arXiv subjects

Morteza Lahijanian

Publications and source records attributed to Morteza Lahijanian.

At least 73 records · Page 4Linked to original sources

arXiv2023

Efficient Symbolic Approaches for Quantitative Reactive Synthesis with Finite Tasks

This work introduces efficient symbolic algorithms for quantitative reactive synthesis. We consider resource-constrained robotic manipulators that need to interact with a human to achieve a complex task expressed in linear temporal logic. Our framework generates reactive strategies that not only guarantee task completion but also seek cooperation with the human when possible. We model the interaction as a two-player game and consider regret-minimizing strategies to encourage cooperation. We use symbolic representation of the game to enable scalability. For synthesis, we first introduce value iteration algorithms for such games with min-max objectives. Then, we extend our method to the regret-minimizing objectives. Our benchmarks reveal that our symbolic framework not only significantly improves computation time (up to an order of magnitude) but also can scale up to much larger instances of manipulation problems with up to 2x number of objects and locations than the state of the art.

cs.RO↗

arXiv2023

Chance-Constrained Multi-Robot Motion Planning under Gaussian Uncertainties

We consider a chance-constrained multi-robot motion planning problem in the presence of Gaussian motion and sensor noise. Our proposed algorithm, CC-K-CBS, leverages the scalability of kinodynamic conflict-based search (K-CBS) in conjunction with the efficiency of the Gaussian belief trees used in the Belief-A framework, and inherits the completeness guarantees of Belief-A's low-level sampling-based planner. We also develop three different methods for robot-robot probabilistic collision checking, which trade off computation with accuracy. Our algorithm generates motion plans driving each robot from its initial state to its goal while accounting for the evolution of its uncertainty with chance-constrained safety guarantees. Benchmarks compare computation time to conservatism of the collision checkers, in addition to characterizing the performance of the planner as a whole. Results show that CC-K-CBS can scale up to 30 robots.

cs.RO↗

arXiv2023

Optimal Cost-Preference Trade-off Planning with Multiple Temporal Tasks

Autonomous robots are increasingly utilized in realistic scenarios with multiple complex tasks. In these scenarios, there may be a preferred way of completing all of the given tasks, but it is often in conflict with optimal execution. Recent work studies preference-based planning, however, they have yet to extend the notion of preference to the behavior of the robot with respect to each task. In this work, we introduce a novel notion of preference that provides a generalized framework to express preferences over individual tasks as well as their relations. Then, we perform an optimal trade-off (Pareto) analysis between behaviors that adhere to the user's preference and the ones that are resource optimal. We introduce an efficient planning framework that generates Pareto-optimal plans given user's preference by extending A* search. Further, we show a method of computing the entire Pareto front (the set of all optimal trade-offs) via an adaptation of a multi-objective A* algorithm. We also present a problem-agnostic search heuristic to enable scalability. We illustrate the power of the framework on both mobile robots and manipulators. Our benchmarks show the effectiveness of the heuristic with up to 2-orders of magnitude speedup.

cs.RO↗

arXiv2023

BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programming

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper bounds on the BNN's predictions for all the points in $T$. The framework is based on an interpretation of BNNs as stochastic dynamical systems, which enables the use of Dynamic Programming (DP) algorithms to bound the prediction range along the layers of the network. Specifically, the method uses bound propagation techniques and convex relaxations to derive a backward recursion procedure to over-approximate the prediction range of the BNN with piecewise affine functions. The algorithm is general and can handle both regression and classification tasks. On a set of experiments on various regression and classification tasks and BNN architectures, we show that BNN-DP outperforms state-of-the-art methods by up to four orders of magnitude in both tightness of the bounds and computational efficiency.

