Optimal Powered Descent Guidance with First-Order Optimization and Expansive Projection

Core Concepts

Introducing a first-order method for solving optimal powered descent guidance problems, addressing nonconvex constraints effectively.

Abstract

This paper presents a novel approach to solve optimal powered descent guidance (PDG) problems by directly handling nonconvex constraints. Traditional methods like lossless convexification and linear approximation have limitations, leading to infeasible solutions or suboptimality. The proposed first-order approach utilizes orthogonal projections onto nonconvex sets, known as expansive projection (ExProj). This method overcomes the challenges faced by conventional techniques, producing feasible solutions even for nonoptimal time of flight cases. Numerical examples demonstrate the effectiveness of this methodology in terms of fuel consumption and flight time. The proposed approach offers enhanced flexibility in devising viable trajectories for planetary soft landing scenarios.

Stats

"The optimal time of flight for the given scenario is found to be t∗f = 46.96 s."
"The LCvx solution marginally underutilizes the maximum thrust, while the ExProj solution utilizes the full maximum thrust."
"For tf < t∗f case, the LCvx solution is infeasible, necessitating a thrust level below the established lower bound."
"In the tf > t∗f case, the LCvx solution uses significantly less thrust than allowed maximum."

Quotes

"We introduce a first-order approach that makes use of orthogonal projections onto nonconvex sets, allowing expansive projection (ExProj)."
"Our analysis substantiates that the proposed approach affords enhanced flexibility in devising viable trajectories for a diverse array of planetary soft landing scenarios."

Key Insights Distilled From

Powered Descent Guidance via First-Order Optimization with Expansive Projection

by Jiwoo Choi,J... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2310.00397.pdf

Deeper Inquiries

How can this first-order optimization method be applied to other aerospace engineering problems

This first-order optimization method can be applied to various other aerospace engineering problems that involve nonconvex constraints and require real-time decision-making. For instance, it can be utilized in trajectory optimization for spacecraft reentry, where the guidance system must navigate through varying atmospheric conditions while adhering to safety constraints. Additionally, this method could enhance autonomous landing systems for drones or unmanned aerial vehicles by efficiently computing optimal trajectories considering obstacles and environmental factors. The algorithm's ability to handle nonconvex sets directly makes it suitable for tasks like path planning in complex environments or optimizing fuel consumption during flight maneuvers.

What are potential drawbacks or limitations of using expansive projections in optimization algorithms

While expansive projections offer advantages in handling nonconvex sets directly without resorting to convex relaxation techniques, they also come with potential drawbacks. One limitation is the computational complexity associated with solving optimization problems involving expansive projections, as these operations may require more iterations compared to traditional methods using nonexpansive projections. Moreover, there might be challenges in guaranteeing convergence when utilizing expansive projections due to the lack of established theoretical results on their performance across all scenarios. Another drawback is the possibility of increased sensitivity to noise or uncertainties in the problem formulation, which could affect the robustness and stability of the algorithm.

How can machine learning techniques be integrated with this optimization approach to further enhance performance

Integrating machine learning techniques with this first-order optimization approach can lead to significant performance improvements in aerospace engineering applications. By incorporating neural networks or reinforcement learning algorithms into the optimization process, it becomes possible to learn from past data and adaptively adjust parameters based on experience gained during operation. Machine learning models can assist in predicting future states accurately, enabling better initialization of variables for the optimization algorithm and potentially reducing convergence time. Furthermore, deep learning frameworks can help optimize complex objective functions by approximating nonlinear relationships within large datasets more effectively than traditional methods alone.