arXiv subjects

Morteza Lahijanian

Publications and source records attributed to Morteza Lahijanian.

83 records · Page 5Linked to original sources

arXiv2021

MAPS-X: Explainable Multi-Robot Motion Planning via Segmentation

Traditional multi-robot motion planning (MMP) focuses on computing trajectories for multiple robots acting in an environment, such that the robots do not collide when the trajectories are taken simultaneously. In safety-critical applications, a human supervisor may want to verify that the plan is indeed collision-free. In this work, we propose a notion of explanation for a plan of MMP, based on visualization of the plan as a short sequence of images representing time segments, where in each time segment the trajectories of the agents are disjoint, clearly illustrating the safety of the plan. We show that standard notions of optimality (e.g., makespan) may create conflict with short explanations. Thus, we propose meta-algorithms, namely multi-agent plan segmenting-X (MAPS-X) and its lazy variant, that can be plugged on existing centralized sampling-based tree planners X to produce plans with good explanations using a desirable number of images. We demonstrate the efficacy of this explanation-planning scheme and extensively evaluate the performance of MAPS-X.

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arXiv2020

LTLf Synthesis on Probabilistic Systems

Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf. We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.

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arXiv2020

Safety Verification of Unknown Dynamical Systems via Gaussian Process Regression

The deployment of autonomous systems that operate in unstructured environments necessitates algorithms to verify their safety. This can be challenging due to, e.g., black-box components in the control software, or undermodelled dynamics that prevent model-based verification. We present a novel verification framework for an unknown dynamical system from a given set of noisy observations of the dynamics. Using Gaussian processes trained on this data set, the framework abstracts the system as an uncertain Markov process with discrete states defined over the safe set. The transition bounds of the abstraction are derived from the probabilistic error bounds between the regression and underlying system. An existing approach for verifying safety properties over uncertain Markov processes then generates safety guarantees. We demonstrate the versatility of the framework on several examples, including switched and nonlinear systems.

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arXiv2020

Online Mapping and Motion Planning under Uncertainty for Safe Navigation in Unknown Environments

Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localisation information, but also their manoeuvrability is constrained by their dynamics and often suffer from uncertainty. In order to cope with these constraints, this manuscript proposes an uncertainty-based framework for mapping and planning feasible motions online with probabilistic safety-guarantees. The proposed approach deals with the motion, probabilistic safety, and online computation constraints by: (i) incrementally mapping the surroundings to build an uncertainty-aware representation of the environment, and (ii) iteratively (re)planning trajectories to goal that are kinodynamically feasible and probabilistically safe through a multi-layered sampling-based planner in the belief space. In-depth empirical analyses illustrate some important properties of this approach, namely, (a) the multi-layered planning strategy enables rapid exploration of the high-dimensional belief space while preserving asymptotic optimality and completeness guarantees, and (b) the proposed routine for probabilistic collision checking results in tighter probability bounds in comparison to other uncertainty-aware planners in the literature. Furthermore, real-world in-water experimental evaluation on a non-holonomic torpedo-shaped autonomous underwater vehicle and simulated trials in the Stairwell scenario of the DARPA Subterranean Challenge 2019 on a quadrotor unmanned aerial vehicle demonstrate the efficacy of the method as well as its suitability for systems with limited on-board computational power.

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arXiv2019

Correct-by-Construction Advanced Driver Assistance Systems based on a Cognitive Architecture

Research into safety in autonomous and semi-autonomous vehicles has, so far, largely been focused on testing and validation through simulation. Due to the fact that failure of these autonomous systems is potentially life-endangering, formal methods arise as a complementary approach. This paper studies the application of formal methods to the verification of a human driver model built using the cognitive architecture ACT-R, and to the design of correct-by-construction Advanced Driver Assistance Systems (ADAS). The novelty lies in the integration of ACT-R in the formal analysis and an abstraction technique that enables finite representation of a large dimensional, continuous system in the form of a Markov process. The situation considered is a multi-lane highway driving scenario and the interactions that arise. The efficacy of the method is illustrated in two case studies with various driving conditions.