cs.LG↗

arXiv2023

Stochastic Robustness Interval for Motion Planning with Signal Temporal Logic

In this work, we present a novel robustness measure for continuous-time stochastic trajectories with respect to Signal Temporal Logic (STL) specifications. We show the soundness of the measure and develop a monitor for reasoning about partial trajectories. Using this monitor, we introduce an STL sampling-based motion planning algorithm for robots under uncertainty. Given a minimum robustness requirement, this algorithm finds satisfying motion plans; alternatively, the algorithm also optimizes for the measure. We prove probabilistic completeness and asymptotic optimality, and demonstrate the effectiveness of our approach on several case studies.

cs.FL↗

arXiv2023

Planning with SiMBA: Motion Planning under Uncertainty for Temporal Goals using Simplified Belief Guides

This paper presents a new multi-layered algorithm for motion planning under motion and sensing uncertainties for Linear Temporal Logic specifications. We propose a technique to guide a sampling-based search tree in the combined task and belief space using trajectories from a simplified model of the system, to make the problem computationally tractable. Our method eliminates the need to construct fine and accurate finite abstractions. We prove correctness and probabilistic completeness of our algorithm, and illustrate the benefits of our approach on several case studies. Our results show that guidance with a simplified belief space model allows for significant speed-up in planning for complex specifications.

cs.RO↗

arXiv2023

Interval Markov Decision Processes with Continuous Action-Spaces

Interval Markov Decision Processes (IMDPs) are finite-state uncertain Markov models, where the transition probabilities belong to intervals. Recently, there has been a surge of research on employing IMDPs as abstractions of stochastic systems for control synthesis. However, due to the absence of algorithms for synthesis over IMDPs with continuous action-spaces, the action-space is assumed discrete a-priori, which is a restrictive assumption for many applications. Motivated by this, we introduce continuous-action IMDPs (caIMDPs), where the bounds on transition probabilities are functions of the action variables, and study value iteration for maximizing expected cumulative rewards. Specifically, we decompose the max-min problem associated to value iteration to $|\mathcal{Q}|$ max problems, where $|\mathcal{Q}|$ is the number of states of the caIMDP. Then, exploiting the simple form of these max problems, we identify cases where value iteration over caIMDPs can be solved efficiently (e.g., with linear or convex programming). We also gain other interesting insights: e.g., in certain cases where the action set $\mathcal{A}$ is a polytope, synthesis over a discrete-action IMDP, where the actions are the vertices of $\mathcal{A}$, is sufficient for optimality. We demonstrate our results on a numerical example. Finally, we include a short discussion on employing caIMDPs as abstractions for control synthesis.

eess.SY↗

arXiv2023

Chance-Constrained Motion Planning with Event-Triggered Estimation

We consider the problem of autonomous navigation using limited information from a remote sensor network. Because the remote sensors are power and bandwidth limited, we use event-triggered (ET) estimation to manage communication costs. We introduce a fast and efficient sampling-based planner which computes motion plans coupled with ET communication strategies that minimize communication costs, while satisfying constraints on the probability of reaching the goal region and the point-wise probability of collision. We derive a novel method for offline propagation of the expected state distribution, and corresponding bounds on this distribution. These bounds are used to evaluate the chance constraints in the algorithm. Case studies establish the validity of our approach, demonstrating fast computation of optimal plans.

cs.RO↗

arXiv2023

Timed Partial Order Inference Algorithm

In this work, we propose the model of timed partial orders (TPOs) for specifying workflow schedules, especially for modeling manufacturing processes. TPOs integrate partial orders over events in a workflow, specifying ``happens-before'' relations, with timing constraints specified using guards and resets on clocks -- an idea borrowed from timed-automata specifications. TPOs naturally allow us to capture event ordering, along with a restricted but useful class of timing relationships. Next, we consider the problem of mining TPO schedules from workflow logs, which include events along with their time stamps. We demonstrate a relationship between formulating TPOs and the graph-coloring problem, and present an algorithm for learning TPOs with correctness guarantees. We demonstrate our approach on synthetic datasets, including two datasets inspired by real-life applications of aircraft turnaround and gameplay videos of the Overcooked computer game. Our TPO mining algorithm can infer TPOs involving hundreds of events from thousands of data-points within a few seconds. We show that the resulting TPOs provide useful insights into the dependencies and timing constraints for workflows.

