Cross-entropy Temporal Logic Motion Planning

This paper presents a method for optimal trajectory generation for discrete-time nonlinear systems with linear temporal logic (LTL) task specifications. Our approach is based on recent advances in stochastic optimization algorithms for optimal trajectory generation. These methods rely on estimation of the rare event of sampling optimal trajectories, which is achieved by incrementally improving a sampling distribution so as to minimize the cross-entropy. A key component of these stochastic optimization algorithms is determining whether or not a trajectory is collision-free. We generalize this collision checking to efficiently verify whether or not a trajectory satisfies a LTL formula. Interestingly, this verification can be done in time polynomial in the length of the LTL formula and the trajectory. We also propose a method for efficiently re-using parts of trajectories that only partially satisfy the specification, instead of simply discarding the entire sample. Our approach is demonstrated through numerical experiments involving Dubins car and a generic point-mass model subject to complex temporal logic task specifications

Combining task and motion planning:challenges and guidelines

Combined Task and Motion Planning (TAMP) is an area where no one-fits-all solution can exist. Many aspects of the domain, as well as operational requirements, have an effect on how algorithms and representations are designed. Frequently, trade-offs have to be made to build a system that is effective. We propose five research questions that we believe need to be answered to solve real-world problems that involve combined TAMP. We show which decisions and trade-offs should be made with respect to these research questions, and illustrate these on examples of existing application domains. By doing so, this article aims to provide a guideline for designing combined TAMP solutions that are adequate and effective in the target scenario

When are Stochastic Transition Systems Tameable?

A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Decisive Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs for short) are needed. In this article, we provide a framework to perform both the qualitative and the quantitative analysis of STSs. First, we define various notions of decisiveness (inherited from [1]), notions of fairness and of attractors for STSs, and make explicit the relationships between them. Then, we define a notion of abstraction, together with natural concepts of soundness and completeness, and we give general transfer properties, which will be central to several verification algorithms on STSs. We further design a generic construction which will be useful for the analysis of {\omega}-regular properties, when a finite attractor exists, either in the system (if it is denumerable), or in a sound denumerable abstraction of the system. We next provide algorithms for qualitative model-checking, and generic approximation procedures for quantitative model-checking. Finally, we instantiate our framework with stochastic timed automata (STA), generalized semi-Markov processes (GSMPs) and stochastic time Petri nets (STPNs), three models combining dense-time and probabilities. This allows us to derive decidability and approximability results for the verification of these models. Some of these results were known from the literature, but our generic approach permits to view them in a unified framework, and to obtain them with less effort. We also derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page

Time-annotated game graphs for synthesis from abstracted systems

The construction of discrete abstractions is a crucial part of many methods for control synthesis of hybrid systems subject to formal specifications. In general, the product of discrete abstractions may not be a discrete abstraction for the product of the underlying continuously-valued systems. Addressing this, we present a control synthesis method for transition systems that are built from components with uncertain timing characteristics. The new device, called here time-annotated game graphs, is demonstrated in a variety of examples. While it is applicable generally to parity games, we consider it in the context of control subject to GR(1) specifications. We show how a nominal strategy obtained without time knowledge can be modified to recover correctness when time information becomes available. The methods are applied to a brief case study of an aircraft electric power system

Event-driven industrial robot control architecture for the Adept V+ platform

Modern industrial robotic systems are highly interconnected. They operate in a distributed environment and communicate with sensors, computer vision systems, mechatronic devices, and computational components. On the fundamental level, communication and coordination between all parties in such distributed system are characterized by discrete event behavior. The latter is largely attributed to the specifics of communication over the network, which, in terms, facilitates asynchronous programming and explicit event handling. In addition, on the conceptual level, events are an important building block for realizing reactivity and coordination. Eventdriven architecture has manifested its effectiveness for building loosely-coupled systems based on publish-subscribe middleware, either general-purpose or robotic-oriented. Despite all the advances in middleware, industrial robots remain difficult to program in context of distributed systems, to a large extent due to the limitation of the native robot platforms. This paper proposes an architecture for flexible event-based control of industrial robots based on the Adept V+ platform. The architecture is based on the robot controller providing a TCP/IP server and a collection of robot skills, and a high-level control module deployed to a dedicated computing device. The control module possesses bidirectional communication with the robot controller and publish/subscribe messaging with external systems. It is programmed in asynchronous style using pyadept, a Python library based on Python coroutines, AsyncIO event loop and ZeroMQ middleware. The proposed solution facilitates integration of Adept robots into distributed environments and building more flexible robotic solutions with eventbased logic