Learning-Accelerated Optimization-based Trajectory Planning for Cooperative Aerial-Ground Handover Missions

The gist: This work presents a learning-augmented trajectory planning framework for cooperative unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) handover missions.

Problem Context

Planning kinematically and dynamically feasible trajectories for multiple robots in cooperative missions, while simultaneously optimizing task-related objectives such as completion time and control effort, remains highly challenging. A widely adopted paradigm is to first compute collision-free paths or waypoints at a geometric or symbolic level, and then generate time-parameterized trajectories that interpolate these waypoints. However, in such hierarchical schemes, system dynamics and constraints are often not enforced from the outset, so the resulting trajectories may not be systematically guaranteed to be dynamically feasible, which can complicate subsequent tracking by low-level controllers. Moreover, trajectories obtained from hand-crafted or heuristically designed paths are rarely optimal for the overall mission, often resulting in conservative solutions that do not fully utilize the system’s capabilities and reduce overall task efficiency.

Proposed Solution Overview

The proposed method addresses the high computational cost of centralized trajectory optimization by introducing a neural surrogate planner to generate informed warm starts. This learning-based warm start generator approximates the mapping from task specifications to cooperative trajectories, enabling rapid generation of decent coordinated trajectories. These predictions serve as informed warm starts for the downstream centralized optimizer, thereby accelerating convergence to dynamically feasible solutions. The overall framework makes several novel contributions, including presenting a surrogate planner based on an artificial neural network that maps task specifications to cooperative trajectories as informed warm starts, using separately trained per-agent networks rather than a single monolithic policy to generate both UAV and UGV trajectories.

Learning-Augmented Pipeline Details

The learning-augmented planning workflow involves an offline training phase followed by an online deployment phase. The pipeline is structured as follows:

1. Offline training data trajectories generated by the planner Eq. for expert demonstrations.

2. Surrogate planner given start and goal states and training for predicted handover trajectories.

3. Online trajectory planner described in Eq. using predicted handover trajectories as warm starts.

The surrogate architecture is based on an agent-decoupled framework, comprising two structurally identical encoder–decoder LSTM subnetworks, one for the UAV and one for the UGV. Given a global task specification as input, each subnetwork shares the same encoder initialization and recurrently produces a sequence of future predicted states for its corresponding robot. The input vector of our surrogate planner is constructed by concatenating the relative start and goal states τ = [x rel ugv,0⊤ x rel uav,0⊤ x rel ugv,N⊤ x rel uav,N⊤]T. Correspondingly, the joint expert trajectory Y ∈ R17×N is defined as a sequence of state vectors over N = 40 steps.

Surrogate Architecture and Training

The surrogate architecture predicts robot-specific trajectories for their corresponding UAV or UGV, denoted as Yˆuav = yˆuav,0 yˆuav,1... yˆuav,39 ∈ R13×40 and Yˆugv = yˆugv,0 yˆugv,1... yˆugv,39 ∈ R5×40. The encoder E: R32 → R2×L×dhid in our framework is implemented as a deep multi-layer perceptron (MLP) to handle the static nature of the task specification. Given the standardized task specification, the encoder initializes the decoder’s hidden dynamical states by predicting the optimal initial hidden states h0 ∈ R L×dhid and the cell states c0 ∈ R L×dhid for each robot agent via. The recurrent state update is given by (hk, ck) = D(ink, hk−1, ck−1) and the subsequent output projection is computed as yˆk = Wouthk + bout. The model minimizes a mean squared error (MSE) loss with time-dependent weights in the form L = 1/BN Σ i=1 N X−1 k=0 wk∥yi,k − yˆi,k∥2 2, where B = 256 is the batch size and N = 40 the horizon.

Performance Evaluation

Benchmark evaluations demonstrate that the learning-augmented planning framework achieves more than a threefold speedup and 100% optimization success rate compared to cold start optimization. Table 1 shows a statistical comparison with and without learning-based warm starts, where the average computation time drops from 4.38 s to 1.44 s. The learning-based warm start framework reduces the average number of optimization-algorithm iterations by approximately 36% and yields a 3.04× speedup in computation time from 4.38 s to 1.44 s, while maintaining comparable solution quality. Furthermore, the success rate increases from 96.0% to 100.0% when using warm starts. The learning-based warm start increases the success rate from 96.0% to 100.0% and improves the solver success rate to 100.0% compared to a standard cold start procedure.

Conclusion

In this work, we introduce a learning-augmented pipeline to accelerate centralized trajectory optimization for heterogeneous robotic handover tasks. Using these initial guesses, our approach achieves a more than 60% reduction in computational overhead and improves the solver success rate to 100% compared to a standard cold start procedure, all while preserving solution quality. As far as we are aware, this is the first work that combines agent-wise learned surrogates with a centralized trajectory optimization framework in a cooperative setting to generate dynamically feasible and optimally coordinated UAV-UGV handover trajectories. Future research will extend this framework to complex environments with dynamic obstacles and include real-world experimental validation.

Acknowledgements This research was supported by the German Research Foundation under Grants 433183605 and 501890093, and through Germany’s Excellence Strategy under Grant EXC 2075-390740016.

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1. Neural Surrogate Planner Integration: The improved system can generate informed warm starts for the downstream centralized optimizer, which accelerates convergence to dynamically feasible solutions by providing a high-quality initial guess derived from task specifications.

2. Decoupled Agent Network Architecture: By using separate trained per-agent networks rather than a single monolithic policy, the system can specialize in the heterogeneous dynamics of each robot while receiving the same global mission context, leading to more efficient and specialized trajectory predictions.

3. Learning-Augmented Pipeline for Optimization: The framework can achieve a threefold speedup in computation time and a 100% optimization success rate compared to cold start optimization, enabling fast and reliable trajectory generation for heterogeneous multirobot systems.