Force-Based Decentralized Planner

• Force-based decentralized planning is a method where individual agents use local sensing and virtual force fields to compute safe, collision-free trajectories.
• It relies on asynchronous updates and distributed optimization to avoid collisions without needing centralized coordination.
• This approach is applied in UAV swarms, autonomous vehicles, and industrial robotics, offering scalability, real-time responsiveness, and enhanced safety.

A force-based decentralized planner is an architectural and algorithmic paradigm in multi-agent robotics wherein each agent computes its own control actions using only locally available information and exchange with select neighbors, and collision avoidance is achieved by modulating each agent’s trajectory according to either explicit inter-agent virtual forces or analogous distributed constraints. Unlike centralized approaches that require global coordination, decentralized planners exploit agent autonomy, partial local communication, and often force field analogies or optimization constraints to achieve safe, scalable, and reactive multi-agent coordination in real time, even in dynamic or partially observable environments.

1. Fundamental Principles of Force-Based Decentralized Planning

In force-based decentralized planning, agents generate their motion based on local information and peer exchange, with avoidance and cooperation encoded through repulsive or attractive virtual “forces” or equivalent decentralized constraints. The planner’s typical objective is to compute, in a parallel and distributed manner, a set of space–time trajectories $P = \{p_1, \ldots, p_n\}$ for $n$ agents $a_1, \ldots, a_n$ in a shared Euclidean workspace $\mathcal{W}$, such that for each agent $p_i(0) = start_i$, $p_i(t_i^{dest}) = dest_i$, and

$\forall i \neq j,\quad \neg C(p_i, p_j)$

where $C(p_i, p_j)$ denotes that the trajectories intersect or violate a specified separation constraint.

A general pattern involves each agent performing:

• Sensing or communication to determine neighboring agents' poses or trajectories
• State prediction or internal model forecasting of other agents’ future evolution
• Calculation of a locally optimal trajectory or control, subject to force-based constraints or distributed avoidance rules
• Local asynchronous adaptation in response to newly received information from neighbors

Approaches that formalize "force" may use explicit potential fields (e.g., gradient-based repulsion), constraints motivated by inter-agent proximity, or encode avoidance as a byproduct of optimization—see, e.g., the convexification strategy in decentralized MPC (Tallamraju et al., 2018), local reactive updates in prioritized planning (Čáp et al., 2012), and penalty-based constraints via signed distance or dynamic separating planes (Tordesillas et al., 2020).

2. Algorithmic Mechanisms and Asynchronous Operation

A key enabler for scalability is the elimination of centralized synchronization. Algorithms such as Asynchronous Decentralized Prioritized Planning (ADPP) (Čáp et al., 2012) operate as follows:

• Each agent is assigned a unique priority.
• Each agent maintains an Agentview containing the latest published trajectories of higher-priority peers.
• Upon receiving a new trajectory (inform message) from a higher-priority agent, the recipient agent immediately sets a CheckFlag and re-evaluates path consistency.
• If a collision is detected, the agent replans using its local "best-path" function, treating all higher-priority paths as constraints to be avoided.
• After successful replanning, updates are messaged to all lower-priority agents, prompting their adaptation.
• Optionally, an interruptible variant (IADPP) preempts ongoing planning to respond to urgent new information.

This asynchronous messaging and update schema, complemented by local constraint enforcement (e.g., through repulsive potential fields in force-based MPC (Tallamraju et al., 2018) or enforced signed distances (Ma et al., 2022)), enables agents to react immediately and independently to changes, eliminating system-wide idle time and benefiting overall system reactivity.

3. Force-Based Formulations and Avoidance Mechanisms

Force-based decentralized planners commonly encode collision avoidance as either:

1. Explicit virtual forces—where the agent's acceleration or direction is determined by the gradient of an artificial potential field
   • Repulsive force for obstacle/agent $O_j$ on agent $R_k$ at horizon step $n$:

   $$F_{rep}^{(R_k, O_j)}(n) = \begin{cases} F_{hyp}^{(R_k, O_j)}(d(n)) \cdot \alpha & \text{if } d(n) < d_{safe} \ 0 & \text{otherwise} \end{cases}$$

   with $d(n)$ the predicted distance, $F_{hyp}$ a hyperbolic function, and $\alpha$ the directional unit vector (Tallamraju et al., 2018). - The sum over all obstacles yields the total force $f_t^{(R_k)}(n)$, which is added as an external input in decentralized MPC.

2. Convexified or penalized optimization constraints—where potential fields are precomputed over the horizon and inserted as input terms, thus keeping the underlying problem convex and tractable (Tallamraju et al., 2018), or where collision avoidance is realized through direct signed distance penalties, separating hyperplanes, or local convex region constraints (Ma et al., 2022, Tordesillas et al., 2020).