cs.FL↗

arXiv2022

Automaton-Guided Control Synthesis for Signal Temporal Logic Specifications

This paper presents an algorithmic framework for control synthesis of continuous dynamical systems subject to signal temporal logic (STL) specifications. We propose a novel algorithm to obtain a time-partitioned finite automaton from an STL specification, and introduce a multi-layered framework that utilizes this automaton to guide a sampling-based search tree both spatially and temporally. Our approach is able to synthesize a controller for nonlinear dynamics and polynomial predicate functions. We prove the correctness and probabilistic completeness of our algorithm, and illustrate the efficiency and efficacy of our framework on several case studies. Our results show an order of magnitude speedup over the state of the art.

eess.SY↗

arXiv2022

Pareto Optimal Strategies for Event-Triggered Estimation

Although resource-limited networked autonomous systems must be able to efficiently and effectively accomplish tasks, better conservation of resources often results in worse task performance. We specifically address the problem of finding strategies for managing measurement communication costs between agents. A well understood technique for trading off communication costs with estimation accuracy is event triggering (ET), where measurements are only communicated when useful, e.g., when Kalman filter innovations exceed some threshold. In the absence of measurements, agents can use implicit information to achieve results almost as well as when explicit data is always communicated. However, there are no methods for setting this threshold with formal guarantees on task performance. We fill this gap by developing a novel belief space discretization technique to abstract a continuous space dynamics model for ET estimation to a discrete Markov decision process, which scalably accommodates threshold-sensitive ET estimator error covariances. We then apply an existing probabilistic trade-off analysis tool to find the set of all optimal trade-offs between resource consumption and task performance. From this set, an ET threshold selection strategy is extracted. Simulated results show our approach identifies non-trivial trade-offs between performance and energy savings, with only modest computational effort.

eess.SY↗

arXiv2022

Gaussian Belief Trees for Chance Constrained Asymptotically Optimal Motion Planning

In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic systems and propose belief-$\mathcal{A}$, a framework that extends any kinodynamical tree-based planner to the belief space for linear (or linearizable) systems. We introduce appropriate sampling techniques and distance metrics for the belief space that preserve the probabilistic completeness and asymptotic optimality properties of the underlying planner. We demonstrate the efficacy of our approach for finding safe low-cost paths efficiently and asymptotically optimally in simulation, for both holonomic and non-holonomic systems.

cs.RO↗

arXiv2022

Conflict-based Search for Multi-Robot Motion Planning with Kinodynamic Constraints

Multi-robot motion planning (MRMP) is the fundamental problem of finding non-colliding trajectories for multiple robots acting in an environment, under kinodynamic constraints. Due to its complexity, existing algorithms either utilize simplifying assumptions or are incomplete. This work introduces kinodynamic conflict-based search (K-CBS), a decentralized (decoupled) MRMP algorithm that is general, scalable, and probabilistically complete. The algorithm takes inspiration from successful solutions to the discrete analogue of MRMP over finite graphs, known as multi-agent path finding (MAPF). Specifically, we adapt ideas from conflict-based search (CBS) - a popular decentralized MAPF algorithm - to the MRMP setting. The novelty in this adaptation is that we work directly in the continuous domain, without the need for discretization. In particular, the kinodynamic constraints are treated natively. K-CBS plans for each robot individually using a low-level planner and and grows a conflict tree to resolve collisions between robots by defining constraints for individual robots. The low-level planner can be any sampling-based, tree-search algorithm for kinodynamic robots, thus lifting existing planners for single robots to the multi-robot settings. We show that K-CBS inherits the (probabilistic) completeness of the low-level planner. We illustrate the generality and performance of K-CBS in several case studies and benchmarks.

