A Temporal Coherent Topology Optimization Approach for Assembly Planning of Bespoke Frame Structures

We present a computational framework for planning the assembly sequence of bespoke frame structures. Frame structures are one of the most commonly used structural systems in modern architecture, providing resistance to gravitational and external loads. Building frame structures requires traversing through several partially built states. If the assembly sequence is planned poorly, these partial assemblies can exhibit substantial deformation due to self-weight, slowing down or jeopardizing the assembly process. Finding a good assembly sequence that minimizes intermediate deformations is an interesting yet challenging combinatorial problem that is usually solved by heuristic search algorithms. In this paper, we propose a new optimization-based approach that models sequence planning using a series of topology optimization problems. Our key insight is that enforcing temporal coherent constraints in the topology optimization can lead to sub-structures with small deformations while staying consistent with each other to form an assembly sequence. We benchmark our algorithm on a large data set and show improvements in both performance and computational time over greedy search algorithms. In addition, we demonstrate that our algorithm can be extended to handle assembly with static or dynamic supports. We further validate our approach by generating a series of results in multiple scales, including a real-world prototype with a mixed reality assistant using our computed sequence and a simulated example demonstrating a multi-robot assembly application.