Building Together: Coordinating Robots for 3D Construction

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Author: Denis Avetisyan

A new approach ensures multiple robots can collaboratively build complex structures with flexibility and scalability.

Two robotic constructors, designated $R_1$ and $R_2$, collaborate to assemble a target structure, executing individual actions indicated by blue arrows and coordinating complex sequences with black arrows-a demonstration of distributed task allocation in a construction system.
Two robotic constructors, designated $R_1$ and $R_2$, collaborate to assemble a target structure, executing individual actions indicated by blue arrows and coordinating complex sequences with black arrows-a demonstration of distributed task allocation in a construction system.

This work presents a decentralized control synthesis based on Supervisory Control Theory for coordinating multi-robot 3D construction, utilizing reactive and permissive strategies.

Coordinating multiple robots for complex construction tasks presents a significant challenge in maintaining both scalability and guaranteed correctness. This paper, ‘A Formal Modular Synthesis Approach for the Coordination of 3-D Robotic Construction with Multi-robots’, addresses this through a decentralized control framework built upon Supervisory Control Theory. Our approach synthesizes reactive controllers from models of individual robots and the target structure, ensuring a correct-by-construction solution for collaborative building. By leveraging permissiveness and modularity, can this method unlock truly autonomous and adaptable multi-robot construction in dynamic environments?

Deconstructing the Collective: A Challenge of Control

The construction of three-dimensional structures by multiple robots introduces a unique set of control problems stemming from the sheer complexity of coordinating numerous independent agents. Each robot’s actions are subject to inherent uncertainties – in sensing, movement, and material manipulation – which propagate and interact as the structure grows, making precise control exceedingly difficult. Unlike tasks with fixed goals, building requires continuous adaptation to an evolving environment created by the robots themselves; a misplaced block early on can cascade into significant errors later. This dynamic interplay demands control strategies capable of not only directing individual robots but also managing the emergent behavior of the collective system, a challenge that pushes the boundaries of traditional robotics control paradigms.

Conventional methods of coordinating multi-robot construction often rely on a central system dictating the actions of each robot, a strategy proving increasingly inadequate as complexity grows. This centralized approach, while seemingly intuitive, introduces a critical bottleneck; the system’s processing demands escalate rapidly with each added robot and structural element, leading to delays and potential failures. Furthermore, these systems struggle to adapt to unforeseen circumstances – a dropped component, a slight miscalculation, or a changing environment – because recalculating optimal trajectories for every robot from scratch is computationally prohibitive. Consequently, the potential of collaborative robotics in dynamic construction scenarios remains largely untapped, as the inherent brittleness of centralized control hinders scalability and resilience.

Achieving complex construction with multiple robots demands control strategies that move beyond simply directing individual movements; these systems must dynamically account for the emerging structure as a collaborative element. Researchers are exploring methods where each robot’s actions are not pre-programmed but are continuously adjusted based on real-time feedback from both its environment and the partially completed structure. This necessitates algorithms capable of predicting how adding a new block will affect the stability of the whole, and adapting subsequent actions accordingly. Successful implementations leverage concepts from distributed control and self-organization, allowing the collective behavior of the robots to create a resilient system-one that can compensate for individual failures or unexpected disturbances while still achieving the desired architectural outcome. The interplay between individual robot actions and the evolving structure itself is thus central to unlocking the full potential of automated collective construction.

The robot's manipulation is constrained by surrounding objects, preventing it from removing the central brick.
The robot’s manipulation is constrained by surrounding objects, preventing it from removing the central brick.

Formalizing the Architecture: A Language of Construction

Supervisory Control Theory (SCT) is utilized to generate reactive control logic for construction tasks, enabling robust operation despite potential uncertainties in robot actions. This approach focuses on specifying desired system behavior as a formal language, representing permissible states and transitions. SCT then synthesizes a supervisor – a controller – that enforces this specification by blocking any robot commands that would lead to unsafe or unsuccessful outcomes. The synthesized controller does not predict future robot behavior; instead, it reacts to commands in real-time, ensuring that only safe and permissible actions are executed, thus guaranteeing construction success even with non-deterministic robot behavior or unexpected events. This reactive approach contrasts with traditional planning methods and provides a formal guarantee of safety and liveness.

The foundation of this construction control methodology involves representing both the target structure and the robotic agents as finite state automata. Each automaton defines a discrete set of states corresponding to the progress of construction or the robot’s operational configuration, respectively. Transitions between these states are governed by specific actions or events, such as the placement of a component or a change in robot orientation. This formalization allows for a precise description of the system’s dynamics; the structure’s automaton tracks assembly stages, while each robot’s automaton models its capabilities and limitations, including movement, manipulation, and sensing. By capturing these states and transitions, the approach enables rigorous analysis of the construction process and facilitates the development of controllers that guarantee safe and predictable behavior.

