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Lensgraf, Samuel ; Itani, Karim ; Zhang, Yinan ; Sun, Zezhou ; Wu, Yijia ; Li, Alberto Quattrini ; Zhu, Bo ; Whiting, Emily ; Wang, Weifu ; Balkcom, Devin ( , International Conference on Robotics and Automation)This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space velocities, yielding a linear programming formulation that allows analysis of systems with thousands of rigid bodies. Potential applications include analysis of collections of modular robots, structural stability perturbation analysis, tolerance analysis for mechanical systems, and formation control of mobile robots.more » « less
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Zhang, Yinan ; Balkcom, Devin ( , Workshop on the Algorithmic Foundations of Robotics)This paper presents a design for interlocking blocks and an algorithm that allows these blocks to be assembled into desired shapes. During and after assembly, the structure is kinematically interlocked if a small number of blocks are immobilized relative to other blocks. There are two types of blocks: cubes and double-height posts, each with a particular set of male and female joints. Layouts for shapes involving thousands of blocks have been planned automatically, and shapes with several hundred blocks have been built by hand. As a proof of concept, a robot was used to assemble sixteen blocks. The paper also describes a method for assembling blocks in parallel.more » « less
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Lensgraf, Samuel ; Itani, Karim ; Zhang, Yinan ; Sun, Zezhou ; Wu, Yijia ; Li, Alberto Q. ; Zhu, Bo ; Whiting, Emily ; Wang, Weifu ; Balkcom, Devin ( , International Conference on Robotics and Automation (ICRA))This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space velocities, yielding a linear programming formulation that allows analysis of systems with thousands of rigid bodies. Potential applications include analysis of collections of modular robots, structural stability perturbation analysis, tolerance analysis for mechanical systems, and formation control of mobile robots.more » « less