Multi-Robot Distributed Optimization

Updated 24 November 2025

Multi-robot distributed optimization is a coordination paradigm that decomposes global tasks into local objectives solved collaboratively through networked consensus.
It employs methods such as distributed gradient descent, ADMM, and sequential convex programming to tackle convex and nonconvex problems with scalability and robustness.
Applications span mapping, formation control, task allocation, and collaborative manipulation, validated through both simulations and real-world robotic platforms.

Multi-robot distributed optimization is a foundational paradigm for coordinating teams of autonomous robots to solve complex, large-scale inference, planning, control, and learning problems without reliance on a central coordinator. Tasks are decomposed into local objectives and constraints, with robots exchanging information over a network topology to reach an optimal solution that satisfies collective goals. Distributed optimization enables robustness to failures, scalability, privacy of local data, and efficient bandwidth use—properties critical in robotics applications such as multi-robot mapping, formation control, localization, collaborative manipulation, task allocation, learning, and exploration. The field spans consensus-based first-order methods, dual and primal–dual decomposition, distributed sequential convex programming, the alternating direction method of multipliers (ADMM), and graph optimization techniques, and encompasses fully distributed protocols for both convex and nonconvex objective functions (Halsted et al., 2021, Shorinwa et al., 2023, Testa et al., 2023).

1. Mathematical Formulation and Problem Classes

Multi-robot distributed optimization is typically formalized as minimizing a global cost function $F(x) = \sum_{i=1}^N f_i(x)$ , subject to private local constraints $g_i(x) = 0$ , $h_i(x)\leq 0$ for each robot $i$ , where $x$ is a shared decision variable or a collection of local copies $x_i$ (Halsted et al., 2021). Key distributed formulations include:

Consensus optimization: Each robot maintains a local copy $x_i$ of the global variable $x$ , with the constraint $x_i = x_j$ for all neighbors $(i,j)$ in the communication graph $\mathcal{G}$ , and solves $\min \sum_i f_i(x_i)$ subject to consensus and private constraints (Shorinwa et al., 2023).
Partition-based optimization: The global variable $x$ is structured into components associated to robots and their neighbors, matching the robotic interdependence structure (Testa et al., 2023).
Constraint-coupled optimization: Robots solve $\min \sum_i f_i(x_i)$ s.t. $\sum_i g_i(x_i) \le 0$ (e.g., coupled resource, time, or capacity limits) (Testa et al., 2023).
Aggregative optimization: Each local cost depends on both $x_i$ and an aggregate $\sigma(x) = \frac{1}{N} \sum_i \phi_i(x_i)$ , as in distributed target encirclement and surveillance (Testa et al., 2023).

All these classes can be embedded in convex, nonconvex, constrained, and time-varying settings, with information exchange restricted to direct communication links in $\mathcal{G}$ (Shorinwa et al., 2023).

2. Algorithmic Frameworks

Distributed optimization algorithms are classified according to their update structure, the nature of the cost/constraints, and communication requirements:

2.1 Distributed First-Order Methods

Distributed Gradient Descent (DGD) & Gradient Tracking: Each robot updates its variable by averaging neighbors' iterates and descending along its local gradient, optionally tracking the global sum of gradients for linear convergence under strongly convex objectives (Shorinwa et al., 2023, Halsted et al., 2021, Shorinwa et al., 2023).
Distributed Dual Averaging and Push-Sum protocols: Enable handling directed/weighted graphs and stochasticity in gradients (Shorinwa et al., 2023).

2.2 Sequential Convex and Second-Order Methods

Distributed Sequential Convex Programming (e.g., NEXT, SONATA): Robots construct and solve local convex surrogates of their nonconvex objectives, with consensus/tracking variables for coupling (Shorinwa et al., 2023, Testa et al., 2023).
Distributed Newton and Quasi-Newton: Newton-based steps distributed via local Hessian blocks, sometimes integrating limited neighbor information (e.g., Network Newton- $K$ , ESOM, D-BFGS) (Shorinwa et al., 2023).

