Intrinsic Successive Convexification: Trajectory Optimization on Smooth Manifolds

TL;DR

This paper introduces intrinsic Successive Convexification (iSCvx) for trajectory optimization on smooth manifolds, addressing the redundancy and representation-dependence of traditional SCvx by performing linearization with intrinsic differentials and retractions. By formulating a geodesic-appropriate cost and a coordinate-free penalty framework, iSCvx achieves a smaller, more robust subproblem and guaranteed feasibility through virtual controls and slack buffers. The approach is demonstrated on constrained attitude guidance with quaternion dynamics, showing improved iteration counts, runtimes, and consistent trajectories compared to Euclidean SCvx, while maintaining similar geodesic trajectory quality. The work offers a path toward representation-invariant, coordinate-free optimal control on manifolds with potential extensions to powered descent and broader sequential convex programming paradigms, underpinned by coordinate-free convergence principles.

Abstract

A fundamental issue at the core of trajectory optimization on smooth manifolds is handling the implicit manifold constraint within the dynamics. The conventional approach is to enforce the dynamic model as a constraint. However, we show this approach leads to significantly redundant operations, as well as being heavily dependent on the state space representation. Specifically, we propose an intrinsic successive convexification methodology for optimal control on smooth manifolds. This so-called iSCvx is then applied to a representative example involving attitude trajectory optimization for a spacecraft subject to non-convex constraints.

Figures (2)

• Figure 1: Visualization of perturbing a trajectory along a tangent space.
• Figure 2: The iterates of SCvx and iSCvx for the constrained attitude guidance problem.

Theorems & Definitions (4)

• Proposition IV.1
• proof
• Lemma IV.2
• proof