Technical Report: A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints

This technical report is an extended version of the paper 'A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints' accepted to the 2013 IEEE International Conference on Robotics and Automation (ICRA). This paper considers the problem of finding the most informative path for a sensing robot under temporal logic constraints, a richer set of constraints than have previously been considered in information gathering. An algorithm for informative path planning is presented that leverages tools from information theory and formal control synthesis, and is proven to give a path that satisfies the given temporal logic constraints. The algorithm uses a receding horizon approach in order to provide a reactive, on-line solution while mitigating computational complexity. Statistics compiled from multiple simulation studies indicate that this algorithm performs better than a baseline exhaustive search approach.Comment: Extended version of paper accepted to 2013 IEEE International Conference on Robotics and Automation (ICRA

Control with Probabilistic Signal Temporal Logic

Autonomous agents often operate in uncertain environments where their decisions are made based on beliefs over states of targets. We are interested in controller synthesis for complex tasks defined over belief spaces. Designing such controllers is challenging due to computational complexity and the lack of expressivity of existing specification languages. In this paper, we propose a probabilistic extension to signal temporal logic (STL) that expresses tasks over continuous belief spaces. We present an efficient synthesis algorithm to find a control input that maximises the probability of satisfying a given task. We validate our algorithm through simulations of an unmanned aerial vehicle deployed for surveillance and search missions.Comment: 7 pages, submitted to the 2016 American Control Conference (ACC 2016) on September, 30, 2015 (under review

Control with probabilistic signal temporal logic

Autonomous agents often operate in uncertain environments where their decisions are made based on beliefs over states of targets. We are interested in controller synthesis for complex tasks defined over belief spaces. Designing such controllers is challenging due to computational complexity and the lack of expressivity of existing specification languages. In this paper, we propose a probabilistic extension to signal temporal logic (STL) that expresses tasks over continuous belief spaces. We present an efficient synthesis algorithm to find a control input that maximises the probability of satisfying a given task. We validate our algorithm through simulations of an unmanned aerial vehicle deployed for surveillance and search missions

Formal methods for motion planning and control in dynamic and partially known environments

This thesis is motivated by time and safety critical applications involving the use of autonomous vehicles to accomplish complex tasks in dynamic and partially known environments. We use temporal logic to formally express such complex tasks. Temporal logic specifications generalize the classical notions of stability and reachability widely studied within the control and hybrid systems communities. Given a model describing the motion of a robotic system in an environment and a formal task specification, the aim is to automatically synthesize a control policy that guarantees the satisfaction of the specification. This thesis presents novel control synthesis algorithms to tackle the problem of motion planning from temporal logic specifications in uncertain environments. For each one of the planning and control synthesis problems addressed in this dissertation, the proposed algorithms are implemented, evaluated, and validated thought experiments and/or simulations. The first part of this thesis focuses on a mobile robot whose success is measured by the completion of temporal logic tasks within a given period of time. In addition to such time constraints, the planning algorithm must also deal with the uncertainty that arises from the changes in the robot's workspace during task execution. In particular, we consider a robot deployed in a partitioned environment subjected to structural changes such as doors that can open and close. The motion of the robot is modeled as a continuous time Markov decision process and the robot's mission is expressed as a Continuous Stochastic Logic (CSL) formula. A complete framework to find a control strategy that satisfies a specification given as a CSL formula is introduced. The second part of this thesis addresses the synthesis of controllers that guarantee the satisfaction of a task specification expressed as a syntactically co-safe Linear Temporal Logic (scLTL) formula. In this case, uncertainty is characterized by the partial knowledge of the robot's environment. Two scenarios are considered. First, a distributed team of robots required to satisfy the specification over a set of service requests occurring at the vertices of a known graph representing the environment is examined. Second, a single agent motion planning problem from the specification over a set of properties known to be satised at the vertices of the known graph environment is studied. In both cases, we exploit the existence of o-the-shelf model checking and runtime verification tools, the efficiency of graph search algorithms, and the efficacy of exploration techniques to solve the motion planning problem constrained by the absence of complete information about the environment. The final part of this thesis extends uncertainty beyond the absence of a complete knowledge of the environment described above by considering a robot equipped with a noisy sensing system. In particular, the robot is tasked with satisfying a scLTL specification over a set of regions of interest known to be present in the environment. In such a case, although the robot is able to measure the properties characterizing such regions of interest, precisely determining the identity of these regions is not feasible. A mixed observability Markov decision process is used to represent the robot's actuation and sensing models. The control synthesis problem from scLTL formulas is then formulated as a maximum probability reachability problem on this model. The integration of dynamic programming, formal methods, and frontier-based exploration tools allow us to derive an algorithm to solve such a reachability problem

