Conflict Resolution & Trajectory Planning

Updated 22 November 2025

Conflict Resolution and Trajectory Planning (CRTP) is a discipline that creates dynamically feasible, safe trajectories for multiple agents while avoiding collisions under uncertainty.
It employs optimization, learning-based, and negotiation methods to detect, quantify, and resolve inter-agent conflicts with minimal deviation and energy criteria.
Hybrid architectures—from centralized to decentralized frameworks—balance global optimality with scalability, ensuring robust performance in air, road, and multi-robot applications.

Conflict Resolution and Trajectory Planning (CRTP) is the technical discipline at the intersection of autonomous vehicle systems, air traffic management, robotics, and human-machine interaction, dedicated to generating dynamically feasible, input-constrained trajectories for multiple agents such that violations of safety constraints (e.g., collision, proximity, actuator/speed constraints) are avoided at all times—even under uncertainty. The goal is not merely trajectory generation but the explicit detection, quantification, and resolution of conflicts arising from agent interactions, workspace constraints, or task allocation, with the resulting plans fulfilling safety, performance, and often minimal-deviation or energy criteria.

1. Formal Problem Structure and Key Concepts

CRTP addresses systems with $N$ agents, each with state $x_i$ , dynamics $\dot x_i = f_i(x_i, u_i)$ (often nonlinear, high-dimensional), and input $u_i$ subject to bounds and physical limitations. For a joint workspace (e.g., road, airspace, shared robot cell), the state and input constraints are coupled via pairwise or groupwise safety sets: for all $i \neq j$ , $d(x_i, x_j) > d_{\mathrm{min}}$ , where $d$ is a task-dependent metric (Euclidean, configuration-space, etc.).

Conflict resolution involves detecting violations of these sets (conflicts) in planned or predicted trajectories, then modifying these trajectories—via online optimization, combinatorial search, negotiation, or rule-based arbitration—so that a conflict-free solution is achieved with minimal cost. Cost functionals include trajectory deviation, energy/fuel, delay (makespan), inter-robot or human-automation disagreement, or complex trade-offs.

Trajectory planning in the multi-agent setting is thus deeply intertwined with conflict detection and resolution, and admits a wide palette of solution methodologies: integer and quadratic programming (Dias et al., 2022, Dias et al., 2020), learning-based control (Shen et al., 2023, Yu et al., 2 Feb 2024), potential field and social-force methods (Hong et al., 17 Sep 2025, Gharibi et al., 8 Jan 2025), mixed centralized/decentralized architectures (Gupta et al., 11 Nov 2025, Čáp et al., 2014), cooperative negotiation (Schneider et al., 22 Oct 2024), and robust/recovery-based approaches (Dias et al., 2020).

2. Centralized, Decentralized, and Hybrid CRTP Architectures

A fundamental division in CRTP strategies is between centralized, decentralized, and hybrid (centralized conflict arbitration atop decentralized planning) system architectures:

Centralized approaches (e.g., mixed-integer programming, search) globally couple all agent decisions, enforcing joint safety directly (Dias et al., 2022, Dias et al., 2020, Dias et al., 2020). This exhibits superior global optimality and conflict-resolution completeness but suffers from severe scaling issues due to the combinatorial growth in decision variables.
Decentralized schemes allocate planning responsibilities to each agent, coordinating through local sensing, message-passing, or broadcasted intent (Shen et al., 2023, Čáp et al., 2014). Safety is maintained by treating other agents as dynamic obstacles (prioritized planning or local MPC), or by iterative negotiation over trajectories.
Hybrid/Arbitrated frameworks incorporate a lightweight centralized node for conflict detection and stop-go arbitration, while agents plan independently otherwise. The “virtual traffic light” scheme halts conflicting agents at the boundaries of shared conflict zones, orchestrating deadlock-free passage while minimizing global communication and planning overhead (Gupta et al., 11 Nov 2025).

The choice of architecture depends on the desired trade-off between global feasibility, runtime/communication, and system scalability.

