Topology Sharing & Global Guidance (TSGG)

• TSGG is a hierarchical framework that uses abstract topological representations to coordinate distributed agents with minimal communication overhead.
• It separates control into a strategic global layer and a tactical local layer, ensuring scalable planning and real-time responsive execution.
• Experimental benchmarks in robotics and microgrid control demonstrate improved efficiency, reduced path lengths, and robust conflict resolution.

Topology Sharing and Global Guidance (TSGG) refers to a class of hierarchical, cooperative control and planning frameworks in which multiple agents—robots or distributed energy resources—share abstracted topological information to achieve globally coordinated objectives while operating with primarily local information and limited low-bandwidth communication. TSGG solves fundamental deficiencies of purely local or purely centralized architectures in multi-agent navigation and distributed control, enabling both strategic, large-scale planning and low-level, real-time responsiveness. The formalism has been demonstrated in domains including decentralized multi-robot navigation in unknown, constrained environments (Mao et al., 10 Oct 2025) and dissipativity-based distributed control of DC microgrids (Najafirad et al., 6 Mar 2025), where it enables robust, efficient, and scalable operation under tight communication constraints.

1. Hierarchical Architecture and Layered Structure

TSGG architectures are conceived as multi-layer systems, typically decomposing the control and planning stack into a low-frequency, global strategic layer and a high-frequency, local tactical (or regulatory) layer.

In decentralized multi-robot systems (Mao et al., 10 Oct 2025), the architecture consists of:

• Strategic (Topological) Layer: Maintains and shares lightweight visibility-graph abstractions of the environment, merging new topological maps upon opportunistic encounters between robots. This layer is responsible for long-horizon, trap-avoiding route planning, outputting waypoints as “topology nodes” for the metric layer.
• Tactical (Metric) Layer: Receives the next waypoints and produces real-time, collision-free, kinodynamically feasible trajectories in the robot’s local reference frame using sensor data and resolves peer conflicts (e.g., via space–time analysis, sampling-based escape strategies, and real-time trajectory optimization).

In dissipativity-based distributed microgrid control (Najafirad et al., 6 Mar 2025), a similar structure materializes:

• Local (DG/Subsystem) Controllers: Typically PI laws acting on local voltage deviation, handling fast regulation.
• Distributed Consensus/Global Controllers: Exchange global setpoints or state abstractions (e.g., normalized currents) along a sparse, optimized communication topology, enforcing desired current sharing through consensus-type feedback.

This separation ensures that global coordination is lightweight and scalable while retaining real-time reactivity and robustness at the local level.

2. Topological Abstraction and Sharing Mechanisms

TSGG leverages abstract topological representations for information sharing, avoiding the high overhead of raw metric or dense map exchange.

Multi-Robot Navigation Topology

Topological maps are encoded as lightweight graphs:

• Vertices ($V$): Obstacle contour points from LiDAR data, start, or goal positions.
• Edges ($E$): Collision-free straight-line segments, with traversal cost $c(v_a, v_b) = \|v_a - v_b\|_2$ and metadata including last verification timestamps.
• Map-Fusion and Graph Merging: When robots meet, they fuse their graphs using vertex clustering (within $\delta$ threshold), edge union, and validity checks, requiring minimal bandwidth (6–7 KB/s per transaction).

Microgrid Communication Topology

Information structure is formalized as a static interconnection matrix ($\Gamma \equiv M$), with blocks corresponding to physical adjacency, communication links ($K_{ij}$ for topology sharing), and disturbance injection. Communication topology is explicitly optimized through sparsity-promoting LMIs.

Both domains exploit opportunistic or co-designed adjacency: sharing occurs upon physical proximity (robots) or is enforced via communication graph optimization (microgrids), fundamentally reducing communication overhead.

3. Global Guidance and Coordination Algorithms

TSGG realizes global guidance by abstract reasoning and consensus atop the shared topology.

Robots: Graph-Based Path Planning

• Algorithmic Core: Robots plan waypoints as sequences through $G=(V,E)$, optimizing $\sum_\ell c(v_\ell, v_{\ell+1})$ using DFS with loop pruning, Dijkstra, or A* heuristics.
• Trap Avoidance: The global graph prevents entrapment in dead ends (e.g., U-shaped regions) by exposing topological bottlenecks.
• Dynamic Re-Planning: New information (from graph fusion or failed local planning) triggers strategic replanning.

