Modified smoothing-homotopy-based sequential convex programming for ascent trajectory optimization with path constraints

Abstract

To meet the growing demands for reliability and onboard performance in launch missions, this paper introduces a modified smoothing-homotopy sequential convex programming (MSH-SCP) approach for endo-atmospheric ascent trajectory optimization problems with strict path constraints. Compared to the original SH-SCP, the proposed method introduces three major enhancements. Firstly, the convolution of the smoothing kernel is extended from the terminal state to all discrete states across the entire time domain. This alleviates the challenges posed by non-convexity in highly nonlinear ascent problems, resulting in an easier and more tractable smoothed problem. Secondly, by replacing states in path constraints with smoothed states, this method eliminates the need to transform path constraints into control constraints, allowing state constraints to be handled directly. Lastly, the continuous-time problem is discretized into a sequence of finite-dimensional sub-problems by parameterizing state and control variables using non-uniform rational basis spline (NURBS) curves. Leveraging from the superior fitting characteristics and strong convex hull properties of NURBS curves, optimization variables and constraints are reduced in number, markedly enhancing computational speed. Numerical simulations reveal that the MSH-SCP method achieves superior convergence behavior and exhibits significant improvements in computational efficiency.