Survey of convex optimization for aerospace applications

Abstract

Convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds exist. Computational efficiency and tractability in aerospace engineering, especially in guidance, navigation, and control (GN&C), are of paramount importance. With theoretical guarantees on solutions and computational efficiency, convex optimization lends itself as a very appealing tool. Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard real-time applications. This paper attempts to provide an overview on the problems to date in aerospace guidance, path planning, and control where convex optimization has been applied. Various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems. Discussions on how to ensure the validity of the convexification process are provided. Some related implementation issues will be introduced as well.

Optimal Guidance and Control with Nonlinear Dynamics Using Sequential Convex Programming

“…Convex optimization problems are easily and efficiently solved, but many common constraints on trajectory generation and control problems are nonconvex and many dynamical systems are nonlinear [12]. Through convexification, relaxation, and approximation some such problems may be fully solved [13,14].…”

“…Typical implementations of SCP use an approximation of the dynamics without addressing this gap between the approximated and actual dynamics since the optimal state trajectory is used more frequently [12,28,29]. Frequently, trust regions are used to keep the successive solutions sufficiently close to mitigate the buildup of error due to linearization [30,31].…”

“…Simulations used CVX, a MATLAB-based convex optimization engine running the Mosek solver[40][41][42]. The nonlinear trajectories were found by numerically integrating the nonlinear dynamics, as seen in Eqs (12),(20). using the optimal control trajectory found using SCP, SCPn, and M-SCPn.…”

Adaptive generalized ZEM-ZEV feedback guidance for planetary landing via a deep reinforcement learning approach

“…Importantly, the convexification methodology has been recently applied to other aerospace guidance problems. A review of the application areas can be found in [11]. Conversely, cently, a three-dimensional, fuel-optimal, powered descent guidance algorithm based on indirect methods has been developed [12].…”

Real-Time Quad-Rotor Path Planning Using Convex Optimization and Compound State-Triggered Constraints

“…Over the past two decades, direct methods for solving optimal control problems have seen a rise in popularity due to the ease of use, performance, and convergence properties offered by modern optimization algorithms [4], [5]. Direct methods are typically used to solve problems with continuous variables, and cannot readily enforce constraints involving discrete decisions.…”