Deep Learning for Optimization of Trajectories for Quadrotors (2309.15191v2)

Abstract: This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic programming (QP) problem with dynamic and collision-free constraints using piecewise trajectory segments through safe flight corridors [1]. We train neural networks to directly learn the time allocation for each segment to generate optimal smooth and fast trajectories. Furthermore, the constrained optimization problem is applied as a separate implicit layer for backpropagation in the network, for which the differential loss function can be obtained. We introduce an additional penalty function to penalize time allocations which result in solutions that violate the constraints to accelerate the training process and increase the success rate of the original optimization problem. To this end, we enable a flexible number of sequences of piece-wise trajectories by adding an extra end-of-sentence token during training. We illustrate the performance of the proposed method via extensive simulation and experimentation and show that it works in real time in diverse, cluttered environments.

• The paper introduces AllocNet, a neural network integrated with quadratic programming to optimally allocate time for quadrotor trajectory segments.
• It employs differentiable implicit layers and penalty functions to flexibly handle variable trajectory segments under dynamic and collision constraints.
• Real-world tests confirm reduced control effort and computation time, demonstrating the method's efficiency and practical applicability in autonomous operations.

Deep Learning for Optimization of Trajectories for Quadrotors

The paper presents a comprehensive paper on the integration of deep learning with model-based optimization techniques for trajectory planning of quadrotors. The authors propose a novel framework that treats the trajectory optimization problem as a quadratic programming (QP) problem, subject to dynamic and collision constraints, using piecewise trajectory segments delineated within safe flight corridors. This innovative approach enhances both the computational efficiency and feasibility of online trajectory generation by leveraging neural networks to learn optimal time allocation for each segment.

Summary of Contributions and Methodology

The paper primarily addresses the challenge of time allocation in trajectory optimization, a task that lacks formalized solutions and thus typically relies on heuristic-driven decoupling. The proposed method integrates a neural network within the quadratic programming framework, applying a differentiable implicit layer for backpropagation to improve training efficacy. Furthermore, a penalty function is introduced to expedite training and increase the QP problem's success rate by penalizing infeasible time allocations.

Key contributions of this work include:

1. Neural Network Architecture: The authors introduce AllocNet, designed to infer optimal time allocations directly from state and corridor constraints. This neural network outputs the time allocations necessary for trajectory segment optimization.
2. Flexible Framework: Incorporating an end-of-sentence token in the network training allows for handling variable sequence lengths in trajectory segments, improving flexibility and adaptability.
3. Real-world Deployment: The framework demonstrates high performance in diverse environments, validated through both simulation and real-world deployment scenarios. This indicates not only the robustness but also the real-time applicability of the proposed solution.

Strong Numerical Results

The experimental results presented validate the efficiency of the proposed method. The method achieves lower control efforts and maintains high success rates across various test environments compared to existing benchmarks. Notably, computation time is significantly reduced, allowing the framework to be implemented in real-time scenarios.

Implications and Future Directions

From a practical perspective, the deployment of such a framework in real-world quadrotor operations could have substantial implications in fields such as agriculture, industrial inspection, and customer service, where autonomous micro aerial vehicles (MAVs) are increasingly prevalent. By ensuring efficient and reliable trajectory planning, this approach could enhance the operational autonomy and safety of MAVs in complex environments.

Theoretically, this research contributes to the growing body of knowledge on the intersection of deep learning and optimization problems. Specifically, it demonstrates how deep learning can effectively handle complex constraints and dynamics in trajectory planning, providing a promising direction for future research in this domain.

Future work could explore the integration of dynamic pathfinding methods for corridor generation and further optimization of the quadratic programming solver to enhance the framework's scalability and adaptability to even more challenging scenarios.

In conclusion, this paper provides a structured methodology for integrating deep learning into trajectory optimization for quadrotors, offering both theoretical insights and practical solutions to a problem of significant complexity and relevance in autonomous systems.