Trajectory Optimization by Pseudospectral Successive Convexification on Riemannian Manifolds

Abstract

This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While pseudospectral successive convexification combines spectral collocation with successive convexification, classical pseudospectral methods are not geometry-consistent on manifolds. This is because interpolation and differentiation are performed in Euclidean coordinates. We introduce a geometry-consistent transcription that enables pseudospectral collocation without imposing manifold constraints extrinsically. The resulting method solves nonconvex manifold-constrained problems through a sequence of convex subproblems. A six-degree-of-freedom landing guidance example with unit quaternions and unit direction vectors demonstrates the practicality of the approach. The proposed method preserves manifold feasibility to machine precision and achieves significant computational speedups.