SOPO-CD, a robotic placement method, was reported to be faster than comparison methods across a set of benchmark tests. In the detailed 3D Bin Packing comparison, its reported advantage over grid search was more than 200 times at the largest grid size. The result comes from an arXiv version 1 preprint dated 25 August 2026.
The tests covered 2D Tangram, 2D Tetris and 3D Bin Packing. The abstract-level summary reports a 10-times Tangram speedup, a 50-times Tetris speedup and a 100-times 3D Bin Packing speedup. It also reports 77% Tetris utility at 20 milliseconds per object in a batch of 8, and 80% 3D Bin Packing utility at 15 milliseconds per object in a batch of 8.
The geometric idea behind the method
SOPO-CD formulates sequential object placement as a differentiable nonlinear optimization problem in decomposed free space. The method divides available space into convex regions, or pieces without inward dents, as it searches for placements.
A central geometric result reduces the placement of a convex object inside a convex hull to a simpler check: the object's vertices must remain inside that hull. SOPO-CD uses this vertex-based constraint in its decomposed free-space formulation.
The placement constraints and their derivatives are expressed in closed form, with calculation reported within 200 nanoseconds. In randomized 2D and 3D state tests, the analytic derivatives matched ForwardDiff values and were reported as almost 10 to 20 times faster.
The implementation uses a custom Sequential Quadratic Programming solver for the placement optimization.
The reported timings varied by task
In a per-object Tangram comparison, the convex-decomposed approach recorded 0.2 to 0.8 milliseconds of SQP time per object and used fewer iterations. The DCOL comparison reached its maximum limit of 50 iterations for the last two objects.
Across the full Tangram sequence, SOPO-CD was reported to perform better than SQP with DCOL. With 8 threads, it placed almost all 7 objects in around 10 milliseconds of total computation time.
The smaller Tetris tests took around 3 to 5 milliseconds for a five-piece case and 7 to 11 milliseconds for an eight-piece case. Reported success increased with thread count and was almost always achieved at 8 threads.
In the full Tetris comparison, occupancy reached 77% with 8 threads and k = 1. At the largest grid size, SOPO-CD was reported to be 50 times faster than grid search.
For 3D Bin Packing, the detailed comparison reported SOPO-CD as more than 200 times faster than grid search at the largest grid size. Successful placements and occupancy increased with solver batch size, while packing performance was described as competitive with grid search.
A physical demonstration, with clear limits
The preprint also describes an open-loop real-world Tangram experiment using an Allegro hand and an Xarm. Calculated goal locations were sent to a motion planner for pick-and-place.
The authors state that hull selection is non-exhaustive. In 3D, the decomposition generates axis-aligned cuboids. Placement is greedy and does not look ahead to future objects, and the object heuristics are predefined.
The reported outcomes focus on computation time, successful placements, and packing utility or occupancy. These measures describe the tested placement tasks and the reported demonstration.
The study does not report the numbers of benchmark instances, random sequences, repeated runs or real-world trials. It also reports no formal uncertainty estimates.
The project reports funding from the European Union's Horizon Europe programme under Grant Agreement No. 101120823 for project MANiBOT.
Paper data and sources
Original title: Sequential Object Placement Optimization with Convex Decomposition
Authors: Yuezhe Zhang, Xiangyu Lyu, Sohan Rudra et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text