Joel M. Esposito

Hierarchical modeling and analysis of embedded systems

This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination.

A Framework and Architecture for Multi-Robot Coordination

In this paper, we present a framework and the software architecture for the deployment of multiple autonomous robots in an unstructured and unknown environment, with applications ranging from scouting and reconnaissance, to search and rescue, to manipulation tasks, to cooperative localization and mapping, and formation control. Our software framework allows a modular and hierarchical approach to programming deliberative and reactive behaviors in autonomous operation. Formal definitions for sequential composition, hierarchical composition, and parallel composition allow the bottom-up development of complex software systems. We demonstrate the algorithms and software on an experimental testbed that involves a group of carlike robots, each using a single omnidirectional camera as a sensor without explicit use of odometry.

Hierarchical Hybrid Modeling of Embedded Systems

This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy, and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools, and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in design of embedded control software using examples from automated highways concerning vehicle coordination.

Accurate Event Detection for Simulating Hybrid Systems

It has been observed that there are a variety of situations in which the most popular hybrid simulation methods can fail to properly detect the occurrence of discrete events. In this paper, we present a method for detecting discrete which, using techniques borrowed from control theory, selects integration step sizes in such a way that the simulation slows down as the state approaches a set which triggers an event (a guard set). Our method guarantees that the state will approach the boundary of this set exponentially; and in the case of linear or polynomial guard descriptions, terminating on it, without entering it. Given that any system with a nonlinear guard description can be transformed to an equivalent system with a linear guard description, this technique is applicable to a broad class of systems. Even in situations where nonlinear guards have not been transformed to the canonical form, the method is still increases the chances of detecting and event in practice. We show how to extend the method to guard sets which are constructed from many simple sets using boolean operators (e.g. polyhedral or semi-algebraic sets) . The technique is easily used in combination with existing numerical integration methods and does not adversely affect the underlying accuracy or stability of the algorithms.

Maintaining wireless connectivity constraints for swarms in the presence of obstacles

The low power requirements of many small radio modems suggest that robust operation is best attained when the transmitter/receiver pair is: (1) separated by less than some maximum distance (range); and (2) not obstructed by large dense objects (line-of-sight). Therefore to maintain a wireless link between two robots, it is desirable to comply with these two spatial constraints. Given a swarm of point robots with specified initial and final configurations and a set of desired communication links consistent with the above criteria, we explore the problem of designing inputs to achieve the final configuration while preserving the desired links for the duration of the motion. Some interesting conclusions about the feasibility of the problem are offered. An algorithm is provided and its operation is demonstrated through both simulation and experimentation on Koala robots

A state event detection algorithm for numerically simulating hybrid systems with model singularities

This article describes an algorithm for detecting the occurrence of events, which signify discontinuities in the first derivative of the state variables, while simulating a set of nonsmooth differential equations. Such combined-discrete continuous systems arise in many contexts and are often referred to as hybrid systems, switched systems, or nonsmooth systems. In all cases, the state events are triggered at simulated times which generate states corresponding to the zeros of some algebraic “event” function. It has been noted that all existing simulators are prone to failure when these events occur in the neighborhood of model singularities---regions of the state space where the right-hand side of the differential equation is undefined. Such model singularities are often the impetus for using nonsmooth models in the first place. This failure occurs because existing algorithms blindly attempt to interpolate across singular regions, checking for possible events after the fact. The event detection algorithm described here overcomes this limitation using an approach inspired by feedback control theory. A carefully constructed extrapolation polynomial is used to select the integration step size by checking for potential future events, avoiding the need to evaluate the differential equation in potentially singular regions. It is shown that this alternate approach gives added functionality with little impact on the simulation efficiency.

An RRT-Based Algorithm for Testing and Validating Multi-Robot Controllers

Abstract : We address the problem of testing complex reactive control systems and validating the effectiveness of multi-agent controllers. Testing and validation involve searching for conditions that lead to system failure by exploring all adversarial inputs and disturbances for errant trajectories. This problem of testing is related to motion planning, with one main difference. Unlike motion planning problems, systems are typically not controllable with respect to disturbances or adversarial inputs and therefore, the reachable set of states is a small subset of the entire state space. In both cases however, there is a goal or specification set consisting of a set of points in state space that is of interest, either for demonstrating failure or for validation. In this paper we consider the application of the Rapidly exploring Random Tree algorithm to the testing and validation problem. Because of the differences between testing and motion planning, we propose three modifications to the original RRT algorithm. First, we introduce a new distance function which incorporates information about the systems dynamics to select nodes for extension. Second, we introduce a weighting to penalize nodes which are repeatedly selected but fail to extend. Third we propose a scheme for adaptively modifying the sampling probability distribution based on tree growth. We demonstrate the application of the algorithm via three simple and one large scale example and provide computational statistics. Our algorithms are applicable beyond the testing problem to motion planning for systems that are not small time locally controllable.

Formal Modeling and Analysis of Hybrid Systems: A Case Study in Multi-robot Coordination

The design of controllers for hybrid systems (i.e. mixed discrete-continuous systems) in a systematic manner remains a challenging task. In this case study, we apply formal modeling to the design of communication and control strategies for a team of autonomous robots to attain specified goals in a coordinated manner. The model of linear hybrid automata is used to describe the high-level design, and the verification software HYTECH is used for symbolic analysis of the description. The goal of the project is to understand tradeoffs among various design alternatives by generating constraints among parameters using symbolic analysis. In this paper, we report on diffculties in modeling a team of robots using linear hybrid automata, results of analysis experiments, promise of the approach, and challenges for future research.

Comprehensive framework for tracking control and thrust allocation for a highly overactuated autonomous surface vessel

In this paper, we present a comprehensive trajectory tracking framework for cooperative manipulation scenarios involving marine surface ships. Our experimental platform is a small boat equipped with six thrusters, but the technique presented here can be applied to a multiship manipulation scenario such as a group of autonomous tugboats transporting a disabled ship or unactuated barge. The primary challenges of this undertaking are as follows: (1) the actuators are unidirectional and experience saturation; (2) the hydrodynamics of the system are difficult to characterize; and (3) obtaining acceptable performance under field conditions (i.e., global positioning system errors, wind, waves, etc.) is arduous. To address these issues, we present a framework that includes trajectory generation, tracking control, and force allocation that, despite actuator limitations, results in asymptotically convergent trajectory tracking. In addition, the controller employs an adaptive feedback law to compensate for unknown—difficult to measure—hydrodynamic parameters. Field trials are conducted utilizing a 3-m vessel in a nearby estuary.

Computational Techniques for Analysis of Genetic Network Dynamics

In this paper we propose modeling and analysis techniques for genetic networks that provide biologists with insight into the dynamics of such systems. Central to our modeling approach is the framework of hybrid systems and our analysis tools are derived from formal analysis of such systems. Given a set of states characterizing a property of biological interest P , we present the Multi-Affine Rectangular Partition (MARP) algorithm for the construction of a set of infeasible states I that will never reach P and the Rapidly Exploring Random Forest of Trees (RRFT) algorithm for the construction of a set of feasible states F that will reach P. These techniques are scalable to high dimensions and can incorporate uncertainty (partial knowledge of kinetic parameters and state uncertainty).We apply these methods to understand the genetic interactions involved in the phenomenon of luminescence production in the marine bacterium V. fischeri.