Extending Sequential Convex Programming for Trajectory Optimization on Lie Groups

Abstract

In this work, we address the solution of nonconvex trajectory optimization problems for control-affine systems evolving in Lie Groups. To this end, we propose an extension of Sequential Convex Programming (SCP), which is a powerful and reliable algorithmic framework for nonconvex optimization. At the core of SCP lies the linearization of all the nonconvexities of the trajectory optimization problem. Thus, since the classical linearization technique is wellposed only in the Euclidean space, all the current SCP implementations assume that the problem variables belong to the Euclidean space. To overcome this restriction, we define an extension of the classical linearization technique that is well-posed for control-affine systems evolving in Lie Groups. This linearization technique is the main result of the thesis and the core of the proposed SCP extension, named LieSCP. In order to test the algorithm, we employ LieSCP to solve an optimal attitude control problem of a 6-DOF rigid body. Moreover, we carry out a Monte Carlo performance comparison between LieSCP and a benchmark solver. The latter solver is applied to an equivalent problem formulation whose variables are all in the Euclidean space. As a result, the statistics of LieSCP testify its superiority against benchmark solvers. in the solution of the considered case study and pave the way to implement LieSCP in real case scenarios.