Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach

Riccardo Bonalli (1) , Andrew Bylard (1) , Abhishek Cauligi (1) , Thomas Lew (2) , Marco Pavone (1)

1 AA Stanford - Department of Aeronautics and Astronautics [Stanford]
2 IDSC - Institute for Dynamic Systems and Control

Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are restricted to Euclidean settings, which precludes their application to problem instances where one must reason about manifold-type constraints (that is, constraints, such as loop closure, which restrict the motion of a system to a subset of the ambient space). The aim of this paper is to fill this gap by extending SCP-based trajectory optimization methods to a manifold setting. The key insight is to leverage geometric embeddings to lift a manifold-constrained trajectory optimization problem into an equivalent problem defined over a space enjoying a Euclidean structure. This insight allows one to extend existing SCP methods to a manifold setting in a fairly natural way. In particular, we present a SCP algorithm for manifold problems with refined theoretical guarantees that resemble those derived for the Euclidean setting, and demonstrate its practical performance via numerical experiments.

Domaines: Optimisation et contrôle [math.OC]

Riccardo Bonalli, Andrew Bylard, Abhishek Cauligi, Thomas Lew, Marco Pavone. Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach. Robotics:Science and Systems 2019, Jun 2019, Fribourg, Germany. ⟨hal-03467721⟩