665 research outputs found

    Incremental Sampling-based Algorithm for Minimum-violation Motion Planning

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    This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that become feasible only if a subset of the safety rules are violated. The proposed algorithm computes a control law, that minimizes the level of unsafety while the desired goal is guaranteed to be reached. This problem is motivated by an autonomous car navigating an urban environment while following rules of the road such as "always travel in right lane'' and "do not change lanes frequently''. Ideas behind sampling based motion-planning algorithms, such as Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees (RRTs), are employed to incrementally construct a finite concretization of the dynamics as a durational Kripke structure. In conjunction with this, a weighted finite automaton that captures the safety rules is used in order to find an optimal trajectory that minimizes the violation of safety rules. We prove that the proposed algorithm guarantees asymptotic optimality, i.e., almost-sure convergence to optimal solutions. We present results of simulation experiments and an implementation on an autonomous urban mobility-on-demand system.Comment: 8 pages, final version submitted to CDC '1

    LIFTS: Learning Featured Transition Systems

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    Motion planning and control: a formal methods approach

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    Control of complex systems satisfying rich temporal specification has become an increasingly important research area in fields such as robotics, control, automotive, and manufacturing. Popular specification languages include temporal logics, such as Linear Temporal Logic (LTL) and Computational Tree Logic (CTL), which extend propositional logic to capture the temporal sequencing of system properties. The focus of this dissertation is on the control of high-dimensional systems and on timed specifications that impose explicit time bounds on the satisfaction of tasks. This work proposes and evaluates methods and algorithms for synthesizing provably correct control policies that deal with the scalability problems. Ideas and tools from formal verification, graph theory, and incremental computing are used to synthesize satisfying control strategies. Finite abstractions of the systems are generated, and then composed with automata encoding the specifications. The first part of this dissertation introduces a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The specification has two parts: (1) a global specification given as an 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. The proposed computational framework 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. The second part of the dissertation focuses on stochastic systems with temporal and uncertainty constraints. A specification language called Gaussian Distribution Temporal Logic is introduced as an extension of Boolean logic that incorporates temporal evolution and noise mitigation directly into the task specifications. A sampling-based algorithm to synthesize control policies is presented that generates a transition system in the belief space and uses local feedback controllers to break the curse of history associated with belief space planning. Switching control policies are then computed using a product Markov Decision Process between the transition system and the Rabin automaton encoding the specification.The approach is evaluated in experiments using a camera network and ground robot. The third part of this dissertation focuses on control of multi-vehicle systems with timed specifications and charging constraints. A rich expressivity language called Time Window Temporal Logic (TWTL) that describes time bounded specifications is introduced. The temporal relaxation of TWTL formulae with respect to the deadlines of tasks is also discussed. The key ingredient of the solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the given formula. The annotated automata are composed with transition systems encoding the motion of all vehicles, and with charging models to produce control strategies for all vehicles such that the overall system satisfies the mission specification. The methods are evaluated in simulation and experimental trials with quadrotors and charging stations

    Multi-agent persistent surveillance under temporal logic constraints

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    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
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