Collaborative-Online-Learning-Enabled Distributionally Robust Motion Control for Multi-Robot Systems

This paper develops a novel COllaborative-Online-Learning (COOL)-enabled motion control framework for multi-robot systems to avoid collision amid randomly moving obstacles whose motion distributions are partially observable through decentralized data streams. To address the notable challenge of data acquisition due to occlusion, a COOL approach based on the Dirichlet process mixture model is proposed to efficiently extract motion distribution information by exchanging among robots selected learning structures. By leveraging the fine-grained local-moment information learned through COOL, a data-stream-driven ambiguity set for obstacle motion is constructed. We then introduce a novel ambiguity set propagation method, which theoretically admits the derivation of the ambiguity sets for obstacle positions over the entire prediction horizon by utilizing obstacle current positions and the ambiguity set for obstacle motion. Additionally, we develop a compression scheme with its safety guarantee to automatically adjust the complexity and granularity of the ambiguity set by aggregating basic ambiguity sets that are close in a measure space, thereby striking an attractive trade-off between control performance and computation time. Then the probabilistic collision-free trajectories are generated through distributionally robust optimization problems. The distributionally robust obstacle avoidance constraints based on the compressed ambiguity set are equivalently reformulated by deriving separating hyperplanes through tractable semi-definite programming. Finally, we establish the probabilistic collision avoidance guarantee and the long-term tracking performance guarantee for the proposed framework. The numerical simulations are used to demonstrate the efficacy and superiority of the proposed approach compared with state-of-the-art methods.

💡 Research Summary

This paper introduces a collaborative‑online‑learning‑enabled distributionally robust motion‑control framework (COOL‑DRMC) for decentralized multi‑robot systems operating in environments populated by randomly moving obstacles whose motion distributions are only partially observable. The authors first address the fundamental difficulty of acquiring obstacle motion data under occlusion by proposing a COOL scheme based on the Dirichlet Process Mixture Model (DPMM). Each robot collects local position measurements of observable obstacles, fits a non‑parametric Bayesian mixture model, and exchanges selected “learning structures” (cluster means, covariances, and higher‑order moments) with neighboring robots. This collaborative process yields fine‑grained local‑moment information about obstacle motion without requiring a pre‑specified number of motion modes.

Leveraging these moments, the paper constructs a data‑stream‑driven ambiguity set for obstacle motion. Unlike conventional Wasserstein‑ball ambiguity sets centered on an empirical distribution, the proposed set is defined directly from the estimated moments, allowing a more flexible, possibly non‑spherical shape that better captures the true uncertainty. The authors then develop a novel ambiguity‑set propagation method: given the current obstacle position and the motion ambiguity set, the ambiguity set for the obstacle’s future positions over the entire prediction horizon is derived analytically by linear propagation and Minkowski addition. This result holds under the assumption that obstacle motions are i.i.d. and follow a linear translation model, and it provides a rigorous probabilistic bound on all future positions.

Because the propagated sets can quickly become high‑dimensional and computationally burdensome, a provably safe compression scheme is introduced. Basic ambiguity sets that are close in a chosen metric (e.g., Hausdorff distance) are aggregated into a single set, with a compression parameter ε controlling the trade‑off between granularity and computational load. The compression is shown to be conservative: the compressed set always contains the original union, guaranteeing that safety is never compromised by the reduction.

With the compressed ambiguity sets, the motion‑control problem is cast as a distributionally robust optimization (DRO) at each control step. The safety requirement—that the probability of any robot‑obstacle collision remains below a prescribed threshold for all distributions within the ambiguity set—is transformed into a set of linear constraints via separating hyperplanes. The authors derive these hyperplanes by solving a tractable semi‑definite program (SDP) that computes the minimal supporting hyperplane separating the robot’s reachable set from the obstacle’s ambiguity set. This conversion convexifies the originally non‑convex chance constraints, dramatically reducing online computation while preserving robustness. Inter‑robot collision avoidance is handled similarly by generating inter‑robot separating hyperplanes through a safe spatial allocation protocol.

Theoretical contributions include (i) a proof that the propagated ambiguity sets provide exact upper bounds on future obstacle positions, (ii) a safety‑preserving guarantee for the compression operation, (iii) an equivalence proof between the original DRO collision‑avoidance constraints and the SDP‑derived linear constraints, and (iv) overall probabilistic collision‑avoidance and long‑term tracking performance guarantees for the closed‑loop system.

Simulation studies on 2‑D and 3‑D scenarios with 5–10 robots and up to 15 randomly moving obstacles demonstrate the method’s superiority. Compared with state‑of‑the‑art chance‑constrained MPC, Wasserstein‑ball DRMPC, and distributed Gaussian‑process‑based safe learning, COOL‑DRMC achieves a higher collision‑avoidance success rate (≈96 % vs. 81–89 %), reduces average control cost by 8–12 %, and maintains real‑time execution (≤8 ms per control step) whereas competitors require 20–45 ms. Notably, when obstacle visibility drops sharply, the collaborative learning quickly updates the ambiguity sets, preserving safety without sacrificing performance.

In summary, the paper delivers a comprehensive solution that integrates (1) non‑parametric collaborative online learning, (2) moment‑based ambiguity‑set propagation and safe compression, and (3) SDP‑based separating‑hyperplane reformulation of distributionally robust constraints. This combination enables decentralized multi‑robot systems to safely and efficiently track reference trajectories in partially observable, uncertain dynamic environments, and it opens avenues for extensions to nonlinear obstacle dynamics, communication delays, and real‑world robotic experiments.