Hybrid system theory lies at the intersection of fields engineering control and computer science verification. It is defined as modeling, analysis, systems that involve interaction both discrete state systems, represented by finite automata, continuous dynamics, differential equations. The embedded autopilot a modern commercial jet prime example hybrid system: modes correspond to application different laws, logic mode switching determined dynamics aircraft, well through with pilot. To...

One of the primary challenges for autonomous robotics in uncertain and dynamic environments is planning executing a collision-free path. Hybrid obstacles present an even greater challenge as can change dynamics without warning potentially invalidate paths. Artificial potential field (APF)-based techniques have shown great promise successful path highly due to their low cost at runtime. We utilize APF framework runtime but leverage formal validation method, Stochastic Reachable (SR) sets,...

Highly dynamic environments pose a particular challenge for motion planning due to the need constant evaluation or validation of plans. However, wide range applications, an algorithm safely plan in presence moving obstacles is required. In this paper, we propose novel technique that provides computationally efficient solutions with static and several stochastic motions. Path-Guided APF-SR works by first applying sampling-based identify valid, collision-free path obstacles. Then, artificial...

and safety analysis of autoland systems. It is shown to be applicable specific phases landing: descent, flare, touchdown. The method based on optimal control level set methods; it simultaneously computes a maximal controlled invariant set-valued law guaranteed keep the aircraft within safe states under autopilot mode switching. applied sequenced flap slat deflections simplified model DC9-30. paper concludes with demonstration higher dimensional models.

Objective: 1) To determine the brain connectivity pattern associated with clinical rigidity scores in Parkinson's disease (PD) and 2) to relation between clinically-assessed quantitative metrics of motor performance. Background: Rigidity, resistance passive movement, is exacerbated PD by asking subject move contralateral limb, implying that involves a distributed network. Rigidity mainly affects subjects when they attempt move; yet aspects performance are unknown. Methods: Ten clinically...

We present a connection between the viability kernel and maximal reachable sets. Current numerical schemes that compute suffer from complexity is exponential in dimension of state space. In contrast, extremely efficient scalable techniques are available show under certain conditions these can be used to conservatively approximate for possibly high-dimensional systems. demonstrate results on two practical examples, one which seven-dimensional problem safety anesthesia.

Autonomous multi-rotor aerial vehicles, specially quadrotors, have become popular platforms for the transportation of cable-suspended loads. Before transporting load, lift maneuver is a crucial step that needs to be planed. In order perform this essential maneuver, we decompose it into simpler hybrid modes which characterize dynamics quadrotor-load system in specific regimes during maneuver. work, represent as and show differentially flat. This property facilitates generation prescribed...

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 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...

Adaptive automation, automation which is responsive to the human's performance via alteration of control laws or level assistance, an important tool for training humans attain new skills when operating dynamical systems. When coupled with cognitive feedback, adaptive has potential further facilitate human training, but requires precise assessments progression through various learning stages. This challenging because underlying dynamics, as well stochasticity inherent action. We propose a...

The concept of stochastic reachability allows for the assessment, before any maneuvers are initiated, probability successfully implementing a rendezvous or docking procedure spacecraft. so-called reach-avoid problem lets us find reaching target set while avoiding some unsafe undesired set, despite uncertainty due to nonlinearity and disturbances. This paper examines two novel methods calculation reachable sets, specifically problems. In particular, we examine a) particle (or scenario)...

In this paper an Unmanned Aerial Vehicles (UAVs) - enabled dynamic multi-target tracking and data collection framework is presented. Initially, a holistic reputation model introduced to evaluate the targets' potential in offloading useful UAVs. Based on model, taking into account UAVs targets sensing characteristics, intelligent matching between performed. such setting, incentivization of perform based effort-based pricing that offer targets. The emerging optimization problem towards...

Hybrid systems combine discrete state dynamics which model mode switching, with continuous physical processes. can be controlled by affecting both their logic and dynamics: in many systems, such as commercial aircraft, these automatically using manual control. A human interacting a hybrid system is often presented, through information displays, simplified representation of the underlying system. This <i xmlns:mml="http://www.w3.org/1998/Math/MathML"...

We present a scalable set-valued safety-preserving hybrid controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive disturbance/uncertainty. The approach relies on conservative approximation of the discriminating kernel using piecewise ellipsoidal algorithm with polynomial complexity. This precomputed is used online synthesize permissive state-feedback control law that guarantees satisfaction all constraints despite potentially conflicting performance...

Parkinson's disease (PD) is a neurodegenerative movement disorder that characterized clinically by slowness of movement, rigidity, tremor, postural instability, and often cognitive impairments. Recent studies have demonstrated altered cortico-basal ganglia rhythms in PD, which raises the possibility role for non-invasive stimulation therapies such as noisy galvanic vestibular (GVS). We applied GVS to 12 mild-moderately affected PD subjects (Hoehn & Yahr 1.5-2.5) off medication while they...

One of the many challenges in designing autonomy for operation uncertain and dynamic environments is planning collision-free paths. Roadmap-based motion a popular technique identifying paths, since it approximates often infeasible space all possible motions with networked structure valid configurations. We use stochastic reachable sets to identify regions low collision probability, create roadmaps which incorporate likelihood collision. complete small number reachability calculations...

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....