600 x 300 x 250 mm) were used. A hot-wire cutter was calibrated for cutting foam blocks into the desired geometry, with component faces perpendicular to the flow of forces (Figure 2). The arm that positions the new block then holds the arch end while the previous arm detaches and gets the next foam block. Generating Compression-Only Structures through Form Finding
To realize structural equilibrium in every construction state without additional supports, a partially assembled compression-only structure bears axial forces. Formfinding techniques like Gaudi’s hanging chain model (Kilian and Ochsendorf 2005; Adriaenssens et al. 2014) were simulated in the “Kangaroo Physics” add-on for the Grasshopper plug-in of Rhinoceros. Two different structures were generated by adding loads vertically and modeling each element of a virtual hanging spring chain. By
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fixing the supports, all the middle joints can move freely in the vertical and horizontal directions. A composite hanging chain form is computed through the Kangaroo solver by finding the balance between the spring forces and the point loads. An arch was found for testing the basic sequential steps of assembling a planar arch (Figure 3a). A chain network was used to compute the form of a multi-branched arch structure for testing a more complex construction process (Figure 3b). Both structures are bearing axial
A core question is how to reduce the number of necessary robot arms to make the approach more practicable. The biggest challenge is the joining of multiple partially
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compression-only forces and were offset with the same cross section of the chosen material for minimizing the necessary cuts (although varying cross sections can be computed based on the force diagram). Reducing the Number of Necessary Robot Arms
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The setup in the first approach: two robotic arms taking turns to cut and assemble foam blocks and provide the necessary force to main equilibrium at the end of a partially constructed compression-only arch.
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The well-established principle of generating compression-only structures through form finding for (a) a planar arch (b) and a multi-branched arch.
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Assembly sequence processing: the number of necessary robot arms for a branching arch structures is n+1 of the highest joint valence n with each red dot being one robotic arm.
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Using a human as the block loader, the number of necessary robots per arch segment is further reduced from 2 to 1, since equilibrium forces in line with the catenary arch are provided through caterpillar tracks that move synchronously with the repositioning of the robotic arm that holds them in order to reposition the support to the new end of the arch.
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a) A to-be-assembled foam block was attached to the robotic arm and passed through a hot-wire cutter and driven directly to the desired assembly position. b) A keystone connecting three branches was cut by aligning the ruled surfaces of each face with the hot wire. c) When one arm was out of working range, the block was transferred to the other arm for finishing the remaining cuts.
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constructed arch segments in a high valence node. Every such arch end needs one robotic arm to maintain equilibrium and an extra robotic arm is needed for adding new arch blocks (Figure 4). With only two robot arms available in our setup, there are not enough supports for a branching structure using the above approach. To still be able to test a multi-branched structure, the number of necessary robots is further reduced by attaching caterpillar tracks to the robot end effector replacing the previous screw fixation of the blocks to the end effector. Precutting the blocks and keystones, our goal is to maintain the equilibrium force by moving the caterpillar tracks synchronously with the movement of the robot arm that is keeping the blocks in compression during the addition of a new block (Figure 5). Hinged by a rod and folded by a linear actuator, the end effector—which has one plate positioned by the robotic arm
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and the other plate angled by the linear actuator—can hold a loaded block and move along it using the combination of caterpillar motion and robotic arm repositioning (Figure 5). Robotic Cutting Arch Components and Keystones
Another challenge is to cut every arch component out of the chosen foam blocks. A hot-wire cutter has been calibrated, and a foam block is manually attached and passed through the wire for trimming off the unwanted parts (Figure 6a). The keystones connecting multiple arch branches are modeled by lofting the to-be-connected faces. A known method is aligning the ruling lines of a surface with the wire (Søndergaard et al. 2016), but cutting the faces of a keystone is prone to exhaust the joint limits of the robotic arm (Figure 6b). Our solution is to use one arm to partially cut the keystone and transfer it to the other arm for the remaining cuts (Figure 6c).
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A first experiment showing the basic sequential process of providing force equilibrium during the assembly of a compression-only arch.
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The synchronization of the movements between robotic arms and end effectors to maintain equilibrium and correct the support angle.
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A further experiment tested maintaining the equilibrium forces using caterpillar tracks during the adjustment of the supporting robotic arm.
RESULTS
Further Experiment for a Compression-Only Multi-
First Experiment for a Compression-Only Arch
branched Assembly
For a first experiment, path-planning of the dual arms and tracks was programmed in “Robots,” an add-on for the Grasshopper plug-in of Rhinoceros (Vicente Soler, Vincent Huyghe, 2016) to sequentially cut an attached foam block with the hot-wire cutter (Figure 6) and then position the fabricated component into the target position. Once a new block arrives, the previous arm can move away so that the arch end is continuously supported, and the released arm is free to load a new component into the structure. Two end effectors were built to hold the foam blocks that were manually secured by screws to the inside surface of the arch foam blocks. Ten foam blocks forming a 3 m wide arch were constructed with our sequential force equilibrium collaborative robotic method. Although adjacent blocks were precisely placed next to each other in sequence, small fabrication errors in the foam blocks caused the arch to slightly slump when the inner arm was released during the handover between robot arms (sequence shown in Figure 7).
For the experiment for the second assembly approach, the most challenging path-planning task is the synchronization of the movements of the robotic arm, the caterpillar tracks, and the linear actuators. This is realized by controlling the end effector with Arduino and sending serial signals to trigger the movements of the above actuators (Figure 8). Another Grasshopper plug-in, “Taco,” was added to read the position of the robots in real time (Frank, Wang, and Sheng 2016). Once the movement of an arm is detected, the caterpillar is turned on to compress the partially constructed structure without losing the equilibrium forces. Once the movement is finished, a linear actuator is triggered to set the hinge of the support plate to the next desired angle (Figure 9).
