Optimal control for a robotic exploration, pick-up and delivery problem

TL;DR

This paper develops and compares approximate optimal control methods for a mobile robot tasked with finding, collecting, and delivering objects in a cluttered environment, balancing computational efficiency and solution quality.

Contribution

It introduces a hybrid optimal control framework with both time-driven and event-driven solutions for complex robotic pick-up and delivery tasks.

Findings

Event-driven approach is computationally more efficient.

Both methods achieve similar qualitative results.

The framework applies to various robotic applications.

Abstract

This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or drop-off of an object. The objects are modeled by point masses with a-priori unknown locations in a bounded two-dimensional space that may contain unknown obstacles. For this hybrid system, an Optimal Control Problem (OCP) is approximately solved by a receding horizon scheme, where the derived lower bound for the cost-to-go is evaluated for the worst and for a probabilistic case, assuming a uniform distribution of the objects. First, a time-driven approximate solution based on time and position space discretization and mixed integer programming is presented. Due to the high computational cost of this solution, an alternative event-driven approximate approach based on a suitable motion parameterization and gradient-based optimization is proposed. The solutions are compared in a numerical example, suggesting that the latter approach offers a significant computational advantage while yielding similar qualitative results compared to the former. The methods are particularly relevant for various robotic applications like automated cleaning, search and rescue, harvesting or manufacturing.