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This paper is about the formulation and numerical solutions of simultaneous optimal experiment design and optimal tracking control problems. Our motivating example is a robot arm that is mounted on a kitchen wall over the hotplates in order to assist humans with cooking. The robot arm can take over simple tasks such as stirring, automatic seasoning, or adding ingredients to a pot following a given recipe. Here, one of the main challenges is that the robot has to learn about the mass, inertial and other properties of the objects it is picking up while satisfying control tasks. Thus, we are facing a classical dual control problem, where system excitation for the purpose of learning has to be trade-off with other objectives such as tracking performance. After reviewing existing approaches, we propose a new formulation which allows to implement a trade-off between experiment design as well as tracking objectives in a systematic way by exploiting recent ideas from the field of economic experiment design. The approach is tested with a dynamic robot arm model performing a simple but illustrative cooking maneuver where learning and control goals are in conflict. |
