Simulation and control of hybrid systems with applications to mobile robotics

As the price-performance ratio of embedded processors increases and the size of microchips decreases, more sophisticated paradigms for software based control have evolved. This trend is particularly evident in mobile robotics because these systems typically have significant onboard computing power, complex mission requirements and the need to process data coming from many types of sensors in real time. Such systems are modeled as Hierarchical Hybrid Systems (HHS). In the first part of the dissertation three novel numerical techniques for simulating HHS are introduced. The first of these addresses the problem of detecting and locating the occurrence of discrete transitions (i.e., control mode or model switches) during the course of a simulation, especially switches which occur near a model singularity—an area in which all competing event detections methods fail. The remaining two simulation techniques seek to circumvent one of the major causes of computational bottle necks in large-scale simulations—the requirement that all differential equations in the system be simulated using a single global choice of step size. In one case differential equations with right hand sides that are partially coupled, without consideration of the mode switches, are considered. The third algorithm is concerned with simulating so-called multi-agent hybrid systems. These systems have decoupled sets of differential equations yet the inequalities which signal mode switches are coupled. Here the challenge is properly detecting transitions when the numerical integration of the various differential equations is performed asynchronously using many local time clocks. In the second part of the dissertation a framework for reactive motion planning and control of mobile robots is presented. It is our approach that reactive control and motion planning schemes for mobile robots are best modeled as Hybrid Systems. We assume a suite of low level controllers have been designed. The problem is how to compose these controllers, either through designing a switching sequence or synthesizing entirely new control modes, in such a way that the aggregate behavior of the system achieves all of the objectives simultaneously, or reports failure if it cannot. The numerical algorithm represents a rigorous approach to modular control law composition