On the Minimal Revision Problem of Specification Automata

As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the requirements are expressed as temporal logic specifications. However, in real-life scenarios, it is to be expected that not all user task requirements can be realized by the robot. In such cases, the robot must provide feedback to the user on why it cannot accomplish a given task. Moreover, the robot should indicate what tasks it can accomplish which are as "close" as possible to the initial user intent. This paper establishes that the latter problem, which is referred to as the minimal specification revision problem, is NP complete. A heuristic algorithm is presented that can compute good approximations to the Minimal Revision Problem (MRP) in polynomial time. The experimental study of the algorithm demonstrates that in most problem instances the heuristic algorithm actually returns the optimal solution. Finally, some cases where the algorithm does not return the optimal solution are presented.Comment: 23 pages, 16 figures, 2 tables, International Joural of Robotics Research 2014 Major Revision (submitted

Robust Sampling for MITL Specifications

Real-time temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specifications on continuous time signals using only discrete time analysis. The motivating idea behind our approach is that if the dynamics of the signal fulfills certain conditions and the discrete time signal robustly satisfies the MITL specification, then the corresponding continuous time signal should also satisfy the same MITL specification

Hybrid Modeling and Experimental Cooperative Control of Multiple Unmanned Aerial Vehicles

Recent years have seen rapidly growing interest in the development of networks of multiple unmanned aerial vehicles (U.A.V.s), as aerial sensor networks for the purpose of coordinated monitoring, surveillance, and rapid emergency response. This has triggered a great deal of research in higher levels of planning and control, including collaborative sensing and exploration, synchronized motion planning, and formation or cooperative control. In this paper, we describe our recently developed experimental testbed at the University of Pennsylvania, which consists of multiple, fixed-wing UAVs. We describe the system architecture, software and hardware components, and overall system integration. We then derive high-fidelity models that are validated with hardware-in-the-loop simulations and actual experiments. Our models are hybrid, capturing not only the physical dynamics of the aircraft, but also the mode switching logic that supervises lower level controllers. We conclude with a description of cooperative control experiments involving two fixed-wing UAVs

Temporal logic motion planning for dynamic robots

In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and obstacle avoidance. Our approach consists of three basic steps. First, we design a control law that enables the dynamic model to track a simpler kinematic model with a globally bounded error. Second, we built a robust temporal logic specification that takes into account the tracking errors of the first step. Finally, we solve the new robust temporal logic path planning problem for the kinematic model using automata theory and simple local vector fields. The resulting continuous time trajectory is provably guaranteed to satisfy the initial user specification

An introduction to multi-valued model checking

Nowadays computer systems have become ubiquitous. Most of the resources in the development of such systems, and especially in the fail-safe ones, are allocated into the simulation and verification of their behavior. One such automated method of verification is model checking. Given a mathematical description of the real system and a specification usually in the form of temporal logics, a model checker verifies whether the specification is satisfied on the model of the system. Recently, a multi-valued extension to the classical model checking has been proposed. In this approach both the model of the system and the specification take truth values over lattices with more then just two values. Such an extension enhances the expressive power of temporal logics and allows reasoning under uncertainty. Some of the applications that can take advantage of the multi-valued model checking are abstraction techniques, reasoning about conflicting viewpoints and temporal logic query checking. In this paper, we present three different approaches to the multi-valued model checking problem. The first is a reduction from multi-valued CTL* to CTL*, the second a multi-valued CTL symbolic model checking algorithm and, finally, a reduction technique from multi-valued μ-calculus to the classical one

Revising temporal logic specifications for motion planning

Abstract — In this paper, we introduce the problem of auto-matic formula revision for Linear Temporal Logic (LTL) motion planning specifications. Namely, if a specification cannot be satisfied on a particular environment, our framework returns information to the user regarding (i) why the specification cannot be satisfied and (ii) how the specification can be modified so it can become satisfiable. This work contributes towards rendering temporal logic motion planning frameworks more user friendly by providing feedback to the user when the LTL planning phase fails. I