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

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

cs.ROOct 18, 2026

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

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

Organizations: School of Astronautics, Beihang University, Beijing 100191, China · Astroup(Beijing) Technology Co., Ltd.

Abstract

Multi-quadrotor passage planning requires coordinated spatial routes and passage times under vehicle dynamics and actuation constraints. Optimizing these decisions jointly couples temporal allocation, nonlinear motion, and inter-vehicle interactions, creating a computational challenge for local trajectory generation. We propose a learning-optimization framework that predicts spatial waypoints and ordered passage events for independently solved quadrotor planners. A common physical time grid aligns the vehicles, with intermediate events fixed by the networks and terminal progress optimized locally to permit different completion metrics. Differentiable sequential convex programming incorporates rigid-body dynamics and rotor-thrust bounds, allowing collision and completion gradients to train both networks through the generated trajectories. In a two-quadrotor evaluation across 24 layouts, the adapted policy passes physical feasibility and sampled separation checks in all five held-out layouts. Their mean completion metric decreases by 1.52% relative to the inherited policy. The median forward time is 21.01 ms on the held-out exchange layout with matching numerical trajectory references. These results demonstrate that learned spatial and event parameters can coordinate independent rigid-body planners while preserving local vehicle constraints in the evaluated scenarios.

Figures & tables

Fig. 1: Schematic of the learning and planning architecture. The waypoint block illustrates two learned intermediate points, which are combined with prescribed gate centers to define the passage events. The event block assigns their temporal locations on a shared grid. The repeated SCP blocks illustrate differentiable local planning under linearized rigid-body dynamics. Dashed green arrows denote gradients of the outer collision and completion objectives. The waypoint count and unrolling depth shown here are example design choices.

Fig. 2: Schematic of event encoding on a shared time grid. (a) Each color illustrates one vehicle’s event: stem heights are the adjacent-node masses

\mu^{\rm enc}

, and the dotted vertical line marks their grid-index expectation

c

. (b) The associated progress

\lambda

decreases from one to zero. The event locations illustrate the representation. Each intermediate code parameterizes a single continuous-time passage constraint at its fractional timestamp.

Parameter	Value
Vehicle mass $m$	0.713 kg
Inertia diagonal $J$	$(0.03,0.03,0.055)$ kg m 2
Arm length $\ell$ ; torque coefficient $c_{\tau}$	0.17 m; 0.01 m
Rotor thrust range	$[1.0,3.3]$ N
Speed; body-rate limit	1.5 m/s; 8 rad/s
Height range	$[0.5,1.5]$ m

TABLE I: Rigid-body planning and training configuration

	Sampled separation passed		Mean $T_{i}$ (s)
Split	Before	After	Before	After
Training	12/14	14/14	2.40039	2.36335
Validation	4/5	5/5	2.40040	2.36397
Held-out test	4/5	5/5	2.40039	2.36384

TABLE II: Layout-level results before and after exchange adaptation

Fig. 3: Top-view projections of all four added goal-exchange layouts: two training layouts, one validation layout, and one held-out test layout. Solid blue and dashed orange lines are the adapted trajectories; faint dotted lines show the inherited-policy trajectories. Open waypoint markers denote learned spatial targets, circles indicate initial positions, and stars indicate final positions. Gray disks are projections of the position tolerance balls used to represent gates. Filled markers and their dotted connector identify both vehicles at the same closest-approach time. All 401 rollout samples per vehicle are used.

Fig. 4: Recorded exchange adaptation. (a) All 36 accepted batch updates and seven validation checkpoints, including update zero. Each batch contains one exchange and one ordinary training layout; validation uses five layouts. (b) Minimum audited scaled separation on the single exchange validation layout. The dotted line is the 0.25 m evaluation threshold. No smoothing or independent-seed confidence interval is applied.

Fig. 5: Audited scaled inter-vehicle separation over the complete common 3 s horizon, including post-event trajectory tails. All four exchange layouts are shown. The metric is

\left\lVert\operatorname{diag}(1,1,1/3)(p_{1}-p_{2})\right\rVert_{2}

. The 0.25 m threshold is exceeded after adaptation in each layout. The panels describe two training layouts, one validation layout, and one held-out test layout.

Layout	Min. scaled distance (m)		$\Delta t_{x}$ (s)
	Before	After	After
Training A	0.01128	0.30550	0.40319
Training B	0.00737	0.28798	0.37837
Validation	0.01877	0.31195	0.42926
Held-out test	0.00724	0.30822	0.40033

TABLE III: Added exchange layouts and their temporal separation

Fig. 6: Controlled thrust-difference penalty experiment with frozen network weights. Each line links the same original test layout with the penalty off and on; all four test layouts are included. Values are the maximum rotor-thrust or acceleration jump over both vehicles and the full common horizon. Two penalty-off layouts use nonlinear recovery after the initial six-step SCP attempt; all penalty-on layouts pass without that recovery.

Fig. 7: All 60 recorded warm-reference forward timings, with 30 calls per setting. Solid horizontal marks show medians and dashed marks show 95th percentiles. Fixed-layout calls use the held-out exchange layout; switching includes two training, one validation, and one held-out layout. Each setting measures repeated solver calls with prepared trajectory references.

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Open paper AskPDF arXiv

Agile quadrotor flight pushes the limits of control, actuation, and onboard perception. While time-optimal trajectory planning has been extensively studied, existing approaches typically neglect the tight coupling between vehicle dynamics, environmental geometry, and the visual requirements of onboard state estimation. As a result, trajectories that are dynamically feasible may fail in closed-loop execution due to degraded visual quality. This paper introduces a unified time-optimal trajectory optimization framework for vision-based quadrotors that explicitly incorporates perception constraints alongside full nonlinear dynamics, rotor actuation limits, aerodynamic effects, camera field-of-view constraints, and convex geometric gate representations. The proposed formulation solves minimum-time lap trajectories for arbitrary racetracks with diverse gate shapes and orientations, while remaining numerically robust and computationally efficient. We derive an information-theoretic position uncertainty metric to quantify visual state-estimation quality and integrate it into the planner through three perception objectives: position uncertainty minimization, sequential field-of-view constraints, and look-ahead alignment. This enables systematic exploration of the trade-offs between speed and perceptual reliability. To accurately track the resulting perception-aware trajectories, we develop a model predictive contouring tracking controller that separates lateral and progress errors. Experiments demonstrate real-world flight speeds up to 9.8 m/s with 0.07 m average tracking error, and closed-loop success rates improved from 55% to 100% on a challenging Split-S course. The proposed system provides a scalable benchmark for studying the fundamental limits of perception-aware, time-optimal autonomous flight.

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