Reachability-based Trajectory Design with Neural Implicit Safety Constraints
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Generating safe motion plans in real-time is a key requirement for deploying robot manipulators to assist humans in collaborative settings.In particular, robots must satisfy strict safety requirements to avoid self-damage or harming nearby humans.Satisfying these requirements is particularly challenging if the robot must also operate in real-time to adjust to changes in its environment.This paper addresses these challenges by proposing Reachability-based Signed Distance Functions (RDFs) as a neural implicit representation for robot safety.RDF, which can be constructed using supervised learning in a tractable fashion, accurately predicts the distance between the swept volume of a robot arm and an obstacle.RDF's inference and gradient computations are fast and scale linearly with the dimension of the system; these features enable its use within a novel real-time trajectory planning framework as a continuoustime collision-avoidance constraint.The planning method using RDF is compared to a variety of state-of-the-art techniques and is demonstrated to successfully solve challenging motion planning tasks for high-dimensional systems faster and more reliably than all tested methods.Code, data, and video demonstrations can be found at https://roahmlab.github.In this technical note, reachability properties of continuous-time positive systems are introduced and characterized. Specifically, first it is shown that reachability and strong reachability are equivalent properties, and thus the characterization of strong reachability derived in is extended to the weaker notion of reachability. In the second part of the technical note, essential reachability is introduced, and necessary and sufficient conditions for this property to hold are provided.
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Reachability analysis and reverse reachability analysis are two important verification techniques for communicating finite state machines (CFSMs). The issue of the relative efficiency of reachability analysis and reverse reachability analysis is still unsettled. We first propose a new theory of reachability and reverse reachability analysis. Based on the new theory we discuss and analyze the suitability of these two reachability analysis methods. We then present a reachability evaluator, which, given any network of CFSMs, will try to estimate the sizes of the reachable and reverse reachable state spaces by taking snapshots of the reachability and reverse reachability spaces. The core of the evaluator is the notion of random state generation with seed states, which extends the idea of random state exploration proposed by West (1986). Results from example applications have shown that the evaluator provides guidance in choosing the better of the two methods.
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In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds of the reachability probability, with which the system starting from a designated initial set will enter a desired target set eventually. Existing sufficient conditions for reachability verification over the infinite time horizon are established based on the Doob's non-supermartingle inequality, which are often restrictive. Recently, a set of equations was proposed in [18], to which the solution is able to characterize the exact reachability probability. Inspired by this result, we in this paper propose sufficient conditions for reachability verification based on relaxing this equation. These sufficient conditions are shown to be weaker than the state-of-the-art ones, consequently being capable of providing more opportunities for verifying the reachability property successfully.
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In this paper, reachability properties of continuous-time positive systems are introduced and characterized in algebraic terms. Specifically, first it is shown that reachability and strong reachability are equivalent properties, and thus the characterization of strong reachability derived in (Commault and Alamir, 2007) is extended to the weaker notion of reachability. In the second part of the paper, essential reachability is introduced, and necessary and sufficient conditions for this property to hold are provided.
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Reachability is one of the significant properties of Petri nets (PNs). For unbounded PNs, how to determine their reachability is an open issue. In this paper, we propose an algorithm that determines whether the reachability set of an unbounded PN is semilinear. Moreover, in the case that the unbounded PN has semilinear reachability set, the proposed algorithm can construct a new reachability tree (NRT) that exactly characterizes its reachability set. In addition, it can be decided based on NRT whether an unbounded PN suffers from deadlocks. The results are illustrated via examples.
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Бұл зерттеужұмысындaКaно моделітурaлы жәнеоғaн қaтыстытолықмәліметберілгенжәнеуниверситетстуденттерінебaғыттaлғaн қолдaнбaлы (кейстік)зерттеужүргізілген.АхметЯссaуи университетініңстуденттеріүшін Кaно моделіқолдaнылғaн, олaрдың жоғaры білімберусaпaсынa қоятынмaңыздытaлaптaры, яғнисaпaлық қaжеттіліктері,олaрдың мaңыздылығытурaлы жәнесaпaлық қaжеттіліктерінеқaтыстыөз университетінқaлaй бaғaлaйтындығытурaлы сұрaқтaр қойылғaн. Осы зерттеудіңмaқсaты АхметЯсaуи университетіндетуризмменеджментіжәнеқaржы бaкaлaвриaт бaғдaрлaмaлaрыныңсaпaсынa қaтыстыстуденттердіңқaжеттіліктерінaнықтaу, студенттердіңқaнaғaттaну, қaнaғaттaнбaу дәрежелерінбелгілеу,білімберусaпaсын aнықтaу мен жетілдіружолдaрын тaлдaу болыптaбылaды. Осы мaқсaтқaжетуүшін, ең aлдыменКaно сaуaлнaмaсы түзіліп,116 студенткеқолдaнылдыжәнебілімберугежәнеоның сaпaсынa қaтыстыстуденттердіңтaлaптaры мен қaжеттіліктерітоптықжұмыстaрaрқылыaнықтaлды. Екіншіден,бұл aнықтaлғaн тaлaптaр мен қaжеттіліктерКaно бaғaлaу кестесіменжіктелді.Осылaйшa, сaпa тaлaптaры төрт сaнaтқa бөлінді:болуытиіс, бір өлшемді,тaртымдыжәнебейтaрaп.Соңындa,қaнaғaттaну мен қaнaғaттaнбaудың мәндеріесептелдіжәнестуденттердіңқaнaғaттaну мен қaнaғaттaнбaу деңгейлерінжоғaрылaту мен төмендетудеосытaлaптaр мен қaжеттіліктердіңрөліaйқын aнықтaлды.Түйінсөздер:сaпa, сaпaлық қaжеттіліктер,білімберусaпaсы, Кaно моделі.
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In this paper we address the reachability of continuous-time positive switched systems. In detail, we first provide the reachability definition and a necessary condition for its existence. We then fully explore the "pattern reachability" problem, namely the problem of reaching, for every subset S of {1, 2,... , n}, at least one nonnegative state vector whose nonzero entries are exactly those corresponding to the elements of S. Finally, for the class of n-dimensional single-input systems switching among n subsystems, necessary and sufficient conditions for reachability are given
Reachability problem
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