Successive Convexification of Non-Convex Optimal Control Problems with State Constraints

TL;DR

This paper introduces a Successive Convexification algorithm for solving complex non-convex optimal control problems with state constraints, enabling efficient, reliable, and real-time trajectory planning for autonomous systems.

Contribution

The paper proposes a novel Successive Convexification method that handles non-convex dynamics and constraints, with proven convergence and suitability for real-time autonomous control.

Findings

Algorithm converges reliably after few iterations.

Suitable for real-time trajectory planning with collision avoidance.

Efficient implementation with interior point methods.

Abstract

This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and non-convex state/control constraints. To tackle the challenge posed by non-convexity, first we utilize exact penalty function to handle the nonlinear dynamics. Then the proposed algorithm successively convexifies the problem via a $ \textit{project-and-linearize} $ procedure. Thus a finite dimensional convex programming subproblem is solved at each succession, which can be done efficiently with fast Interior Point Method (IPM) solvers. Global convergence to a local optimum is demonstrated with certain convexity assumptions, which are satisfied in a broad range of optimal control problems. The proposed algorithm is particularly suitable for solving trajectory planning problems with collision avoidance constraints. Through numerical simulations, we demonstrate that the algorithm converges reliably after only a few successions. Thus with powerful IPM based custom solvers, the algorithm can be implemented onboard for real-time autonomous control applications.