Optimal, Multi-Modal Control with Applications in Robotics

The objective of this dissertation is to incorporate the concept of optimality to multi-modal control and apply the theoretical results to obtain successful navigation strategies for autonomous mobile robots. The main idea in multi-modal control is to breakup a complex control task into simpler tasks. In particular, number of control modes are constructed, each with respect to a particular task, and these modes are combined according to some supervisory control logic in order to complete the overall control task. This way of modularizing the control task lends itself particularly well to the control of autonomous mobile robot, as evidenced by the success of behavior-based robotics. Many challenging and interesting research issues arise when employing multi-modal control. This thesis aims to address these issues within an optimal control framework. In particular, the contributions of this dissertation are as follows: We first addressed the problem of inferring global behaviors from a collection of local rules (i.e., feedback control laws). Next, we addressed the issue of adaptively varying the multi-modal control system to further improve performance. Inspired by adaptive multi-modal control, we presented a constructivist framework for the learning from example problem. This framework was applied to the DARPA sponsored Learning Applied to Ground Robots (LAGR) project. Next, we addressed the optimal control of multi-modal systems with infinite dimensional constraints. These constraints are formulated as multi-modal, multi-dimensional (M3D) systems, where the dimensions of the state and control spaces change between modes to account for the constraints, to ease the computational burdens associated with traditional methods. Finally, we used multi-modal control strategies to develop effective navigation strategies for autonomous mobile robots. The theoretical results presented in this thesis are verified by conducting simulated experiments using Matlab and actual experiments using the Magellan Pro robot platform and the LAGR robot. In closing, the main strength of multi-modal control lies in breaking up complex control task into simpler tasks. This divide-and-conquer approach helps modularize the control system. This has the same effect on complex control systems that object-oriented programming has for large-scale computer programs, namely it allows greater simplicity, flexibility, and adaptability.Ph.D.Committee Chair: Egerstedt, Magnus; Committee Member: Ferri, Bonnie; Committee Member: Lee, Chin-Hui; Committee Member: Reveliotis, Spyros; Committee Member: Yezzi, Anthon

A Characterization Theorem for a Modal Description Logic

Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles

Topic-Sensitive Epistemic 2D Truthmaker ZFC and Absolute Decidability

This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance an epistemic two-dimensional truthmaker semantics, if hyperintenisonal approaches are to be preferred to possible worlds semantics. I examine the relation between epistemic truthmakers and epistemic set theory