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

TL;DR

This work addresses collision avoidance for decentralized multi-robot systems under uncertain, occluded obstacle motions. It introduces COOL-DRMC, which couples collaborative online learning via a Dirichlet Process Mixture Model with distributionally robust motion control, constructing locally informative ambiguity sets and propagating them over the prediction horizon. Separating hyperplane reformulations render the collision-avoidance constraints tractable via SDP/LMIs, and a safe ambiguity-set compression balances control performance and computation time while providing safety guarantees. Simulation results across multimodal, nonlinear, and time-varying scenarios demonstrate improved tracking, reduced computation, scalability to large teams, and robust handling of online distribution shifts.

Abstract

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.

Figures (7)

• Figure 1: Construction of a compressed ambiguity set
• Figure 2: Separating hyperplanes between robot 1 and both obstacle 1 and robot 2 from the view of robot 1
• Figure 3: Trajectories of the quadrotors with different methods in simulation 1 (The positions of the obstacles and the quadrotors correspond to the positions at $T = 100s$)
• Figure 4: Trajectories of the vehicles with different methods (The positions of the obstacles and the vehicles correspond to the positions at $T = 100s$).
• Figure 5: Trajectories of robots with different control methods in simulation 2. (Rectangles represent static obstacles and circles represent the robots and obstacles. Numbers on the circles denote the indices of robots or obstacles and the different colors of the circles indicate the robots controlled by different methods as shown in the legend.)