The N-5 Scaling Law: Topological Dimensionality Reduction in the Optimal Design of Fully-actuated Multirotors

arXiv:2512.23619 · cs.RO, math.GT, math.OC · Submitted 2025-12-29 · Read on arXiv

cs.RO, math.GT, math.OC

Submitted: 2025-12-29

Updated: 2026-09-25

Code: https://github.com/antoniofranchi/omnidesign-optimizer

Terminology

• Redundancy — 18× in this paper · explained in 2 episodes
• Alignment — 9× in this paper · explained in 1 episode
• Clustering — 5× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Degrees of Freedom — 4× in this paper
• Ablation — 3× in this paper · explained in 1 episode
• Benchmarking — 3× in this paper · explained in 3 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Decoupling — 3× in this paper · explained in 2 episodes
• Ablation study — 2× in this paper · explained in 1 episode
• Admissibility — 2× in this paper · explained in 2 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• International Conference on Robotics and Automation — 2× in this paper
• Objective Function — 2× in this paper · explained in 2 episodes
• Point Clouds — 2× in this paper · explained in 2 episodes
• Pruning — 2× in this paper · explained in 4 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Scaling Laws — 2× in this paper · explained in 4 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Center of Mass — 1× in this paper
• Center of Mass (CoM) — 1× in this paper · explained in 2 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Energy Efficiency — 1× in this paper · explained in 3 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Local Optimization — 1× in this paper · explained in 2 episodes
• Multi-Rotor Aerial Vehicle — 1× in this paper
• Principal Component Analysis — 1× in this paper
• Principal Component Analysis (PCA) — 1× in this paper · explained in 4 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Sequential Quadratic Programming — 1× in this paper
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Performance-guided Task-specific Optimization for Multirotor Design

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