2.3 ADMM and Variants

Consensus ADMM (C-ADMM): Each robot alternately solves a local augmented Lagrangian subject to neighbor-wise consensus constraints, then updates dual variables, achieving robust and often linear convergence for strongly convex problems (Halsted et al., 2021, Shorinwa et al., 2023, Shorinwa et al., 2023). Shared-variable variants (SOVA) and edge-wise duals support complex coupling structures.

2.4 Nonconvex and Learning-Driven Methods

Block Coordinate Descent (BCD): Enables large-scale optimization (e.g., pose graph, sensor network localization), with exact block solves for each agent and coordination via inter-agent variable sharing (Wu et al., 2023).
Reinforcement Learning and GNNs: Used, for example, to learn distributed pose-graph optimization policies that scale in team size and structure (Ghanta et al., 26 Oct 2025).
Cognitive-based Adaptive Optimization (CAO): Supports mission environments with a priori unknown cost models by learning cost function approximators online with perturbation-based updates (Kapoutsis et al., 2021).

A summary of major algorithm class features is provided below.

Algorithm	Computational Load	Communication/Iteration	Convexity	Convergence Rate	Suitability
DGD, Gradient-Tracking	1 gradient eval	1–2 vector broadcasts	Convex/Strongly Convex	$O(1/k)$ (sublinear), $O(\rho^k)$ (linear, strongly convex)	Large-scale, simple constraints
Sequential Convex (NEXT, ESOM)	1 Hessian approx + grad	1– $K$	Convex/Nonconvex	$O(1/k)$ ; locally fast	Nonconvex objectives, trajectory planning, SLAM
C-ADMM	Local subproblem solve	1 broadcast	Convex/Strongly Convex	Linear if strong convexity	General, strongly convex, constraint-coupled problems
BCD, Nonconvex	Block QP/NLP solve	1 block (local)	Convex/Nonconvex	Sublinear (general); local optima (nonconvex)	Estimation, pose graph, collaborative perception

(Halsted et al., 2021, Shorinwa et al., 2023, Testa et al., 2023, Shorinwa et al., 2023, Wu et al., 2023)

3. Applications in Multi-Robot Systems

Distributed optimization is central in many prominent robotics domains:

Task Allocation, Scheduling, and Mission Planning: Assigning mission primitives under cross-schedule dependencies via distributed metaheuristics (e.g., evolutionary genetic algorithms with peer-to-peer gene exchange) (Ferreira et al., 2021); multi-objective Pareto front optimization.
Collaborative Mapping, Localizaion, and SLAM: Distributed pose-graph optimization using ADMM or reinforcement learning–driven GNN policies, with consensus over separator variables post local subgraph refinement (Ghanta et al., 26 Oct 2025, Tian et al., 2021, Latif et al., 2022).
Formation, Encirclement, and Surveillance: Aggregative optimization frameworks for target encirclement and multi-agent formation, leveraging consensus on macroscopic configuration and feedback optimization (Pichierri et al., 30 Sep 2024).
Resource and Energy Management: Constraint-coupled and aggregative optimization for scheduling (e.g., EV charging, infrastructure allocation), where global constraints depend on all agents (Testa et al., 2023).
Distributed Machine Learning and Mapping: Consensus-based distributed deep learning (e.g., DiNNO) and uncertainty-weighted robust neural mapping under severe communication constraints (UDON) (Yu et al., 2021, Zhao et al., 16 Sep 2025).
Contact-Rich Collaborative Manipulation: Distributed contact-implicit trajectory optimization (DisCo) for multi-robot manipulation/planning, splitting the problem via ADMM and solving local contact constraints in parallel (Shorinwa et al., 30 Oct 2024).