3. Optimization-Based and Learning-Based Resolution Methods

Formally, CRTP is often posed as an optimization problem:

$\min_{\{\mathcal{T}_i\}} \sum_{i=1}^N J_i(\mathcal{T}_i)$

subject to dynamics, input, and safety constraints. Solution approaches include:

Mixed-Integer Programming: Globally optimal approaches solve for headings, speeds, and (in two-stage architectures) optimal times to “recover” from avoidance maneuvers back to preferred trajectories (Dias et al., 2022, Dias et al., 2020). These formulations encode separation constraints via disjunctive or robustified linear or nonlinear inequalities, coupled with logical (binary) variables. Successive stages allow anticipation of recovery costs, producing solutions in realistic times for up to 30 agents.
Potential Field and Gradient-Descent: In dense robotic or airspace applications, pairwise repulsive fields (artificial potential or social-force) are used for trajectory modification within high-level search frameworks such as Enhanced Conflict-Based Search (ECBS) (Hong et al., 17 Sep 2025, Gharibi et al., 8 Jan 2025). Gradient-descent on joint-space repulsion terms guides conflicting agents smoothly apart—reducing constraint tree size and computational burden.
Multi-Agent Reinforcement Learning (RL): Offline-trained multiagent RL policies can encode effective conflict resolution strategies in a discretized environment. During online execution, each agent simulates joint rollouts to derive a conflict-free strategy, followed by distributed MPC for tracking in continuous space (Shen et al., 2023). This achieves real-time feasibility and smooth operation under high constraint.
Implicit Neural Representation: Neural Trajectory Models (NTM) encode the map from $(\text{start}, \text{goal})$ pairs (single or multi-agent) to nearly optimal, collision-free trajectories in an implicit transformer-based architecture. NTMs can refine initially suboptimal/conflicting trajectories provided by traditional planners, achieving sub-millisecond inference and extremely low collision rates up to $N=64$ agents (Yu et al., 2 Feb 2024).
Cooperative Bargaining and Consensus: In human-machine shared control, CRTP is recast as a bargaining or consensus process at the trajectory level. Each agent proposes a “best” trajectory (human intent, automation optimum), and a Pareto-weighted compromise is computed via optimization, ensuring safety and mutual acceptability prior to action-level execution. Game-theoretic negotiation, attention-weighting, and iterative best-responses are core algorithmic motifs (Schneider et al., 22 Oct 2024).

4. Conflict Detection, Resolution, and Deadlock Avoidance Mechanisms

CRTP frameworks deploy diverse mechanisms for detecting and resolving conflicts across planning horizons:

Pairwise and Groupwise Conflict Check: Spatiotemporal collision or separation checks, via segment-time traversals and Minkowski-inflated path intersection, enable dynamic formation of conflict clusters. In air/roadspace, clustering conflict points and vertical/lateral dispersion organize the search space (Gupta et al., 11 Nov 2025, Gharibi et al., 8 Jan 2025).
Deadlock Resolution: Auxiliary control injections (e.g., rotated velocity vectors at incipient collision) and proactive detection of near-zero velocity states avoid symmetric deadlocks, especially in high-density or reciprocal blocking situations. Lyapunov-stable augmentation of the tracking controller preserves global convergence (Li et al., 7 Jan 2025).
Virtual Traffic Light Arbitration: Periodic conflict clustering and stop-go priority assignment enable deadlock-free, scalable operation of multi-robot and intersection systems without central planning of full trajectories (Gupta et al., 11 Nov 2025).
Minimally Invasive Recovery: Two-stage approaches explicitly model post-avoidance trajectory recovery, balancing the trade-off between initial avoidance deviation and recovery time/cost (Dias et al., 2022, Dias et al., 2020).

