Distributed model predictive control (DMPC) concerns how to online control multiple robotic systems with constraints effectively. However, the nonlinearity, nonconvexity, and strong interconnections of dynamic system models and constraints can make the real-time and real-world DMPC implementations nontrivial. Reinforcement learning (RL) algorithms are promising for control policy design. However, how to ensure safety in terms of state constraints in RL remains a significant issue. This paper proposes a barrier function-based safe reinforcement learning algorithm for DMPC of nonlinear multi-robot systems under state constraints. The proposed approach is composed of several local learning-based MPC regulators. Each regulator, associated with a local system, learns and deploys the local control policy using a safe reinforcement learning algorithm in a distributed manner, i.e., with state information only among the neighbor agents. As a prominent feature of the proposed algorithm, we present a novel barrier-based policy structure to ensure safety, which has a clear mechanistic interpretation. Both simulated and real-world experiments on the formation control of mobile robots with collision avoidance show the effectiveness of the proposed safe reinforcement learning algorithm for DMPC.

Based on the shape characteristics of the sample distribution in the clustering problem, this paper proposes an extended clustering algorithm based on cluster shape boundary (ECBSB). The algorithm automatically determines the number of clusters and classification discrimination boundaries by finding the boundary closures of the clusters from a global perspective of the sample distribution. Since ECBSB is insensitive to local features of the sample distribution, it can accurately identify clusters on complex shape and uneven density distribution. ECBSB first detects the shape boundary points of the cluster in the sample set with edge noise points eliminated, and then generates boundary closures around the cluster based on the boundary points. Finally, the cluster labels of the boundary are propagated to the entire sample set by a nearest neighbor search. The proposed method is evaluated on multiple benchmark datasets. Exhaustive experimental results show that the proposed method achieves highly accurate and robust clustering results, and is superior to the classical clustering baselines on most of the test data.