Smoothing-homotopy-based sequential convex programming for trajectory optimization - Zhao, Mengxin; Pan, Binfeng; Hou, Xiyu; Huang, Longxin (Aerospace science and technology, 2025)
This paper proposes a new smoothing-homotopy-based sequential convex programming (SCP) method for general trajectory optimization problems. The surrogates, derived from convolving the smoothing kernel with the terminal states, are firstly incorporated into the terminal constraints as replacements of the original ones. The smoothing parameter, taken as the homotopic parameter, decreases from a larger value to zero, with which the corresponding optimization problem gradually transitions from an easier and smoothed counterpart to the original one. Both the modified Chebyshev-Picard iteration (MCPI) approach and the trapezoidal rule are employed to transcribe the continuous-time optimization problem into a series of finite-dimensional sub-problems, respectively, which are then solved by the primal-dual interior-point solver with the aid of convexity techniques. Numerical simulations for an ascent trajectory optimization problem are provided to demonstrate the performance of the proposed method, showcasing its superior convergence compared to the standard SCP methods. •A novel smoothing-homotopy-based sequential convex programming (SCP) method is proposed.•The smoothing kernel convolves the terminal states within the time domain, replacing the original states in the SCP problem.•The modified Chebyshev-Picard iteration approach is employed.•The convergence and efficiency of the proposed method are validated through Monte Carlo tests.