thesis David Jan Liedtke author 55557 Christian Scheideler supervisor 79 department Motivated by the prospect of computing agents that explore unknown environments and construct convex hulls on the nanoscale, we investigate the capabilities and limitations of a single deterministic finite automaton robot in the three-dimensional hybrid model for programmable matter. In this model, active robots move on a set of passive tiles, called configuration, with the geometric shape of rhombic dodecahedra on the adjacency graph of the face-centered cubic sphere-packing. We show that the exploration problem is equally hard in the hybrid model and in three-dimensional mazes, in which tiles have the shape of cubes and are positioned at the vertices of $\mathbb{Z}^3$. Thereby, a single robot with a constant number of pebbles cannot solve this problem in the hybrid model on arbitrary configurations. We provide algorithms for a robot with two pebbles that solve the exploration problem in the subclass of compact configurations of size $n$ in $\O(n^3)$ rounds. Further, we investigate the robot's capabilities of detection and hull construction in terms of restricted orientation convexity. We show that a robot without any pebble can detect strong $\O$-convexity in $\O(n)$ rounds, but cannot detect weak $\O$-convexity, not even if provided with a single pebble. Assuming that a robot can construct tiles from scratch and deconstruct previously constructed tiles, we show that the strong $\O$-hull of any given configuration of size $n$ can be constructed in $\O(n^4)$ rounds, even if the robot cannot distinguish constructed from native tiles. https://ris.uni-paderborn.de/download/25126/25128/Master - Thesis.pdf application/pdf 2021 eng Robot ExplorationFinite AutomatonHybrid Model for Programmable MatterConvex Hull Liedtke, David Jan. <i>Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model</i>, 2021. D. J. Liedtke, <i>Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model</i>. 2021. Liedtke DJ. <i>Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model</i>.; 2021. Liedtke, D. J. (2021). <i>Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model</i>. @book{Liedtke_2021, title={Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model}, author={Liedtke, David Jan}, year={2021} } D.J. Liedtke, Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model, 2021. Liedtke, David Jan. <i>Exploration and Convex Hull Construction in the Three-Dimensional Hybrid Model</i>. 2021. 251262021-09-29T12:37:39Z2022-01-06T06:56:53Z