FLIP: Distributed Formation Planning

• FLIP is a distributed formation planning method that reformulates coordination as a spatiotemporal point cloud registration problem to improve scalability and efficiency.
• Each agent computes its own Optimal Formation Position Sequence through robust registration, enabling decentralized trajectory optimization under dynamic constraints.
• The method demonstrates high resilience and real-time performance in large-scale swarms, maintaining formation fidelity even with up to 12% faulty agents.

FLIP is a distributed formation planning method for large-scale robotic swarms that reformulates formation coordination as a spatiotemporal point cloud registration problem. The name denotes Formation planning for Large-scale d*Istributed swarms via **P*oint cloud registration. Its stated objective is to avoid the two dominant failure modes of traditional large-scale formation planning: oversimplified formation representations, which lead to poor performance, and complete collaborative relationships, which impose excessive computational load. In FLIP, each agent derives its own Optimal Formation Position Sequence (OFPS) by distributively computing the matching result between current positions and desired formation positions, then optimizes its cooperative trajectory using that OFPS (Zhou et al., 28 May 2026).

1. Problem setting and design objective

FLIP targets scalability, efficiency, and resilience in formation planning for large-scale swarms, including drone teams of more than 100 robots. The motivating setting is cooperative formation flight under practical disturbances such as obstacles, failed or malfunctioning agents, communication dropouts, and transient deviations from the intended formation. The central requirement is to maintain high formation fidelity without incurring the computational burden of globally dense coupling.

The method is explicitly framed against two classes of prior formulations. One class simplifies the formation representation to reduce computation, but at the cost of degraded formation performance. Another class uses complete collaborative relationships, which improves coordination fidelity but scales poorly. FLIP addresses this trade-off by retaining global formation context while avoiding a fully coupled optimization.

A key architectural feature is that each agent computes only its own local optimization while using the current or planned trajectories of all other agents via communication. This yields a distributed planning mechanism in which every agent constructs its own target sequence relative to the desired formation template, rather than relying on a centralized assignment or a fixed sparse graph abstraction.

2. Reformulation as spatiotemporal point cloud registration

The core methodological step in FLIP is the reformulation of the Optimal Formation Position Sequence calculation into a spatiotemporal Point Cloud Registration (PCR) problem. At each time step, or over a planning horizon, the current positions of agents are interpreted as a source point cloud and the desired formation as a target point cloud. Each agent then solves a registration problem with outlier rejection to estimate a transformation aligning the live swarm to the formation template (Zhou et al., 28 May 2026).

The stated alignment model is a similarity transformation with rotation $\mathbf{R}$, translation $\mathbf{t}$, and scaling $s$:

$$\hat e_{dist}= \mathop{\rm min}_{\mathbf R, \mathbf t, s} \sum_{i=1}^{N_a} \| p_i^{des} - (s \mathbf R p_i^{cur} + \mathbf t) \|_2$$

Here, $N_a$ is the number of agents, $p_i^{des}$ is the desired position for agent $i$, and $p_i^{cur}$ is the current position for agent $i$. The paper identifies this explicitly as a Sim(3) point cloud registration task.

For agent-specific OFPS construction, the large-scale formulation excludes the agent’s own state from the matching set:

$$\min_{\mathbf{R}, \mathbf{t}, s} \sum_{j \in N_a \setminus \{i\}} \| p_j^{des} - (s \mathbf{R} p_j^{cur} + \mathbf{t}) \|_2$$

This distributed registration step is then repeated across the planning horizon, producing a sequence rather than a single static target pose. A plausible implication is that FLIP replaces explicit pairwise inter-agent coordination constraints with a geometric alignment primitive that is global in information content but relatively compact in representation.

3. Optimal Formation Position Sequence and trajectory generation

Once the registration parameters are obtained, FLIP converts them into the agent’s OFPS. At time step $\mathbf{t}$0, the corresponding optimal formation position is

$\mathbf{t}$1

where $\mathbf{t}$2, $\mathbf{t}$3, and $\mathbf{t}$4 are the optimal PCR parameters at that time step (Zhou et al., 28 May 2026).

The OFPS is then used as a moving soft constraint inside each agent’s trajectory optimization. The paper describes polynomial trajectory optimization, for example with MINCO representation, using the objective

$\mathbf{t}$5

subject to formation, collision, dynamic-feasibility, and related constraints. The formation term is written as

$\mathbf{t}$6

where $\mathbf{t}$7 denotes the OFPS at time index $\mathbf{t}$8.