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CONCLUSION We developed a method of collaborative robotic assembly for force-equilibrium compression-only structures. Using the robotic arms sequentially allows all in-between states of the arch during construction to stay in equilibrium, thus removing the need for scaffolding. Major limitations
come from the robotic reach envelope and the load limits. For large-scale structures, a solution might be the use of roaming platforms for unlimited horizontal reach envelopes. By implementing the caterpillar loading gripper, we successfully reduced the number of necessary robots for an arch branch further down to one. Future work includes the feedback-enabled driving of the caterpillar tracks so that the robotic system can adjust its toolpaths according to the sensed forces in real time. Considering scaffold waste as a design constraint for compression-only structures, robotic force equilibrium assemblies maintain the material efficiency by avoiding waste. We believe our method can enhance the overall efficiency of compression-only structures, including their construction process, by reducing material waste and speeding up construction, thus cutting costs. If the method can be successfully scaled, it may open up new possibilities for the use of catenary structures in architecture and engineering.
ACKNOWLEDGEMENTS The authors want to specially thank Ryan Luke Johns for his great efforts on the calibration of the dual-arm system and preparing a specific library for the “Robots” add-on of Grasshopper that can work with our machine setups. We also want to thank our lab manager Grey Wartinger for the related installation and hardware solutions in this project.
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Blickfeld. http://blickfeld7.com/architecture/rhino/grasshopper/ Taco/ Kilian, Axel, and John Ochsendorf. 2005. “Particle-Spring Systems for Structural Form Finding.” Journal of the International Association for Shell and Spatial Structures 46 (2): 77–84. Parascho, Stefana, Augusto Gandia, Ammar Mirjan, Fabio Gramazio, and Matthias Kohler. 2017. “Cooperative Fabrication of Spatial Metal Structures.” In Fabricate 2017: Rethinking Design and Construction, edited by Achim Menges, Bob Sheil, Ruairi Glynn, and Marilena Skavara, 24–29. London: UCL Press. Rust, Romana, David Jenny, Fabio Gramazio, and Matthias Kohler. 2016. “Spatial Wire Cutting: Cooperative Robotic Cutting of Non-ruled Surface Geometries for Bespoke Building Components.” In Living Systems and Micro-Utopias: Towards Continuous Designing, Proceedings fo the 21st Annual Conference of the Association for Computer-Aided Architectural Design Research in Asia, edited by S. Chien, S. Choo, M. A. Schnabel, W. Nakapan, M. J. Kim, and S. Roudavski, 529–38. Melbourne, Australia: CAADRIA. Søndergaard, Asbjørn, and Jelle Feringa. 2017. “Scaling Architectural Robotics Construction of The Kirk Kapital Headquarters.” In Fabricate 2017: Rethinking Design and Construction, edited by Achim Menges, Bob Sheil, Ruairi Glynn, and Marilena Skavara, 264–71. London: UCL Press. Søndergaard, Asbjørn, Jelle Feringa, Toke Nørbjerg, Kasper Steenstrup, David Brander, Jens Graversen, Steen Markvorsen, Andreas Bærentzen, Kiril Petkov, and Jesper Hattel. 2016. “Robotic Hot-Blade Cutting.” In Robotic Fabrication in Architecture, Art and Design 2016, edited by Dagmar Reinhardt, Rob Saunders, and Jane Burry, 150–64. Cham, Switzerland: Springer.
A. Pigram. 2014. “Ribbed Tiled Vaulting: Innovation Through Two Design-Build Workshops.” In Fabricate 2014: Negotiating Design
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Langenberg, 22–29. London: UCL Press. FABRICATE 2014. Block, Philippe, Tom Van Mele, Matthias Rippmann, and Noelle Paulson. 2017. Beyond Bending: Reimagining Compression Shells.
IMAGE CREDITS All images are created by the authors.
Munich: Edition Detail. Davis, Lara, Matthias Rippmann, Tom Pawlofsky, and Philippe Block. 2012. “Innovative Funicular Tile Vaulting: A Prototype Vault in Switzerland.” Structural Engineer 90 (11): 46–55. Deuss, Mario, Daniele Panozzo, Emily Whiting, Yang Liu, Philippe Block, Olga Sorkine-Hornung, and Mark Pauly. 2014. “Assembling Self-Supporting Structures.” ACM Transactions on Graphics 33 (6): 214. Frank, Florian, Shih-Yuan Wang, Yu-Ting Sheng. 2016. “Taco.”
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Kaicong Wu is a PhD Candidate at the School of Architecture of Princeton University. He received a Master of Architecture from University of Pennsylvania and a Bachelor of Architecture from Shanghai Jiao Tong University. His research focuses on robotic assembly and architectural design generation.
Axel Kilian has taught and researched as an Assistant Professor at Princeton University and Delft University of Technology, and as a Postdoctoral Associate at MIT. He holds a PhD in Design and Computation and a Master of Science in Architectural Studies from MIT, as well as a professional degree in architecture from the University of the Arts Berlin. He attended MIT on a GermanAmerican Fulbright scholarship. His most recent research work in architectural robotics has been exhibited in the 2016 Istanbul Design Biennale and the 2017 Seoul Biennale of Architecture and Urbanism. His current research is on embodied computation.
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