Expected Time-Optimal Control: a Particle Model Predictive Control-based Approach via Sequential Convex Programming

TL;DR

This paper introduces a sequential convex programming approach to solve expected time-optimal control problems for uncertain dynamical systems, enabling efficient mission planning for planetary exploration.

Contribution

It converts stochastic minimum-time control problems into deterministic, tractable formulations using SCP combined with model predictive control and weighted norms.

Findings

Successfully applied to linear and nonlinear systems

Demonstrated effectiveness in mission-critical scenarios

Provides a numerically efficient control algorithm

Abstract

In this paper, we consider the problem of minimum-time optimal control for a dynamical system with initial state uncertainties and propose a sequential convex programming (SCP) solution framework. We seek to minimize the expected terminal (mission) time, which is an essential capability for planetary exploration missions where ground rovers have to carry out scientific tasks efficiently within the mission timelines in uncertain environments. Our main contribution is to convert the underlying stochastic optimal control problem into a deterministic, numerically tractable, optimal control problem. To this end, the proposed solution framework combines two strategies from previous methods: i) a partial model predictive control with consensus horizon approach and ii) a sum-of-norm cost, a temporally strictly increasing weighted-norm, promoting minimum-time trajectories. Our contribution is to adopt these formulations into an SCP solution framework and obtain a numerically tractable stochastic control algorithm. We then demonstrate the resulting control method in multiple applications: i) a closed-loop linear system as a representative result (a spacecraft double integrator model), ii) an open-loop linear system (the same model), and then iii) a nonlinear system (Dubin's car).