ItemBehavior modeling for hybrid robotic vehicles(Department of Mechanical Engineering, University of Delaware, 2011-10) Rawal, ChetanThe behavior of a certain class of hybrid robotic systems can be expressed using formal languages. In this work, we show how languages can be generated from discrete abstractions of such hybrid systems; that these languages are regular; and they belong to the star free (SF) class of the Sub-regular hierarchy. Planning and control of hybrid systems is typically difficult due to the computational cost involved in predicting the system’s future states, since the states can take infinite values while evolving along the trajectories of continuous dynamics. A discrete abstraction of the hybrid system can reduce these values to a finite number, thereby fascilitating the solution to the reachability problem. Abstraction enables us to focus on planning the system’s overall behavior through controller sequences observed in the abstract system, instead of dealing with the dynamics associated with each controller. ItemTopology Optimization in Cellular Neural Networks(Department of Mechanical Engineering, University of Delaware, 2010-07) Bhambhani, Varsha; Tanner, HerbertThis paper establishes a new constrained combinatorial optimization approach to the design of cellular neural networks with sparse connectivity. This strategy is applicable to cases where maintaining links between neurons incurs a cost, which could possibly vary between these links. The cellular neural network’s interconnection topology is diluted without significantly degrading its performance, the network quantified by the average recall probability for the desired patterns engraved into its associative memory. The dilution process selectively removes the links that contribute the least to a metric related to the size of system’s desired memory pattern attraction regions. The metric used here is the magnitude of the network’s nodes’ stability parameters, which have been proposed as a measure for the quality of memorization. Further, the efficiency of the method is justified by comparing it with an alternative dilution approach based on probability theory and randomized algorithms. We demonstrate by means of an example that this method of network dilution based on combinatorial optimization produces cheaper associative memories that in general trade off performance for cost, and in many cases the performance of the diluted network is on par with the original system. Also the randomized algorithm based method results in same network performance in terms of network recall probability. ItemMulti-agent navigation functions: Have we missed something?(Department of Mechanical Engineering, University of Delaware, 2010-08) Tanner, Herbert; Boddu, AdithyaThis paper presents a methodology for designing (centralized) control laws which can probably steer a group of robotic agents to fall into a formation of arbitrary shape, while following collision free trajectories. The scheme is based on the concept of navigation functions, a special type of artificial potential functions without local minima, and the paper describes how this idea can be generalized from its original formulation for single-robot systems, to multi-robot formations. We indicate why existing solutions that have appeared in literature, although potentially functional, may not have been accompanied with sufficient guarantees against the possibility of the system ever getting stuck in non-optimal configurations. The problem is therefore revisited here under a new set of assumptions, a new construction is proposed, and the properties of this new centralized potential function are analytically demonstrated. ItemComposition of Context-Free Motion Description Languages(Department of Mechanical Engineering, University of Delaware, 2010) Zhang, Wenqi; Tanner, HerbertWe introduce a new formalism to define compositions of interacting heterogeneous systems, described by extended motion description languages (MDLes). The novelty of the formalism is in producing a composed system with a behavior that could be a superset of the union of the behaviors of its generators. We prove closedness of MDLes under this composition and we indicate that in the class of systems modeled using MDLes, language equivalence is decidable. Our approach consists of representing MDLes as normed processes, recursively defined as a guarded system of recursion equations in restricted Greibach Normal Form over a basic process algebra. Basic processes have well defined semantics for composition, which we exploit to establish the properties of our composed MDLes. ItemRandomized Model Predictive Navigation(Department of Mechanical Engineering, University of Delaware, 2010-02) Tanner, Herbert; Piovesan, JorgeA new methodology for implementing nonlinear receding horizon optimization is presented, with direct application to robot navigation in cluttered environments. The methodology combines elements from statistical learning theory with nonlinear receding horizon schemes that use control Lyapunov functions as terminal costs, while relaxing the conditions on the time derivatives of the latter, based on a new result for stability of nonlinear systems with switching dynamics. As the theoretical analysis indicates, and numerical results verify, the proposed receding horizon scheme can utilize terminal costs that are not control Lyapunov functions. The resulting strategy is shown to outperform traditional potential field-based techniques, even when additional optimization objectives are imposed, and allows for trade-offs between performance and computational complexity. ItemModeling of a Hexapod Robot; Kinematic Equivalence to a Unicycle(Department of Mechanical Engineering, University of Delaware, 2009-04) Panagou, Dimitra; Tanner, HerbertThis report describes the kinematic and dynamic modeling of a hexapod robot. The 6-DOF (degrees of freedom) analytical kinematic and dynamic equations of motion are derived following the classical Newtonian mechanics. Under certain task-specific assumption, it is shown that the complex 6-DOF model can be simplified, resulting in an abstract model. Specifically, the motion of the robot on the horizontal plane in particular is described by the unicycle model with dynamic extension. The abstract unicycle model exhibits restricted behavior compared to the concrete hexapod model, but facilitates motion planning and control design and ensures that higher level control plans are implementable as low level control laws.