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 behaviorbased 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. To this end, 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). Given a collection of modes, an algorithm, that characterizes the expressiveness of the multi-modal system and learns control programs that complete a desired task while minimizing a prescribed performance criterion, is presented. Next, we addressed the issue of adaptively varying the multi-modal control system to further improve performance. A variational framework for adaptive multi-modal control is developed, where a given collection of modes is adaptively improved by adding new modes to the set. This augmentation of the mode set increases the expressiveness and the performance of the system as well as reduces the complexity of the control programs. Adaptive multi-modal control led to an interesting application to the the Learning From Example problem, where new controllers are learned from training examples. First, a variational framework is used to learn new modes as needed to approximate a given training trajectories. Next, this framework was applied to the DARPA sponsored Learning Applied to Ground Robots (LAGR) project. The LAGR project motivated a need for new solutions not relying on differentiability assumptions (as the variational approach does), which was addressed by posing the learning problem as an combinatorial optimization problem, and an algorithm for solving this problem using a hill climbing method is presented. Next, we addressed the optimal control of multi-modal systems with infinite dimensional constraints. These constraints are formulated as multi-modal, multidimensional (M3 D) 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. The optimality conditions for this formulation are derived and an algorithmic framework for the optimal control of M3D systems is presented. 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 in a lab setting using the Magellan Pro mobile robot platform. Moreover, human operated training runs are used to develop effective navigation strategies following the constructivist framework for the learning from example problem. These results were successfully verified on the LAGR robot to learn effective strategies for the LAGR competition. 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 objectoriented programming has for large-scale computer programs, namely it allows greater simplicity, flexibility, and adaptability.