Microgrids: Global Consensus on Power Flow

• Distributed Feedback Law: For each DG $i$, $$u_{iG} = \sum_{j \in \mathcal{F}_i^-} k_{ij} \left(\frac{I_{ti}}{P_{ni}} - \frac{I_{tj}}{P_{nj}}\right)$$, enforcing convergence of normalized currents to a global consensus scalar $I_s$.
• Voltage Regulation and Proportional Sharing: Local PI acts on voltage; consensus ensures $I_{ti}/P_{ni} \rightarrow I_s$ for fair load distribution.
• Global Guidance Emergence: The feedback topology, synthesized with the controller, dictates steady-state setpoints and robustness to link changes.

4. Local Tactical Control and Conflict Resolution

TSGG’s tactical or regulatory layer performs local trajectory generation or regulation, guaranteeing feasibility and safety.

Multi-Robot Local Planning

• Waypoint Translation: The topological waypoint is mapped to a local goal with graph-distance lookahead.
• Trajectory Generation: Uses A* in local grids, followed by space–time conflict detection.
• Sampling-Based Escape: If blocked, generates candidate local escape goals $e_i$ in sampled forward/backward sectors, minimizing a cost $J(e)$ balancing progress, obstacle avoidance, and heading smoothness.
• Smoothness and Constraint Enforcement: Final path is a piecewise polynomial $p(t)$, minimizing $\int_0^T \|p^{(3)}(t)\|^2 dt$ plus barrier-style penalties for obstacles and kinodynamic limits.

Microgrid Regulators

• PI Laws: Local controllers $$u_{iL}=k_{i0}^P(V_i-V_{ri}) + k_{i0}^I \int(V_i-V_{ri})$$ maintain voltage tracking.
• Robustness to Disturbances: Controller design ensures $L_2$-gain bounds from disturbances via subsystem dissipativity, subject to feasibility conditions formalized in coupled LMIs.

5. Communication and Integration Between Layers

TSGG incorporates mechanisms for robust inter-layer integration under limited or failing communication.

• Upward Feedback: If tactical planning is infeasible, requests are issued to the strategic layer for topological updates or path re-routing.
• Downward Guidance: Whenever new topology information arrives, the strategic layer immediately provides updated waypoints to the tactical layer.
• Resilience to Packet Loss: In robot experiments, even 80% packet drop led only to a 12% increase in completion time; at full dropout, behavior reverted to a local-only baseline (Mao et al., 10 Oct 2025).
• Plug-and-Play Architecture: In microgrids, the co-synthesis via convex LMIs enables adaptive changes in communication/physical topology and controller reconfiguration as units join or leave (Najafirad et al., 6 Mar 2025).

6. Experimental Benchmarks and Performance

TSGG frameworks have been validated in simulated and real-world scenarios, demonstrating substantial improvements over classical baselines.

Method (Robots)	Success %	Avg. Time [s]	Path Len [m]	Path Eff.
TSGG (full)	100	47.7	74.1	0.51
w/o topology sharing	100	69.3	110.4	0.41
w/o conflict resolution	25	42.4	66.1	0.58
Baseline (car-like)	0	–	–	–

• Multi-Robot Navigation: TSGG achieves 100% task success, 23–26% shorter paths and lower travel times compared to local-only or conflict-agnostic variants. Communication overhead remains $<$7 KB/s per robot pair, map fusion $<$3 ms, and full trajectory optimization $<$80 ms (Mao et al., 10 Oct 2025).
• Microgrid Control: Voltage deviations and current sharing errors are reduced by 80–90% compared with conventional droop control (max $|V_i−V_r| < 0.02$ V vs 0.15 V; sharing error $<$1% vs $\approx$8% under load steps). Co-designed topology and control law sustain performance under topology and load changes (Najafirad et al., 6 Mar 2025).
• Hardware Validation: Real-world robot trials show reliable operation with noisy LiDAR, odometry drift, and mesh network jitter.

7. Theoretical Foundations and Synthesis Methods

The design of TSGG frameworks relies on sound mathematical formalisms, particularly for stability and performance guarantees.

• Convex Co-Design via LMIs: In microgrids, system-wide performance and communication topology are optimized jointly via linear matrix inequalities coupling dissipativity indices, controller gains, and adjacency constraints (Najafirad et al., 6 Mar 2025).
• Dissipativity and Passivity Theory: Guarantees are grounded in equilibrium-independent input/output dissipativity for all subsystems, ensuring robustness to plug-and-play changes and external disturbances.
• Hierarchical Problem Decomposition: The multi-level architecture enables separation-of-concerns—abstract strategic reasoning is insulated from high-frequency, real-time reactivity.

TSGG thus achieves scalable, high-performance multi-agent coordination in both robotics and cyber-physical energy systems, providing an exemplar for the integration of topological sharing and global guidance under strict communication and information constraints.