Optimal exploration and control for a robotic pick-up and delivery problem in two dimensions

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 objects are modeled by point masses with a priori unknown locations in a bounded two-dimensional space. The robot has forth-order dynamics that change instantaneously at any pick-up or drop-off of an object. The corresponding hybrid Optimal Control Problem (OCP) is solved by a receding horizon scheme, where the derived lower bound for the cost-to-go is evaluated for the worst- and a probabilistic case, assuming a uniform distribution of the objects. We first present a time-driven approximate solution based on time and position space discretization. Due to the high computational cost of this solution, we alternatively propose an event-driven approximate approach based on a suitable motion parameterization. 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.