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arXiv2019

Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems

This work targets the development of an efficient abstraction method for formal analysis and control synthesis of discrete-time stochastic hybrid systems (SHS) with linear dynamics. The focus is on temporal logic specifications, both over finite and infinite time horizons. The framework constructs a finite abstraction as a class of uncertain Markov models known as interval Markov decision process (IMDP). Then, a strategy that maximizes the satisfaction probability of the given specification is synthesized over the IMDP and mapped to the underlying SHS. In contrast to existing formal approaches, which are by and large limited to finite-time properties and rely on conservative over-approximations, we show that the exact abstraction error can be computed as a solution of convex optimization problems and can be embedded into the IMDP abstraction. This is later used in the synthesis step over both finite- and infinite-horizon specifications, mitigating the known state-space explosion problem. Our experimental validation of the new approach compared to existing abstraction-based approaches shows: (i) significant (orders of magnitude) reduction of the abstraction error; (ii) marked speed-ups; and (iii) boosted scalability, allowing in particular to verify models with more than 10 continuous variables.

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arXiv2017

Resource-Performance Trade-off Analysis for Mobile Robot Design

The design of mobile autonomous robots is challenging due to the limited on-board resources such as processing power and energy. A promising approach is to generate intelligent schedules that reduce the resource consumption while maintaining best performance, or more interestingly, to trade off reduced resource consumption for a slightly lower but still acceptable level of performance. In this paper, we provide a framework to aid designers in exploring such resource-performance trade-offs and finding schedules for mobile robots, guided by questions such as "what is the minimum resource budget required to achieve a given level of performance?" The framework is based on a quantitative multi-objective verification technique which, for a collection of possibly conflicting objectives, produces the Pareto front that contains all the optimal trade-offs that are achievable. The designer then selects a specific Pareto point based on the resource constraints and desired performance level, and a correct-by-construction schedule that meets those constraints is automatically generated. We demonstrate the efficacy of this framework on several robotic scenarios in both simulations and experiments with encouraging results.

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arXiv2017

Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes

Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that prevents the knowledge of the exact transition probabilities. In this paper, we consider the problem of multi-objective robust strategy synthesis for interval MDPs, where the aim is to find a robust strategy that guarantees the satisfaction of multiple properties at the same time in face of the transition probability uncertainty. We first show that this problem is PSPACE-hard. Then, we provide a value iteration-based decision algorithm to approximate the Pareto set of achievable points. We finally demonstrate the practical effectiveness of our proposed approaches by applying them on several case studies using a prototypical tool.

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arXiv2012

Temporal Logic Motion Control using Actor-Critic Methods

In this paper, we consider the problem of deploying a robot from a specification given as a temporal logic statement about some properties satisfied by the regions of a large, partitioned environment. We assume that the robot has noisy sensors and actuators and model its motion through the regions of the environment as a Markov Decision Process (MDP). The robot control problem becomes finding the control policy maximizing the probability of satisfying the temporal logic task on the MDP. For a large environment, obtaining transition probabilities for each state-action pair, as well as solving the necessary optimization problem for the optimal policy are usually not computationally feasible. To address these issues, we propose an approximate dynamic programming framework based on a least-square temporal difference learning method of the actor-critic type. This framework operates on sample paths of the robot and optimizes a randomized control policy with respect to a small set of parameters. The transition probabilities are obtained only when needed. Hardware-in-the-loop simulations confirm that convergence of the parameters translates to an approximately optimal policy.

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arXiv2011

Least Squares Temporal Difference Actor-Critic Methods with Applications to Robot Motion Control

We consider the problem of finding a control policy for a Markov Decision Process (MDP) to maximize the probability of reaching some states while avoiding some other states. This problem is motivated by applications in robotics, where such problems naturally arise when probabilistic models of robot motion are required to satisfy temporal logic task specifications. We transform this problem into a Stochastic Shortest Path (SSP) problem and develop a new approximate dynamic programming algorithm to solve it. This algorithm is of the actor-critic type and uses a least-square temporal difference learning method. It operates on sample paths of the system and optimizes the policy within a pre-specified class parameterized by a parsimonious set of parameters. We show its convergence to a policy corresponding to a stationary point in the parameters' space. Simulation results confirm the effectiveness of the proposed solution.

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arXiv2011

Probabilistically Safe Vehicle Control in a Hostile Environment

In this paper we present an approach to control a vehicle in a hostile environment with static obstacles and moving adversaries. The vehicle is required to satisfy a mission objective expressed as a temporal logic specification over a set of properties satisfied at regions of a partitioned environment. We model the movements of adversaries in between regions of the environment as Poisson processes. Furthermore, we assume that the time it takes for the vehicle to traverse in between two facets of each region is exponentially distributed, and we obtain the rate of this exponential distribution from a simulator of the environment. We capture the motion of the vehicle and the vehicle updates of adversaries distributions as a Markov Decision Process. Using tools in Probabilistic Computational Tree Logic, we find a control strategy for the vehicle that maximizes the probability of accomplishing the mission objective. We demonstrate our approach with illustrative case studies.

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