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.Comment: 8 pages, 4 figures, to appear in International Conference on Intelligent Robots and Systems (IROS) 202

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.Comment: Submitted to IROS 202

Promises of Deep Kernel Learning for Control Synthesis

Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes. Hence, it is potentially a promising tool to learn and control complex dynamical systems. In this work, we develop a scalable abstraction-based framework that enables the use of DKL for control synthesis of stochastic dynamical systems against complex specifications. Specifically, we consider temporal logic specifications and create an end-to-end framework that uses DKL to learn an unknown system from data and formally abstracts the DKL model into an Interval Markov Decision Process (IMDP) to perform control synthesis with correctness guarantees. Furthermore, we identify a deep architecture that enables accurate learning and efficient abstraction computation. The effectiveness of our approach is illustrated on various benchmarks, including a 5-D nonlinear stochastic system, showing how control synthesis with DKL can substantially outperform state-of-the-art competitive methods.Comment: 9 pages, 4 figures, 3 table

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.Comment: Proceedings at IEEE CAVS 201

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.Comment: 8 pages, accepted to IEEE Conference on Decision and Control 202

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

Formal Abstraction of General Stochastic Systems via Noise Partitioning

Verifying the performance of safety-critical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with non-standard (e.g., non-affine, non-symmetric, non-unimodal) noise distributions for verification purposes. The method uses a finite partitioning of the noise domain to construct an interval Markov chain (IMC) abstraction of the system via transition probability intervals. Noise partitioning allows for a general class of distributions and structures, including multiplicative and mixture models, and admits both known and data-driven systems. The partitions required for optimal transition bounds are specified for systems that are monotonic with respect to the noise, and explicit partitions are provided for affine and multiplicative structures. By the soundness of the abstraction procedure, verification on the IMC provides guarantees on the stochastic system against a temporal logic specification. In addition, we present a novel refinement-free algorithm that improves the verification results. Case studies on linear and nonlinear systems with non-Gaussian noise, including a data-driven example, demonstrate the generality and effectiveness of the method without introducing excessive conservatism.Comment: 6 pages, 6 figures, submitted jointly to IEEE Control Systems Letters and 2024 AC

Introducing Delays in Multi-Agent Path Finding

We consider a Multi-Agent Path Finding (MAPF) setting where agents have been assigned a plan, but during its execution some agents are delayed. Instead of replanning from scratch when such a delay occurs, we propose delay introduction, whereby we delay some additional agents so that the remainder of the plan can be executed safely. We show that the corresponding decision problem is NP-Complete in general. However, in practice we can find optimal delay-introductions using CBS for very large numbers of agents, and both planning time and the resulting length of the plan are comparable, and sometimes outperform, the state-of-the-art heuristics for replanning. We also examine the benefits of our method from an explainability point of view.Comment: 10 pages, 8 figures, and 2 table

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