Event-driven optimal control for a robotic exploration, pick-up and delivery problem

This paper addresses an Optimal Control Problem (OCP) 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 represented by point masses in a bounded two-dimensional space that may contain unknown obstacles. The OCP is formulated assuming either a worst-case positioning, or a uniform distribution of the objects (probabilistic case). Modeling the robotic problem by a hybrid system facilitates an event-driven receding horizon solution based on motion parameterization and gradient-based optimization. A comparison of the proposed methods to two simple heuristic approaches in simulation suggests that the event-driven approach offers significant advantages - a lower execution time (on average) and the ability to handle obstacles - over the simple solutions, at the price of a moderately increased computational effort. The methods are relevant for various robotic applications, e.g. the motion control of mobile manipulators for home-care, search and rescue, harvesting, manufacturing etc.