Morteza Lahijanian

Temporal Logic Motion Planning and Control With Probabilistic Satisfaction Guarantees

We describe a computational framework for automatic deployment of a robot with sensor and actuator noise from a temporal logic specification over a set of properties that are satisfied by the regions of a partitioned environment. We model the motion of the robot in the environment as a Markov decision process (MDP) and translate the motion specification to a formula of probabilistic computation tree logic (PCTL). As a result, the robot control problem is mapped to that of generating an MDP control policy from a PCTL formula. We present algorithms for the synthesis of such policies for different classes of PCTL formulas. We illustrate our method with simulation and experimental results.

Motion planning and control from temporal logic specifications with probabilistic satisfaction guarantees

We present a computational framework for automatic deployment of a robot from a temporal logic specification over a set of properties of interest satisfied at the regions of a partitioned environment. We assume that, during the motion of the robot in the environment, the current region can be precisely determined, while due to sensor and actuation noise, the outcome of a control action can only be predicted probabilistically. Under these assumptions, the deployment problem translates to generating a control strategy for a Markov Decision Process (MDP) from a temporal logic formula.We propose an algorithm inspired from probabilistic Computation Tree Logic (PCTL) model checking to find a control strategy that maximizes the probability of satisfying the specification. We illustrate our method with simulation and experimental results.

Iterative temporal motion planning for hybrid systems in partially unknown environments

This paper considers the problem of motion planning for a hybrid robotic system with complex and nonlinear dynamics in a partially unknown environment given a temporal logic specification. We employ a multi-layered synergistic framework that can deal with general robot dynamics and combine it with an iterative planning strategy. Our work allows us to deal with the unknown environmental restrictions only when they are discovered and without the need to repeat the computation that is related to the temporal logic specification. In addition, we define a metric for satisfaction of a specification. We use this metric to plan a trajectory that satisfies the specification as closely as possible in cases in which the discovered constraint in the environment renders the specification unsatisfiable. We demonstrate the efficacy of our framework on a simulation of a hybrid second-order car-like robot moving in an office environment with unknown obstacles. The results show that our framework is successful in generating a trajectory whose satisfaction measure of the specification is optimal. They also show that, when new obstacles are discovered, the reinitialization of our framework is computationally inexpensive.

A probabilistic approach for control of a stochastic system from LTL specifications

We consider the problem of controlling a continuous-time linear stochastic system from a specification given as a Linear Temporal Logic (LTL) formula over a set of linear predicates in the state of the system. We propose a three-step solution. First, we define a polyhedral partition of the state space and a finite collection of controllers, represented as symbols, and construct a Markov Decision Process (MDP). Second, by using an algorithm resembling LTL model checking, we determine a run satisfying the formula in the corresponding Kripke structure. Third, we determine a sequence of control actions in the MDP that maximizes the probability of following the satisfying run. We present illustrative simulation results.

Towards manipulation planning with temporal logic specifications

Manipulation planning from high-level task specifications, even though highly desirable, is a challenging problem. The large dimensionality of manipulators and complexity of task specifications make the problem computationally intractable. This work introduces a manipulation planning framework with linear temporal logic (LTL) specifications. The use of LTL as the specification language allows the expression of rich and complex manipulation tasks. The framework deals with the state-explosion problem through a novel abstraction technique. Given a robotic system, a workspace consisting of obstacles, manipulable objects, and locations of interest, and a co-safe LTL specification over the objects and locations, the framework computes a motion plan to achieve the task through a synergistic multi-layered planning architecture. The power of the framework is demonstrated through case studies, in which the planner efficiently computes plans for complex tasks. The case studies also illustrate the ability of the framework in intelligently moving away objects that block desired executions without requiring backtracking.

Formal Verification and Synthesis for Discrete-Time Stochastic Systems

Formal methods are increasingly being used for control and verification of dynamic systems against complex specifications. In general, these methods rely on a relatively simple system model, such as a transition graph, Markov chain, or Markov decision process, and require abstraction of the original continuous-state dynamics. It can be difficult or impossible, however, to find a perfectly equivalent abstraction, particularly when the original system is stochastic. Here we develop an abstraction procedure that maps a discrete-time stochastic system to an Interval-valued Markov Chain ( IMC ) and a switched discrete-time stochastic system to a Bounded-parameter Markov Decision Process ( BMDP ). We construct model checking algorithms for these models against Probabilistic Computation Tree Logic ( PCTL ) formulas and a synthesis procedure for BMDP s. Finally, we develop an efficient refinement algorithm that reduces the uncertainty in the abstraction. The technique is illustrated through simulation.

Control of Markov decision processes from PCTL specifications

We address the problem of controlling a Markov Decision Process (MDP) such that the probability of satisfying a temporal logic specification over a set of properties associated to its states is maximized. We focus on specifications given as formulas of Probabilistic Computation Tree Logic (PCTL) and show that controllers can be synthesized by adapting existing PCTL model checking algorithms. We illustrate the approach by applying it to the automatic deployment of a mobile robot in an indoor-like environment with respect to a PCTL specification.

Iterative Temporal Planning in Uncertain Environments With Partial Satisfaction Guarantees

This paper introduces a motion-planning framework for a hybrid system with general continuous dynamics to satisfy a temporal logic specification consisting of cosafety and safety components in a partially unknown environment. The framework employs a multilayered synergistic planner to generate trajectories that satisfy the specification and adopt an iterative replanning strategy to deal with unknown obstacles. When the discovery of an obstacle renders the specification unsatisfiable, a division between the constraints in the specification is considered. The cosafety component of the specification is treated as a soft constraint, whose partial satisfaction is allowed, while the safety component is viewed as a hard constraint, whose violation is forbidden. To partially satisfy the cosafety component, inspirations are taken from indoor-robotic scenarios, and three types of (unexpressed) restrictions on the ordering of subtasks in the specification are considered. For each type, a partial satisfaction method is introduced, which guarantees the generation of trajectories that do not violate the safety constraints while attending to partially satisfying the cosafety requirements with respect to the chosen restriction type. The efficacy of the framework is illustrated through case studies on a hybrid car-like robot in an office environment.

Asymptotically Optimal Stochastic Motion Planning with Temporal Goals

This work presents a planning framework that allows a robot with stochastic action uncertainty to achieve a high-level task given in the form of a temporal logic formula. The objective is to quickly compute a feedback control policy to satisfy the task specification with maximum probability. A top-down framework is proposed that abstracts the motion of a continuous stochastic system to a discrete, bounded-parameter Markov decision process (bmdp), and then computes a control policy over the product of the bmdp abstraction and a dfa representing the temporal logic specification. Analysis of the framework reveals that as the resolution of the bmdp abstraction becomes finer, the policy obtained converges to optimal. Simulations show that high-quality policies to satisfy complex temporal logic specifications can be obtained in seconds, orders of magnitude faster than existing methods.

Automatic deployment of autonomous cars in a Robotic Urban-Like Environment (RULE)

We present a computational framework and experimental setup for deployment of autonomous cars in a miniature Robotic Urban-Like Environment (RULE). The specifications are given in rich, human-like language as temporal logic statements about roads, intersections, and parking spaces. We use transition systems to model the motion and sensing capabilities of the robots and the topology of the environment and use tools resembling model checking to generate robot control strategies and to verify the correctness of the solution. The experimental setup is based on Khepera III robots, which move autonomously on streets while observing traffic rules.