5. Robustness, Uncertainty, and Cooperative Extensions

Modern CRTP addresses trajectory prediction uncertainty and agent heterogeneity:

Robust Optimization: Disturbances on vehicle dynamics (e.g., due to atmospheric perturbations) are incorporated via polyhedral or budgeted uncertainty sets, with Bertsimas–Sim linearization techniques yielding tractable robust mixed-integer formulations. For typical uncertainty levels (e.g., $±5\%$ velocity error), robust CRTP is feasible for small/medium traffic; above density or uncertainty thresholds, infeasibilities emerge, necessitating vertical maneuver or hybrid strategies (Dias et al., 2020).
Agent Learning, Adaptation, and Negotiation: RL, data-driven reachability (e.g., learned discrepancy functions for reachable set over-approximation), and trajectory-level bargaining algorithms systematically adapt to changes in task, environment, and human state (Schneider et al., 22 Oct 2024, Shen et al., 2023, Taye et al., 2023).
Extensible Frameworks: Algorithms like Cluster & Disperse expose malleable, modular neighborhood structures for conflict resolution, allowing rapid integration of domain constraints—e.g., climb/descent scheduling, prohibited zones, dynamic sectorization—without wholesale reengineering (Gharibi et al., 8 Jan 2025).

6. Empirical Performance, Scalability, and Limitations

Recent results demonstrate successful real and simulated deployments:

Method/Domain	Agents (max)	Runtime / Step	Collision Rate	Key Strengths	Reference
2-stage MIP (aircraft)	30+	<10min / soln	0	Global optimality, recovery	(Dias et al., 2022)
RL + dist. MPC (vehicles)	4	0.02s / MPC	0	Real-time, distributed	(Shen et al., 2023)
APF-modified ECBS (robots)	8	0.6-1.0s/inst	0	10x fewer nodes, hardware tested	(Hong et al., 17 Sep 2025)
NTM (robots, GPU)	64	2.7ms / query	Inter-CR 0.0164	Ultra-fast, scalable	(Yu et al., 2 Feb 2024)
Virtual TL (robots)	10	10Hz / cycle	0	Deadlock-free, hybrid	(Gupta et al., 11 Nov 2025)
CRTP (UAM MDP)	32	0.2s / cycle	NMAC < 1	Decentralized, 6D, scalable	(Taye et al., 2023)

Limitations acknowledged across frameworks include scaling of centralized models, conservative avoidance in local-only schemes, sensitivity to agent modeling errors or bad predictions (requiring robustification), and the computational cost of real-time combinatorial search. Future extensions focus on further scaling (e.g., 3D CRTP, hundreds of agents), hierarchical planning, adaptive negotiation weights, and leveraging learning/predictive techniques for dynamic and uncertain environments.

7. Domain-Specific Applications and Extensions

Air Traffic Conflict Resolution: CRTP has produced heuristics (Cluster & Disperse), robust MILP and MIQCP formulations, and agent-based models reproducing controller tactics including “directs” and local rerouting (Gharibi et al., 8 Jan 2025, Dias et al., 2020, Bongiorno et al., 2016). Empirical studies confirm that tactical optimization steps not only improve efficiency but reduce downstream controller workload, even under uncertainty.
Autonomous Vehicle Formations: Bi-level architectures guarantee conflict-free formation changes in lane-drops and merges, using combinatorial assignment in relative coordinates, discrete conflict analysis and low-level optimal control (Cai et al., 2021).
Multi-Robot Coordination in Shared Environments: Extensions of prioritized planning, ECBS with repulsive modifications, and learning-based decentralized schemes achieve robust, collision-free operation in high-density, real-world scenarios (Gupta et al., 11 Nov 2025, Čáp et al., 2014, Hong et al., 17 Sep 2025).
Human–Machine Shared Control: Multi-objective compromise over trajectory space, with negotiation-theoretic or intention-sensitive arbitration, is critical in cooperative CRTP for mixed human/autonomy agents (e.g., agricultural machinery, assisted mobility) (Schneider et al., 22 Oct 2024).

Conflict Resolution and Trajectory Planning is thus a vibrant, rapidly evolving research field, leveraging combinatorial optimization, model-predictive control, distributed coordination, data-driven representation, and game-theoretic negotiation. Its principled frameworks are foundational for safety assurance and performance in high-density, multi-agent autonomous and semi-autonomous systems across domains.