Cristian Ioan Vasile

Sampling-based temporal logic path planning

In this paper, we propose a sampling-based motion planning algorithm that finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a set of properties satisfied by some regions in a given environment. The algorithm has three main features. First, it is incremental, in the sense that the procedure for finding a satisfying path at each iteration scales only with the number of new samples generated at that iteration. Second, the underlying graph is sparse, which guarantees the low complexity of the overall method. Third, it is probabilistically complete. Examples illustrating the usefulness and the performance of the method are included.

An Automata-Theoretic Approach to the Vehicle Routing Problem

We propose a new formulation and algorithms for the Vehicle Routing Problem (VRP). To accommodate persistent surveillance missions, which require executions in infinite time, we define Persistent VRP (P-VRP). The vehicles consume a resource, such as gas or battery charge, which can be replenished when they visit replenish stations. The mission specifications are given as rich, temporal logic statements about the sites, their service durations, and the time intervals in which services should be provided. We define a temporal logic, called TimeWindow Temporal Logic (TWTL), whose formulae allow for simple, intuitive descriptions of such specifications. Two different optimization criteria are considered. The first is the infinite-time limit of the duration needed for the completion of a surveillance round. The second penalizes the long-term average of the same quantity. The proposed algorithms, which are based on concepts and tools from formal verification and optimization, generate collision-free motion plans automatically from the temporal logic statements and vehicle characteristics such as maximum operation time and minimum replenish time. Illustrative simulations and experimental trials for a team of quadrotors involved in persistent surveillance missions are included.

Provably Correct Persistent Surveillance for Unmanned Aerial Vehicles Subject to Charging Constraints

In this work, we present a novel method for automating persistent surveillance missions involving multiple vehicles. Automata-based techniques were used to generate collision-free motion plans for a team of vehicles to satisfy a temporal logic specification. Vector fields were created for use with a differential flatness-based controller, allowing vehicle flight and deployment to be fully automated according to the motion plans. The use of charging platforms with the vehicles allows for truly persistent missions. Experiments were performed with two quadrotors over 50 runs to validate the theoretical results.

Dynamic routing of energy-aware vehicles with Temporal Logic Constraints

This paper addresses a persistent vehicle routing problem, where a team of vehicles is required to achieve a task repetitively. The task is given as a Time-Window Temporal Logic (TWTL) formula defined over the environment. The fuel consumption of each vehicle is explicitly captured as a stochastic model. As vehicles leave the mission area for refueling, the number of vehicles may not always be sufficient to achieve the task. We propose a decoupled and efficient control policy to achieve the task or its minimal relaxation. We quantify the temporal relaxation of a TWTL formula and present an algorithm to minimize it. The proposed policy has two layers: 1) each vehicle decides when to refuel based on its remaining fuel, 2) a central authority plans the joint trajectories of the available vehicles to achieve a minimally relaxed task. We demonstrate the proposed approach via simulations and experiments involving a team of quadrotors that conduct persistent surveillance.

Reactive Sampling-Based Temporal Logic Path Planning

We develop a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The mission specification has two parts: (1) a global specification given as a Linear Temporal Logic (LTL) formula over a set of static service requests that occur at the regions of a known environment, and (2) a local specification that requires servicing a set of dynamic requests that can be sensed locally during the execution. Our method consists of two main ingredients: (a) an off-line sampling-based algorithm for the construction of a global transition system that contains a path satisfying the LTL formula, and (b) an on-line sampling-based algorithm to generate paths that service the local requests, while making sure that the satisfaction of the global specification is not affected. Building on our previous work [1], the focus of this paper is on the on-line part of the overall method.

Persistent surveillance for unmanned aerial vehicles subject to charging and temporal logic constraints

In this work, we present a novel method for automating persistent surveillance missions involving multiple vehicles. Automata-based techniques are used to generate collision-free motion plans for a team of vehicles to satisfy a temporal logic specification. Vector fields are created for use with a differential flatness-based controller, allowing vehicle flight and deployment to be fully automated according to the motion plans. The use of charging platforms with the vehicles allows for truly persistent missions. Experiments were performed with two quadrotors for two different missions over 50 runs each to validate the theoretical results.

Control in belief space with Temporal Logic specifications

In this paper, we present a sampling-based algorithm to synthesize control policies with temporal and uncertainty constraints. We introduce a specification language called Gaussian Distribution Temporal Logic (GDTL), an extension of Boolean logic that allows us to incorporate temporal evolution and noise mitigation directly into the task specifications, e.g. “Go to region A and reduce the variance of your state estimate below 0.1 m2.” Our algorithm generates a transition system in the belief space and uses local feedback controllers to break the curse of history associated with belief space planning. Furthermore, conventional automata-based methods become tractable. Switching control policies are then computed using a product Markov Decision Process (MDP) between the transition system and the Rabin automaton encoding the task specification. We present algorithms to translate a GDTL formula to a Rabin automaton and to efficiently construct the product MDP by leveraging recent results from incremental computing. Our approach is evaluated in hardware experiments using a camera network and ground robot.

Time window temporal logic

This paper introduces time window temporal logic (TWTL), a rich expressivity language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks, which are typically seen in robotics and control applications. This paper also discusses the relaxation of TWTL formulae with respect to deadlines of tasks. Efficient automata-based frameworks to solve synthesis, verification and learning problems are also presented. The key ingredient to the presented solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the specification. Case studies illustrating the expressivity of the logic and the proposed algorithms are included.

Minimum-violation scLTL motion planning for mobility-on-demand

This work focuses on integrated routing and motion planning for an autonomous vehicle in a road network. We consider a problem in which customer demands need to be met within desired deadlines, and the rules of the road need to be satisfied. The vehicle might not, however, be able to satisfy these two goals at the same time. We propose a systematic way to compromise between delaying the satisfaction of the given demand and violating the road rules. We utilize scLTL formulas to specify desired behavior and develop a receding horizon approach including a periodically interacting routing algorithm and a RRT∗-based motion planner. The proposed solution yields a provably minimum-violation trajectory. An illustrative case study is included.

Localization of a Ground Robot by Aerial Robots for GPS-Deprived Control with Temporal Logic Constraints

In this work, we present a novel vision-based solution for operating a vehicle under Gaussian Distribution Temporal Logic (GDTL) constraints without global positioning infrastructure. We first present the mapping component that builds a high-resolution map of the environment by flying a team of two aerial vehicles in formation with sensor information provided by their onboard cameras. The control policy for the ground robot is synthesized under temporal and uncertainty constraints given the semantically labeled map. Finally, the ground robot executes the control policy given pose estimates from a dedicated aerial robot that tracks and localizes the ground robot. The proposed method is validated using a two-wheeled ground robot and a quadrotor with a camera for ten successful experimental trials.