4. Theoretical and Practical Properties

Key guarantees and empirical characteristics established across surveys and representative works:

Convergence: For convex objectives, distributed first-order, ADMM, and block-coordinate methods converge globally, with linear rates under strong convexity and proper spectral gap conditions (Shorinwa et al., 2023, Halsted et al., 2021, Shorinwa et al., 2023). For nonconvex objectives (e.g., pose-graph, mapping, contact-rich planning), convergence is to stationary points or local minima (Ghanta et al., 26 Oct 2025, Shorinwa et al., 30 Oct 2024, Tian et al., 2021, Wu et al., 2023).
Scalability: All prominent algorithms (DGD, C-ADMM, BCD, metaheuristics) scale with team size under bounded node/edge degree, since communication and computation remain local and parallelizable (Shorinwa et al., 2023, Halsted et al., 2021, Wu et al., 2023, Ghanta et al., 26 Oct 2025).
Communication: Communication is typically restricted to single-hop exchanges (neighbor-to-neighbor), thus robust to link failure and central node absence (Shorinwa et al., 2023, Testa et al., 2023, Asgharivaskasi et al., 28 Apr 2024). Adaptive compression (octrees, quantization) and event-triggered protocols further reduce bandwidth (Asgharivaskasi et al., 14 Feb 2024, Pichierri et al., 30 Sep 2024).
Robustness: ADMM and block-coordinate methods handle moderate asynchrony and stochastic packet drops (Shorinwa et al., 2023, Zhao et al., 16 Sep 2025). Fault tolerance is addressed via resilient local updates or plug-and-play subproblems (Kapoutsis et al., 2021).
Privacy and Decomposition: Many schemes avoid raw data sharing; only parameter, map, or state variables are exchanged (e.g., DiNNO for learning, DisCo for manipulation) (Yu et al., 2021, Shorinwa et al., 30 Oct 2024).

5. Infrastructures and Experimental Validation

Distributed optimization methods are implemented in widely accessible software frameworks and evaluated on both simulated and physical platforms:

Toolboxes: DISROPT (Python/MPI), ChoiRbot (ROS 2), CrazyChoir (Crazyflie/ROS 2), support distributed algorithm deployment on real and simulated robots, offering primitives for consensus, dual decomposition, aggregative tracking, and more (Testa et al., 2023).
Experiments: Hardware demonstrations include multi-robot formation with real-time task swapping, SAR robotics with tactile mapping, collaborative SLAM with TurtleBots/Crazyflies, neural mapping on low-bandwidth micro-robots, and modular truss rolling via distributed contact optimization. Reported metrics include convergence time, task allocation efficiency, map quality and coverage, artifact rate, and robustness to communication loss (Karpe et al., 2021, Ibrahimov et al., 7 Oct 2025, Shorinwa et al., 30 Oct 2024, Zhao et al., 16 Sep 2025, Yu et al., 2021).

6. Limitations, Research Challenges, and Future Directions

Key open directions and limitations are documented in state-of-the-art surveys:

Nonconvex and Constrained Problems: General real-time, distributed protocols for constrained nonconvex problems remain a research frontier (collision-avoidance constraints, complex mission logic) (Shorinwa et al., 2023).
Communication and Synchrony: Asynchronous algorithms and methods tolerant to severe packet loss or changing topology are needed for practical large teams and field deployments (Shorinwa et al., 2023, Zhao et al., 16 Sep 2025).
Scalable Solver Acceleration: Lightweight solvers for embedded systems, handling high-dimensional state/action spaces, are increasingly essential (Shorinwa et al., 2023, Ghanta et al., 26 Oct 2025).
Integration with Learning and Adaptation: Deep learning–based policies, online adaptation, and plug-and-play coordination in dynamic, unknown environments pose ongoing theoretical and systems-level challenges (Kapoutsis et al., 2021, Ghanta et al., 26 Oct 2025, Zhao et al., 16 Sep 2025).

The consensus in current literature is that distributed optimization is the mathematical and algorithmic backbone for cooperative multi-robot autonomy. The active integration of robust, scalable, fully-distributed methods—spanning convex, nonconvex, and learning-centric optimization—remains a central trajectory for both academic research and real-world deployments in multi-robot systems (Halsted et al., 2021, Shorinwa et al., 2023, Testa et al., 2023).