Provably-Correct Task Planning for Autonomous Outdoor Robots

Autonomous outdoor robots should be able to accomplish complex tasks safely and reliably while considering constraints that arise from both the environment and the physical platform. Such tasks extend basic navigation capabilities to specify a sequence of events over time. For example, an autonomous aerial vehicle can be given a surveillance task with contingency plans while complying with rules in regulated airspace, or an autonomous ground robot may need to guarantee a given probability of success while searching for the quickest way to complete the mission. A promising approach for the automatic synthesis of trusted controllers for complex tasks is to employ techniques from formal methods. In formal methods, tasks are formally specified symbolically with temporal logic. The robot then synthesises a controller automatically to execute trusted behaviour that guarantees the satisfaction of specified tasks and regulations. However, a difficulty arises from the lack of expressivity, which means the constraints affecting outdoor robots cannot be specified naturally with temporal logic. The goal of this thesis is to extend the capabilities of formal methods to express the constraints that arise from outdoor applications and synthesise provably-correct controllers with trusted behaviours over time. This thesis focuses on two important types of constraints, resource and safety constraints, and presents three novel algorithms that express tasks with these constraints and synthesise controllers that satisfy the specification. Firstly, this thesis proposes an extension to probabilistic computation tree logic (PCTL) called resource threshold PCTL (RT-PCTL) that naturally defines the mission specification with continuous resource threshold constraints; furthermore, it synthesises an optimal control policy with respect to the probability of success. With RT-PCTL, a state with accumulated resource out of the specified bound is considered to be failed or saturated depending on the specification. The requirements on resource bounds are naturally encoded in the symbolic specification, followed by the automatic synthesis of an optimal controller with respect to the probability of success. Secondly, the thesis proposes an online algorithm called greedy Buchi algorithm (GBA) that reduces the synthesis problem size to avoid the scalability problem. A framework is then presented with realistic control dynamics and physical assumptions in the environment such as wind estimation and fuel constraints. The time and space complexity for the framework is polynomial in the size of the system state, which is efficient for online synthesis. Lastly, the thesis proposes a synthesis algorithm for an optimal controller with respect to completion time given the minimum safety constraints. The algorithm naturally balances between completion time and safety. This work proves an analytical relationship between the probability of success and the conditional completion time given the mission specification. The theoretical contributions in this thesis are validated through realistic simulation examples. This thesis identifies and solves two core problems that contribute to the overall vision of developing a theoretical basis for trusted behaviour in outdoor robots. These contributions serve as a foundation for further research in multi-constrained task planning where a number of different constraints are considered simultaneously within a single framework

Multi-agent persistent surveillance under temporal logic constraints

This thesis proposes algorithms for the deployment of multiple autonomous agents for persistent surveillance missions requiring repeated, periodic visits to regions of interest. Such problems arise in a variety of domains, such as monitoring ocean conditions like temperature and algae content, performing crowd security during public events, tracking wildlife in remote or dangerous areas, or watching traffic patterns and road conditions. Using robots for surveillance is an attractive solution to scenarios in which fixed sensors are not sufficient to maintain situational awareness. Multi-agent solutions are particularly promising, because they allow for improved spatial and temporal resolution of sensor information. In this work, we consider persistent monitoring by teams of agents that are tasked with satisfying missions specified using temporal logic formulas. Such formulas allow rich, complex tasks to be specified, such as "visit regions A and B infinitely often, and if region C is visited then go to region D, and always avoid obstacles." The agents must determine how to satisfy such missions according to fuel, communication, and other constraints. Such problems are inherently difficult due to the typically infinite horizon, state space explosion from planning for multiple agents, communication constraints, and other issues. Therefore, computing an optimal solution to these problems is often infeasible. Instead, a balance must be struck between computational complexity and optimality. This thesis describes solution methods for two main classes of multi-agent persistent surveillance problems. First, it considers the class of problems in which persistent surveillance goals are captured entirely by TL constraints. Such problems require agents to repeatedly visit a set of surveillance regions in order to satisfy their mission. We present results for agents solving such missions with charging constraints, with noisy observations, and in the presence of adversaries. The second class of problems include an additional optimality criterion, such as minimizing uncertainty about the location of a target or maximizing sensor information among the team of agents. We present solution methods and results for such missions with a variety of optimality criteria based on information metrics. For both classes of problems, the proposed algorithms are implemented and evaluated via simulation, experiments with robots in a motion capture environment, or both