The Synchronous Product is a mathematical operation used in control theory to create a combined automaton representing the concurrent behavior of multiple systems. Specifically, it defines the combined state space as the Cartesian product of the individual automata’s states, and the transition relation is defined such that a transition exists in the combined system only if all constituent automata have a corresponding transition in their respective systems. This allows for systematic analysis of all possible combined behaviors and, crucially, the identification of conflicts where the actions of the structure and the robots are incompatible or lead to unsafe states, enabling the synthesis of controllers to avoid these scenarios. The resulting automaton provides a formal framework for verifying the safety and correctness of the construction process.

The construction site is formally defined as a bounded and closed environment, meaning it possesses clearly defined spatial limits and is isolated from external disturbances. This definition is not merely physical; it fundamentally shapes the control strategy by allowing for a complete enumeration of possible states and transitions within the system. By treating the construction site as a closed system, the Supervisory Control Theory (SCT) framework can accurately predict and prevent unsafe or unsuccessful construction scenarios. The boundaries of the site dictate the scope of the automata models representing both the structure and the robots, limiting the complexity of the state space and enabling the synthesis of a feasible and verifiable control supervisor. Any interaction with elements outside these defined boundaries is considered a system failure, reinforcing the importance of maintaining a closed operational environment.

Guaranteeing Robustness: Reactive Control in Action

The synthesized ‘Supervisor’ functions as a reactive controller by continuously monitoring the robot’s state and environment, and dynamically adjusting planned actions to both prevent the execution of unsafe commands and maintain forward progress towards task completion. This is achieved through real-time assessment of potential collisions, joint limits, and stability criteria, triggering immediate adjustments to robot trajectories or actions when deviations from safe operating parameters are detected. The controller operates on a cycle of sensing, planning, and execution, enabling it to respond to unforeseen circumstances and disturbances during operation, thereby ensuring the system remains within defined operational boundaries and continues towards achieving the designated task goals.

The synthesized control system is designed with two key operational properties: Nonblocking Control and Task-Observer functionality. Nonblocking Control ensures continuous system operation by preventing situations where the robots become stalled or unable to proceed, even in complex environments or with unforeseen obstacles. This is achieved through proactive monitoring and adjustment of robot actions. Simultaneously, the Task-Observer property guarantees that robots are capable of executing the necessary actions to fulfill the assigned construction task. This includes verifying the availability of required resources, validating action sequences, and intervening if a robot attempts an invalid or unproductive maneuver. These properties work in concert to ensure both consistent progress and successful task completion.

The system’s controller enforces ‘Totally Reciprocal’ behavior by ensuring each robot’s actions do not create states that prevent other robots from completing their assigned tasks. This is achieved through a mechanism that actively monitors potential conflicts and adjusts actions to maintain forward progress for all agents. Specifically, if one robot’s action would render another robot unable to proceed, the controller intervenes, either by modifying the first robot’s action or by providing assistance to the blocked robot, thus guaranteeing collaborative and non-interfering operation throughout the construction process.

The ‘Permissive Supervisor’ implements a control strategy that does not enforce a single, predetermined construction sequence. Instead, it validates multiple feasible pathways for completing a task, allowing the robotic system to adapt to unforeseen circumstances and uncertainties in the environment or execution. This approach contrasts with strictly defined controllers and provides increased robustness; if one path is blocked or becomes inefficient due to external factors, the system can dynamically switch to an alternative validated sequence without halting progress. The Supervisor assesses each potential action based on its validity within the defined construction goals, rather than prescribing a specific order of operations, thereby maximizing flexibility and overall system resilience.

Beyond Bricks and Mortar: Implications for Scalable Automation

Current automated construction often relies on centralized control systems, where a single computer dictates the actions of all robotic elements – a framework that struggles with scalability and robustness in dynamic, real-world environments. This research presents a fundamentally different approach, demonstrating that complex three-dimensional construction tasks can be achieved through decentralized control. Each robotic unit operates autonomously, making local decisions based on its immediate surroundings and pre-programmed goals, while coordinating with its peers through simple communication protocols. This distributed architecture overcomes the bottlenecks inherent in centralized systems, allowing for more flexible, resilient, and scalable automation. The demonstrated feasibility unlocks potential for robotic teams to tackle larger, more intricate projects, adapting to unforeseen challenges without requiring constant external intervention, and ultimately redefining the possibilities for automated construction and beyond.

