CompCPZ Stops Robots From Parking Between ‘This or That’
Tell a robot “put it near the red plate or the blue plate,” and a lot of planners aim for the gap. The arm looks successful. The cup is in empty air.
CompCPZ, from Technical University of Munich (Zhen Zhang, Ahmad Hafez, Peng Xie, Yanliang Huang, Wenyuan Wu, Amr Alanwar), treats that as a representation bug, not a tuning bug. The paper, arXiv:2608.17717, posted August 18, wraps language-conditioned systems with constrained polynomial zonotopes so a disjunction stays as separate feasible blobs.
The silent miss
The authors call it a silent semantic failure: geometry says you arrived, the instruction says you did not. They prove a lower bound: any sound encoding with fewer connected components than the instruction has modes misses the true set by at least half the gap between modes. A planner that commits to one point before it sees which mode is free has worst-case success 1/k under a symmetric k-mode instruction.
CompCPZ parses the sentence into a small grammar (near, avoid, between, negation), builds a two-sided enclosure per clause, then composes with intersection, union, and complement. Coverage is split-conformal. Runtime on composition is under 0.25 ms at depth 4, under 1.1 ms at a worst-case depth 7.
Parser is GPT-4o with chain-of-thought. Detector in the closed-loop tests is a fine-tuned YOLOv8n (200 synthetic frames, about 33 minutes on one GPU). Off-the-shelf Grounding-DINO+SAM2 sat at 0.20 in-GT-mode; the in-domain detector hit 1.00 in their ablation.
Sim table, then a dog
On a 18-family ManiSkill3 closed-loop Franka servo (200 seeds each), both CompCPZ and a convex AABB baseline reach the commanded point at ≥0.99 geometric success. Only CompCPZ lands inside an analytic ground-truth mode. Pooled: 1.00 vs 0.13 in-GT-mode, 1,900 / 1,918 paired wins. On clean disjunctions such as “red ∨ blue,” convex scores 0.00. OpenVLA-7B, run zero-shot on the multi-modal families, hit 30.8% in-GT-mode.
The same compiler, untuned, ran on a Unitree Go2 under ~100 Hz NOKOV motion capture. Four planar scenarios, 36 trials. CompCPZ was in a true mode 12/12. The convex hull was 0/12, and on the negation scene it put the dog on the forbidden rug 3/3. A single-clause planner that commits to the first disjunct failed the blocked-mode scene 0/3.
Limits they state: depth-independent stability is proved for axis-aligned grammars; the real robot is planar locomotion, not contact-rich Franka hardware.
A Human’s Take
“Or” is a child’s word and a planner’s trap. I like a paper that treats the gap between two plates as a failure, not a compromise.
The Go2 photos are the receipt: same room, same boxes, one path into a mode, one path onto the rug. That is the demo I want on every VLA that claims it follows instructions.