Material Detail

This university-level open learning module provides a rigorous mathematical and algorithmic foundation in Swarm and Multi-Agent Robotics. The module covers decentralized coordination, algebraic graph theory, distributed dynamical control, and modern scientific machine learning architectures:

• Network Representation & Algebraic Graph Theory: Graph topology models G = (V, E), localized spatial neighborhoods, adjacency matrices, and diagonal degree matrices.

• Dynamic Consensus Protocols: Discrete-time convex updates, continuous-time dynamics, row-stochastic coupling conditions, and asymptotic convergence proofs for average consensus.

• Graph Laplacian Spectra & Network Stability: Matrix formulation L = D - A, stability analysis of linear consensus differential equations, and the operational significance of the Fiedler eigenvalue (algebraic connectivity lambda_2) in dictating convergence speed and link failure tolerance.

• Formation Control & Leader-Follower Architectures: Relative inter-agent displacement stabilization, pinning control gains for virtual trajectory tracking, and artificial potential field vector fields for local collision avoidance.

• Distributed Convex Optimization: Collaborative parameter optimization via the Distributed Subgradient Method (DSM), minimizing aggregate private objective functions without a central master node.

• Contemporary 2026 AI-Era Formulations: Multi-Agent Reinforcement Learning (MARL) via Centralized Training with Decentralized Execution (CTDE / MAPPO / QMIX), and Decentralized Physics-Informed Neural Networks (Dec-PINNs) with consensus loss regularization for mapping continuous environmental fields.

Pedagogical components include 10 conceptual review questions, 12 thought-provoking analytical problems, and 12 step-by-step numerical engineering derivations.

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