In this formulation, $\mathbf{t}$9 is the $s$0-order derivative representing control effort, and $s$1 is a time regularization weight. The optimizer can be solved efficiently, for example using L-BFGS. The resulting decomposition is conceptually important: PCR supplies a geometrically coherent target sequence, while the local optimizer enforces dynamics, collision avoidance, and feasibility. This separation suggests why the method can remain distributed without reducing formation planning to a purely topological consensus process.

4. Robust registration and resilience to failures

FLIP uses PCR with outlier rejection, specifically RANSAC or similar robust registration methods, to exclude agents whose states should not influence the formation transformation. The paper identifies failed or malfunctioning agents, communication dropouts, and temporarily deviating agents as principal sources of outliers (Zhou et al., 28 May 2026).

This mechanism serves two purposes simultaneously. First, it improves scalability because PCR can operate efficiently on large point sets, including hundreds or thousands of agents. Second, it improves resilience because faulty states are automatically excluded from the transformation estimate. The paper states that this prevents suboptimal trajectories and failed agents from propagating through the cooperative network and affecting more agents.

The resilience claim is not merely qualitative. In outlier experiments, FLIP maintains the remainder of the swarm in tight formation with up to 12% of agents acting as outliers, with average error $s$2. The comparison drawn in the paper is that full-graph Laplacian methods can propagate local errors globally, while methods that perform outlier handling only in a single preprocessing step are insufficient for high outlier rates.

A common misconception would be to interpret the distributed nature of FLIP as implying only local geometric knowledge. The method is distributed in optimization, not in informational scope: each agent uses global formation context by receiving the planned or current trajectories of all other agents, but computes its own OFPS and trajectory locally.

5. Empirical performance and benchmarking

The effectiveness of FLIP is demonstrated through large-scale simulations of a 120-drone formation, including a rocket formation, and through benchmarking against state-of-the-art methods. The reported results emphasize computation time, swarm scale, and robustness (Zhou et al., 28 May 2026).

Scenario	Reported result
Per-agent planning, 100 agents	$s$3 s
Per-agent planning, 120 agents	average $s$4 s
PCR/OFPS computation, 1000 agents	$s$5 s per iteration
Outlier robustness	up to 12% outliers with $s$6

The comparative benchmarks reported in the paper distinguish FLIP from two baseline tendencies. Methods using full graph Laplacians, identified as Quan’s, have $s$7 complexity; their computation time grows rapidly, exceeding 1 s for 40 agents and failing at 100 or more agents. Sparse-graph methods, identified as Zhou’s, improve time but lose formation accuracy as scale increases, with approximately 0.93 s at 100 agents.

The paper’s interpretation is that FLIP maintains real-time performance up to and beyond 100 agents while also keeping low formation error. It also reports shape adaptability: unlike Laplacian-based approaches, which are described as prone to poor performance on elongated or non-uniform formations, the PCR-based design preserves formation fidelity across diverse geometries.

The experimental presentation includes Table 1 for computation time and formation error over swarm sizes from 20 to 100 agents, Fig. 1 for the 120-drone rocket formation, Fig. 4 for outlier experiments, and Figs. 5 and 6 for shape-based comparisons.

6. Conceptual significance and scope

FLIP’s central contribution is methodological rather than merely implementational: it recasts formation maintenance as a registration problem in geometric data association, then uses the registration output as a soft target in distributed trajectory optimization. This differs from graph-Laplacian and consensus-heavy approaches by making the desired formation a point cloud template rather than a set of pairwise relational constraints (Zhou et al., 28 May 2026).

Its reported advantages are therefore threefold. Scalability arises from efficient PCR on large point sets. Resilience arises from outlier rejection during registration. Distributed execution arises because each agent computes only its own OFPS and trajectory while still exploiting the full swarm context communicated by peers.

The paper’s evaluation is simulation-based, and the reported demonstrations focus on large-scale drone formations, including scenarios with 120 and 1000 agents. This suggests strong suitability for real-time large-swarm planning in settings where agent failures or temporary deviations must be tolerated. A plausible implication is that the approach is especially well matched to formations whose geometry is poorly captured by sparse relational graphs, since the target is represented directly as a spatial template rather than as an edge-weighted interaction structure.

Within the formulation presented, FLIP is best understood as a hybrid of robust geometric matching and constrained distributed motion optimization: registration determines where the swarm should be, and per-agent optimization determines how each agent should move there under collision, dynamics, and feasibility constraints.