cs.RO↗

arXiv2022

Conflict-Based Search for Explainable Multi-Agent Path Finding

In the Multi-Agent Path Finding (MAPF) problem, the goal is to find non-colliding paths for agents in an environment, such that each agent reaches its goal from its initial location. In safety-critical applications, a human supervisor may want to verify that the plan is indeed collision-free. To this end, a recent work introduces a notion of explainability for MAPF based on a 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. Then, the explainable MAPF problem asks for a set of non-colliding paths that admits a short-enough explanation. Explainable MAPF adds a new difficulty to MAPF, in that it is NP-hard with respect to the size of the environment, and not just the number of agents. Thus, traditional MAPF algorithms are not equipped to directly handle explainable-MAPF. In this work, we adapt Conflict Based Search (CBS), a well-studied algorithm for MAPF, to handle explainable MAPF. We show how to add explainability constraints on top of the standard CBS tree and its underlying A* search. We examine the usefulness of this approach and, in particular, the tradeoff between planning time and explainability.

cs.AI↗

arXiv2022

Formal Control Synthesis for Stochastic Neural Network Dynamic Models

Neural networks (NNs) are emerging as powerful tools to represent the dynamics of control systems with complicated physics or black-box components. Due to complexity of NNs, however, existing methods are unable to synthesize complex behaviors with guarantees for NN dynamic models (NNDMs). This work introduces a control synthesis framework for stochastic NNDMs with performance guarantees. The focus is on specifications expressed in linear temporal logic interpreted over finite traces (LTLf), and the approach is based on finite abstraction. Specifically, we leverage recent techniques for convex relaxation of NNs to formally abstract a NNDM into an interval Markov decision process (IMDP). Then, a strategy that maximizes the probability of satisfying a given specification is synthesized over the IMDP and mapped back to the underlying NNDM. We show that the process of abstracting NNDMs to IMDPs reduces to a set of convex optimization problems, hence guaranteeing efficiency. We also present an adaptive refinement procedure that makes the framework scalable. On several case studies, we illustrate the our framework is able to provide non-trivial guarantees of correctness for NNDMs with architectures of up to 5 hidden layers and hundreds of neurons per layer.

eess.SY↗

arXiv2022

Let's Collaborate: Regret-based Reactive Synthesis for Robotic Manipulation

As robots gain capabilities to enter our human-centric world, they require formalism and algorithms that enable smart and efficient interactions. This is challenging, especially for robotic manipulators with complex tasks that may require collaboration with humans. Prior works approach this problem through reactive synthesis and generate strategies for the robot that guarantee task completion by assuming an adversarial human. While this assumption gives a sound solution, it leads to an "unfriendly" robot that is agnostic to the human intentions. We relax this assumption by formulating the problem using the notion of regret. We identify an appropriate definition for regret and develop regret-minimizing synthesis framework that enables the robot to seek cooperation when possible while preserving task completion guarantees. We illustrate the efficacy of our framework via various case studies.

cs.RO↗

arXiv2022

Synergistic Offline-Online Control Synthesis via Local Gaussian Process Regression

Autonomous systems often have complex and possibly unknown dynamics due to, e.g., black-box components. This leads to unpredictable behaviors and makes control design with performance guarantees a major challenge. This paper presents a data-driven control synthesis framework for such systems subject to linear temporal logic on finite traces (LTLf) specifications. The framework combines a baseline (offline) controller with a novel online controller and refinement procedure that improves the baseline guarantees as new data is collected. The baseline controller is computed offline on an uncertain abstraction constructed using Gaussian process (GP) regression on a given dataset. The offline controller provides a lower bound on the probability of satisfying the LTLf specification, which may be far from optimal due to both discretization and regression errors. The synergy arises from the online controller using the offline abstraction along with the current state and new data to choose the next best action. The online controller may improve the baseline guarantees since it avoids the discretization error and reduces regression error as new data is collected. The new data are also used to refine the abstraction and offline controller using local GP regression, which significantly reduces the computation overhead. Evaluations show the efficacy of the proposed offline-online framework, especially when compared against the offline controller.

eess.SY↗

arXiv2022

Strategy Synthesis for Partially-known Switched Stochastic Systems

We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTLf specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems.

eess.SY↗