Decentralized Multi-Quadrotor Trajectory Planning

THE CENTRAL IDEA

Keep every vehicle’s trajectory planner independent and physics-complete. Move the coordination burden to two small learned outputs—spatial waypoints and ordered passage events—then train them end-to-end by differentiating through the planners themselves.

Decentralized Multi-Quadrotor Trajectory Planning

The challenge: coupled space, time, and interaction

Planning passage for multiple quadrotors means deciding, for each vehicle, which corridor to take and when to be there—under rigid-body dynamics and rotor-thrust bounds, while vehicles’ choices affect one another. Optimizing routes and passage times jointly couples temporal allocation, nonlinear motion, and inter-vehicle interaction into one problem. That coupling is exactly what makes centralized joint optimization expensive and brittle as the vehicle count grows, and what makes purely decentralized planning produce conflicts at shared passages.

The same structure appears in orbit: multiple free-flying robots inspecting or assembling one structure must negotiate who passes which worksite first, without a ground station arbitrating in real time. The paper’s question—what is the smallest set of shared decisions that makes independent planners cooperate—is therefore directly relevant to multi-robot space operations, not only to drone swarms.

Learn the interface, not the trajectory

The proposed framework is a learning-optimization hybrid. Neural networks predict spatial waypoints and ordered passage events; each vehicle then solves its own trajectory problem independently, conditioned on those shared predictions. The planners remain full rigid-body optimizers with thrust bounds, so feasibility is guaranteed by optimization rather than hoped for from a network. Learning supplies the coordination interface—the handful of discrete-ish decisions where vehicles actually interact—while physics stays where it belongs.

This division of labor is the architectural lesson. A monolithic learned policy would have to implicitly encode dynamics, actuation limits, and collision geometry in weights; here the network only encodes the cooperative structure, and the optimizer enforces everything physics can state explicitly. When a constraint changes—thrust derating after an actuator fault, for instance—the planner adapts by re-solving, without retraining the coordination networks.

A shared time grid with locally optimized terminals

A common physical time grid aligns the vehicles: passage events predicted by the networks fix intermediate times on that grid, while terminal progress is optimized locally by each planner. This permits different vehicles to optimize different completion metrics—one may minimize time, another energy—without breaking the temporal alignment that keeps passages conflict-free. The design separates "when we meet the shared schedule" from "how each of us finishes."

For decentralized systems this is a pragmatic contract: only the event times cross vehicle boundaries, and everything downstream of them is local computation. Communication needs are modest and the failure mode is benign—if coordination messages are lost, each vehicle still holds a feasible local plan rather than half of a joint one.

Differentiable SCP: gradients through the planner

Training signal flows through the planners themselves. Differentiable sequential convex programming embeds rigid-body dynamics and rotor-thrust bounds in a form whose solutions can be differentiated, so collision costs and completion metrics computed on the generated trajectories backpropagate into both networks. The networks are thus trained on what actually matters—the quality of the trajectories the optimizers will produce—instead of on surrogate imitation targets that may diverge from downstream behavior.

θ ← θ − η · ∇θ [ Jcollision( traj(θ) ) + Jcompletion( traj(θ) ) ]

Differentiable optimization layers are still young in flight software, but the pattern here is conservative: gradients are used offline during training only. At runtime the system executes ordinary convex solves with fixed predicted parameters, which keeps the onboard computational profile identical to a conventional planner pipeline.

Results: feasibility held, completion improved

In a two-quadrotor evaluation across 24 layouts, the adapted policy passes physical feasibility and sampled separation checks in all five held-out layouts. The mean completion metric improves by 1.52% relative to the inherited policy, and the median forward pass takes 21.01 ms on the held-out exchange layout, with numerical trajectory references matching. The numbers are modest but the combination is the point: generalization to unseen layouts, constraint satisfaction everywhere, and a coordination cost measured in milliseconds.

Read carefully, the 1.52% is an average improvement on top of an already-optimized baseline, achieved without violating feasibility anywhere—similar in spirit to the paired-outcome work in the same research line: accept bounded average gains in exchange for per-case safety. For coordination problems, "never infeasible on held-out layouts" is the property that decides whether the method can leave the lab.

Engineering mapping to multi-robot space operations

Mapped to a constellation-servicing scenario, each free-flyer keeps its onboard trajectory optimizer; a coordination layer—running on one vehicle or exchanged as compact messages—predicts waypoints and passage events for shared structures such as docking corridors or robotic work envelopes. Because intermediate events are pinned to a common time grid and terminals stay local, vehicles with heterogeneous actuators or mission priorities can still participate without sharing their full dynamics models.

Integration should respect the usual assurance order: first shadow-mode the coordination networks against the existing sequential negotiation protocol, then enable them for low-consequence passages, and only then for proximity operations. At every step the independent planners’ feasibility guarantees remain the safety floor—the learned layer can degrade coordination quality, but it must never be able to degrade constraint satisfaction.

Limits and an adoption evaluation plan

The evaluation is deliberately scoped: two quadrotors, 24 layouts, five held out. Open questions for adoption include scaling to larger teams, richer obstacle geometry, and non-cooperative agents; the authors present the results as evidence that learned spatial and event parameters can coordinate independent rigid-body planners in the evaluated scenarios, not as a general swarm solution. Adoption work should therefore start by reproducing the held-out-layout discipline with the target vehicles’ own dynamics, then widening the layout distribution until separation margins—not averages—set the limit.

A concrete evaluation plan: build a layout matrix that oversamples tight passages and asymmetric priorities; report per-layout worst-case separation and completion metrics, with feasibility as a hard gate; freeze the networks and run disclosed post-freeze diagnostics; and measure forward-pass latency under the onboard computer’s thermal and power envelope. The 21 ms figure is encouraging, but it must survive the hardware that will actually fly.

SOURCE PAPER & REFERENCE MATERIAL

Learning Waypoints and Passage Events for Decentralized Multi-Quadrotor Trajectory Planning

Yunhan Shi, Jia Deng, Zehao Jia, Lin Cheng, Shengping Gong

arXiv preprint arXiv:2610.25024 · 2026

Decentralized Multi-Quadrotor Trajectory Planning去中心化多旋翼集群轨迹规划

The challenge: coupled space, time, and interaction挑战：空间、时间与交互的三重耦合

Learn the interface, not the trajectory学习接口，而不是轨迹

A shared time grid with locally optimized terminals公共时间网格与本地优化的终端

Differentiable SCP: gradients through the planner可微序列凸规划：穿过规划器的梯度

Results: feasibility held, completion improved结果：可行性保持，完成指标改进

Engineering mapping to multi-robot space operations面向多空间机器人作业的工程映射

Limits and an adoption evaluation plan边界与采用评估方案