A cornerstone of this research lies in the application of formal verification techniques, which offer a mathematically rigorous assurance of both safety and completeness in robotic task execution. Unlike traditional testing methods that can only demonstrate the absence of errors in specific scenarios, formal verification proves the system will always behave as intended, even in unforeseen circumstances. This is achieved by constructing a formal model of the robotic system and its environment, then using automated theorem proving or model checking to verify that the system satisfies pre-defined safety properties – for example, preventing collisions or ensuring structural integrity. The resulting guarantees are paramount for deployment in real-world applications, particularly in safety-critical domains like construction and manufacturing, where even minor errors can have significant consequences. This approach minimizes risk and builds confidence in the autonomous operation of complex robotic systems, offering a pathway towards truly reliable and scalable automation.

The capacity for robotic teams to coordinate and build complex structures with minimal human oversight represents a significant leap towards scalable automation. This advancement moves beyond the constraints of traditional, centrally-controlled robotic systems, which often struggle with the dynamic and unpredictable nature of real-world environments. By distributing control and enabling robots to react autonomously to changing conditions and the actions of their peers, applications extend far beyond construction. Manufacturing processes can become more flexible and responsive, while industries like logistics and disaster relief stand to benefit from adaptable, self-organizing robotic swarms capable of operating in complex and unstructured settings. This paradigm shift unlocks the potential for truly resilient and efficient automation, reducing reliance on constant human intervention and maximizing productivity across diverse fields.

This research establishes a framework for collective robotic construction that transcends specific tasks, offering principles applicable to diverse scenarios demanding adaptable, self-organizing systems. The core methodology, demonstrated through the creation of complex structures from simple ‘Brick’ components, suggests a pathway towards resilient automation in fields beyond construction, such as manufacturing and disaster response. While the synthesis process exhibits a time complexity of $O(N^2 + N^2M)$, where N represents the number of states and M the number of transitions, ongoing optimization efforts aim to further refine computational efficiency and scalability, ultimately enabling the deployment of robust, decentralized robotic teams capable of tackling increasingly complex challenges.

A three-dimensional structure built from equal bricks is represented as a two-dimensional grid, where each cell displays the number of bricks stacked at that location, with indices increasing from top to bottom and left to right.
A three-dimensional structure built from equal bricks is represented as a two-dimensional grid, where each cell displays the number of bricks stacked at that location, with indices increasing from top to bottom and left to right.

The pursuit of decentralized control, as detailed in the paper’s modular synthesis approach, echoes a fundamental tenet of understanding complex systems: dissecting them into manageable, interacting components. This mirrors the belief that reality is, at its core, an open-source project awaiting full comprehension. As Barbara Liskov aptly stated, “Programs must be right first before they are fast.” The paper prioritizes correctness and scalability through permissive control – a cautious, iterative approach to building complex robotic constructions. This methodical decomposition and verification, ensuring each module functions correctly before integration, exemplifies the process of ‘reading the code’ of a robotic construction problem, identifying potential flaws before they manifest as system-wide failures. The synthesis method’s focus on reactive control further emphasizes this ‘debugging’ process, allowing the robots to adapt to unforeseen circumstances and maintain stability-much like refining code through rigorous testing.

Beyond the Blueprint

The presented work achieves a degree of formal coordination for multi-robot construction, a feat not insignificant. However, the true test lies not in demonstrating control, but in relinquishing it-or, more precisely, in understanding the limits of that relinquishment. The permissiveness inherent in the reactive control strategy, while fostering scalability, begs the question: how much unforeseen interaction can the system absorb before formal guarantees erode? It’s a question less about refining the automata, and more about acknowledging the inevitable messiness of physical reality-the dust, the slight misalignments, the unmodeled disturbances.

Future investigations should deliberately court failure. Stress-testing the boundaries of permissiveness-introducing increasingly complex disturbances and observing the emergent behavior-will reveal not only the system’s weaknesses, but also the surprisingly robust qualities that formal methods often overlook. The focus shouldn’t be on preventing deviation, but on characterizing it. After all, a truly intelligent system doesn’t eliminate uncertainty; it anticipates and exploits it.

Ultimately, the value of this formal approach may not reside in its ability to dictate robot behavior, but in its capacity to serve as a precise language for describing what can go wrong. Transparency, not obfuscation, is the key to genuine security-a point often lost in the pursuit of perfect control. The next step is not to build a more perfect supervisor, but to build a better debugger.

Original article: https://arxiv.org/pdf/2512.16555.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-21 18:34