Successive Convexification for Nonlinear Model Predictive Control with Continuous-Time Constraint Satisfaction

TL;DR

This paper introduces a novel NMPC framework that guarantees continuous-time constraint satisfaction and efficient computation by leveraging successive convexification, multiple shooting, and a convergence-guaranteed SCP algorithm, demonstrated through a reference-tracking example.

Contribution

It presents a new NMPC approach combining successive convexification with multiple shooting and a proximal SCP method for efficient, constraint-satisfying control.

Findings

Ensures continuous-time constraint satisfaction in NMPC.

Achieves computational efficiency through warm-starting and first-order methods.

Demonstrates effectiveness in a reference-tracking and obstacle avoidance scenario.

Abstract

We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational efficiency. We leverage the recently proposed successive convexification framework for trajectory optimization, where: (1) the path constraints and running cost are equivalently reformulated by augmenting the system dynamics, (2) multiple shooting is used for exact discretization, and (3) a convergence-guaranteed sequential convex programming (SCP) algorithm, the prox-linear method, is used to solve the discretized receding-horizon optimal control problems. The resulting NMPC framework is computationally efficient, owing to its support for warm-starting and premature termination of SCP, and its reliance on first-order information only. We demonstrate the effectiveness of the proposed NMPC framework by means of a numerical example with reference-tracking and obstacle avoidance. The implementation is available at https://github.com/UW-ACL/nmpc-ctcs