We present SReachTools, an open-source MATLAB toolbox for performing stochastic reachability of linear, potentially time-varying, discrete-time systems that are perturbed by a disturbance. The addresses the problem target tube, which also encompasses terminal-time hitting reach-avoid and viability problems. tube maximizes likelihood state system will remain within collection time-varying sets give time horizon, while respecting dynamics bounded control authority. SReachTools implements...

We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy NSSM. The major benefit our approach is that instead relying solely on data from single target system, utilizes diverse set source systems, enabling learning limited data, as well with few online training iterations. Through benchmark examples,...

We consider the spatial classification problem for monitoring using data collected by a coordinated team of mobile robots. Such problems arise in several applications including search-and-rescue and precision agriculture. Specifically, we want to classify regions search environment into interesting uninteresting as quickly possible sensors charging stations. develop data-driven strategy that accommodates noise sensed limited energy capacity sensors, generates collision-free motion plans...

We propose a scalable method for forward stochastic reachability analysis uncontrolled linear systems with affine disturbance. Our uses Fourier transforms to efficiently compute the reach probability measure (density) and set. This is applicable bounded or unbounded disturbance sets. also examine convexity properties of set its density. Motivated by problem robot attempting capture stochastically moving, non-adversarial target, we demonstrate our on two simple examples. Where traditional...

We present a scalable underapproximation of the terminal hitting time stochastic reach-avoid probability at given initial condition, for verification high-dimensional LTI systems. While several approximation techniques have been proposed to alleviate curse dimensionality associated with dynamic programming, these cannot handle larger, more realistic method that uses Fourier transforms compute an systems disturbances arbitrary densities. characterize sufficient conditions Borel-measurability...

We present a scalable algorithm to construct polytopic underapproximation of the terminal hitting time stochastic reach-avoid set, for verification high-dimensional LTI systems with arbitrary disturbance. prove existence by characterizing sufficient conditions under which set and proposed open-loop are compact convex. formulating solving series convex optimization problems. These set-theoretic properties also characterize circumstances problem admits bang-bang optimal Markov policy....

We consider the problem of safe multi-agent motion planning for drones in uncertain, cluttered workspaces. For this problem, we present a tractable planner that builds upon strengths reinforcement learning and constrained-control-based trajectory planning. First, use single-agent to learn plans from data reach target but may not be collision-free. Next, convex optimization, chance constraints, set-based methods constrained control ensure safety, despite uncertainty workspace, agent motion,...

We examine Lagrangian techniques for computing under approximations of finite-time horizon, stochastic reach-avoid level sets discrete-time, nonlinear systems. use the concept reachability a target tube to define robust which are parameterized by set, safe and set disturbance is drawn from. unify two existing approaches compute these sets, establish that there exists an optimal control policy Markov policy. Based on results, we characterize subset space whose corresponding given guaranteed...

We study the problem of safe multi-agent motion planning in cluttered environments. Existing reinforcement learning-based planners only provide approximate safety enforcement. propose a learning algorithm that leverages single-agent for target regulation and subsequent convex optimization-based filtering ensures collective system. Our approach yields safe, real-time implementable planner is simpler to train enforces as hard constraints. can handle state control constraints on agents, enforce...

Identifying collision-free paths over long time windows in environments with stochastically moving obstacles is difficult, part because long-term predictions of obstacle positions typically have low fidelity, and the region possible occupancy large. As a result, planning methods that are restricted to identifying probability collision may not be able find valid path. However, allowing higher limit detection imminent collisions. In this paper, we present Dynamic Risk Tolerance (DRT),...

This report presents the results of a friendly competition for formal verification and policy synthesis stochastic models. The took place as part workshop Applied Verification Continuous Hybrid Systems (ARCH) in 2018. In this first edition, we present five benchmarks with different levels complexities flavours. We make use six tools frameworks (in alphabetical order): Barrier Certificates, FAUST2, FIRM-GDTL, Modest, SDCPN modelling & MC simulation SReachTools; attempt to solve...

We propose a method to efficiently compute the forward stochastic reach (FSR) set and its probability measure. consider nonlinear systems with an affine disturbance input, that is bounded. This model includes uncontrolled priori known controller, often arises in problems obstacle avoidance mobile robotics. When used as constraint finite horizon controller synthesis, FSR measure facilitate probabilistic collision avoidance. contrast traditional game-theoretic approaches which presume...

This paper considers the problem of stochastic optimal control a Gaussian-perturbed linear system subject to soft polytopic state constraints, hard input and convex cost function. We propose two conservative approaches using risk allocation that can be implemented via existing solvers, characterize approximations. Unlike approaches, we do not decouple from controller synthesis. first show in conjunction with synthesis introduces reverse constraints into optimization problem. Next, use...

We address the stochastic reach-avoid problem for linear systems with additive uncertainty. seek to compute maximum probability that states remain in a safe set over finite time horizon and reach target at final time. employ sampling-based methods provide lower bound on number of scenarios required guarantee our estimate provides an underapproximation. Due probabilistic nature methods, underapproximation is probabilistic, proposed can be used satisfy prescribed confidence level. To decrease...

In this demo, we present SReachTools, an open-source MATLAB toolbox for performing stochastic reachability of linear, potentially time-varying, discrete-time systems that are perturbed by a disturbance [8]. The addresses the problem target tube, which also encompasses terminal-time hitting reach-avoid [7] and viability problems [1]. As illustrated in Figure 1, tube maximizes likelihood state system will remain within collection time-varying sets give time horizon, while respecting dynamics...

We investigate the problem of data-driven, on-the-fly control systems with unknown nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side information on are available. Such may include knowledge regularity dynamics, monotonicity states, or decoupling in between states. Specifically, we develop two algorithms, DaTaReach DaTaControl, to over-approximate reachable set design signals for system fly. constructs differential inclusion that contains vector...

This paper presents robust Koopman model predictive control (RK-MPC), a framework that leverages the training errors of data-driven models to improve constraint satisfaction. Koopman-based has enabled fast nonlinear feedback using linear tools, but existing approaches ignore modeling error during control, which can lead violations. Our approach assumes unknown dynamics are Lipschitz-continuous and uses approximate Lipschitz constant for state- control-dependent error. We then use bound...

We discuss the multiple pursuer-based intercept of a threat unmanned aerial system (UAS) with stochastic dynamics via pursuing UASs, using forward reachability and receding horizon control techniques. formulate model for that can emulate potentially adversarial behavior is amenable to existing scalable results in literature. The optimal state each individual pursuer obtained log-concave optimization problem, open-loop paths are convex problem. With stochasticity modeled as Gaussian process,...

We propose an affine controller synthesis technique that maximizes the probability of state lying in a time-varying collection safe sets for Gaussian-perturbed linear system under bounded control authority. Specifically, we solve chance constrained optimization problem obtained by relaxing hard bounds to probabilistic constraint with user-specified threshold. also construct lower bound true maximal reach probability, when proposed is saturated satisfy bounds. For tractability, formulate into...

In this paper, we propose a motion planner for quadrotors in windy environments. We extend well-known convex polynomial optimization (CPO) method to incorporate known stochastic input uncertainties. particular, focus on quadrotor unmanned aerial vehicle (UAV), and new objective direct minimization of the squared ${{{\mathcal{L}}}_2}$-norm UAV thrust, $\left\| f \right\|_{{{{\mathcal{L}}}_2}}^2$. show that first two moments \right\|_{{{{\mathcal{L}}}_2}}^2$ are variables CPO problem, can be...