Some planners enhance robustness through additional mechanisms to avoid local minima associated with potential fields, e.g.,

• Swiveling the robot’s destination dynamically based on cost gradients
• Adding angular or tangential force components to escape complex obstacle geometries
• Employing count-based exploration penalties or tie-breaking bonuses in “force-analogous” Q functions for motion primitive selection (Guo et al., 19 Feb 2024).

4. Communication, Local Sensing, and Information Exchange

Decentralization is predicated on each agent using primarily local information or directly received peer messages. Communication protocols often involve:

• Exchange of current predicted trajectories, velocities, or motion intentions at regular intervals
• Broadcasting of polynomial coefficients or trajectory signatures (for use in continuous collision checking (Ma et al., 2022))
• Asynchronous message-passing for rapid convergence and event-driven replanning

The planner may couple this with local map-building via onboard sensors (e.g., LiDAR, cameras) and integrate object-based maps or object detection outputs. Accurate state sharing enables prediction of neighbor trajectories, necessary for forward simulation and proactive planning.

Systems like Robust MADER (Kondo et al., 2022, Kondo et al., 2023) enhance communication robustness by

• Broadcasting both optimized and committed trajectories
• Entering a delay check phase to ensure new plans are validated against late-arriving peer updates
• Guaranteeing safety provided that the verification window exceeds the maximum communication delay

5. Performance, Scalability, and Practical Applications

Experimental studies in both simulation and hardware validate the core claims:

• Asynchronous force-based decentralized planners, such as ADPP and its interruptible version, reduce wall-clock time by up to 65% versus centralized solvers and 45% versus synchronous decentralized planners in highly conflicting or heterogeneous-agent settings (Čáp et al., 2012).
• Solution quality typically incurs a modest increase in total cost (e.g., 10% longer cumulative traversal times), but this is offset by more efficient parallel computation and improved scalability.
• When instantiated as convex decentralized MPC with externalized forces, planners handle dynamic, dense, and partially unknown environments robustly and in real time, supporting 5–10 agents with rapid convergence (11–15 seconds in aerial MAV experiments (Tallamraju et al., 2018)).
• Decentralized execution generalizes to complex agent and motion models, including non-holonomic vehicles (Ma et al., 2022), multi-arm manipulation (Ha et al., 2020), real-time collaborative load towing (Chen et al., 23 Mar 2025), and even risk-aware probabilistic planning under Gaussian noise (Huang et al., 2018).

The approach is particularly suited for robotic swarms in domains where global communication is limited or latency-prone, such as urban UAS traffic management, underwater AUV teams, and decentralized ground robot fleets.

6. Theoretical Guarantees, Limitations, and Extensions

Decentralized prioritized planning algorithms provide strong theoretical guarantees:

• Termination and correctness are proved inductively by agent priority: once higher-priority agents cease updating, lower-priority agents stabilize, with the final set of trajectories guaranteed to be conflict-free (Čáp et al., 2012).
• Interruptible variants enhance efficiency, ensuring that ongoing planning work is not wasted on obsolete solutions if environmental data changes mid-computation.

Known limitations include:

• Increased message complexity (though implementable with lightweight state/trajectory payloads).
• Occasional suboptimality in global–cost terms compared to globally optimal centralized solvers.
• Susceptibility to oscillatory or deadlock behaviors if not mitigated by force design or count-based heuristics.

Recent frameworks incorporate additional features:

• Risk-aware allocation and temporal obstacle modeling for chance constraints (Huang et al., 2018).
• Robustness to communication delays via explicit delay checks and two-step commitment mechanisms (Kondo et al., 2022, Kondo et al., 2023).
• Event-driven replanning in response to significant deviations from expected force profiles (Lödige et al., 17 Sep 2024).

A diverse suite of extensions encompasses differentiable force-inspired GNN-based planners (Sharma et al., 2022), hybrid RL-optimization integration (He et al., 2021), and fully distributed inference using Gaussian Belief Propagation (Patwardhan et al., 2022).

7. Implications for Force-Based Decentralized Design

The cumulative body of work indicates that modern force-based decentralized planners benefit from an overview of:

• Asynchronous, event-driven agent updates via message-driven architectures
• Integration of explicit or implicit force/motion constraints as part of convex or penalized optimization routines
• Robust local minima avoidance, scalable communication, and delay-tolerant operation

This framework enables robust navigation, cooperation, and formation adaptation in real-world, real-time robotic teams across highly dynamic and uncertain environments. Application domains encompass multi-UAV and UGV operation, industrial mobile robot coordination, warehouse and logistics automation, and collaborative manipulation or assembly tasks.

Empirical and mathematical evidence affirms the effectiveness of force-based decentralized planning in achieving safety, scalability, and adaptability without resorting to centralized computation or global synchronization.