Hybrid System Reachability-Based Analysis of Dynamical Agents

Aaron, Eric

doi:10.1007/11964995_21

Cited by 1 publication

(6 citation statements)

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“…In spite of this, several approaches have been developed to compute approximate reachable sets of states for these nonlinear systems [11,16,21]. The verification work described in this paper, in particular, is based on the hybridization ideas presented in [3,12]. This approach to analysis of nonlinear systems is based on the decomposition of nonlinear systems into simpler systems that can be more easily analyzed.…”

Section: Simulation Environmentmentioning

confidence: 99%

“…Nonlinear systems affine approximation. This section describes the process of hybridization of a nonlinear system, as described in [3,12]. Given a simplicial mesh of Ω, a nonlinear dynamical system defined by ∂ x ∂t = f ( x) can be approximated by a piecewise affine dynamical system, such that each affine piece corresponds exactly to a simplex in the mesh.…”

Section: Hybridization Of Nonlinear Systemsmentioning

confidence: 99%

“…This section describes a relatively fast method for analyzing nonlinear differential equations-based autonomous systems, based on [3]. This method is similar to the formal verification method described in Section 6.2 in that it analyzes the dynamics of an approximating piecewise affine system in each mesh element (in each simplex, for this paper).…”

Section: Heuristic Reachability Analysismentioning

confidence: 99%

“…A measure of relative difficulty of a system starting in an initial region X 0 , for example, can be obtained, as described in [3], by comparing the estimated probability that the system evolves from X 0 into a good state (i.e., the agent reaches the target) against the probability that the system evolves from X 0 into a bad state (i.e., the agent collides or never reaches the target). To do this, according…”

Section: Heuristic Reachability Analysismentioning

confidence: 99%

“…to [3], each simplex that intersects the initial region X 0 is labeled as good, bad, or neutral: a good simplex is one that either contains the target, or is more likely to evolve into a good simplex than into a bad simplex; a bad simplex is one that contains an obstacle or is more likely to evolve into a bad simplex than a good simplex; a neutral simplex is one where neither of these conditions holds (e.g., the system will certainly evolve out of Ω) The procedure for labeling a simplex is given by Algorithm 3. There are two essential parts of the procedure that are not yet defined by Algorithm 3: the method for estimating the probability that the system evolves from S to S i , P (S, S i ), and a measure for whether that probability is high enough to be considered.…”

Section: Heuristic Reachability Analysismentioning

confidence: 99%

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Dynamical Systems-based Navigation: Modeling and Verification

Mendoza¹

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I need to thank my family first, because each one of them has contributed in many ways to make me a person capable of taking on a project like this. They all know how thankful I am and how much I love them, but this time I want to thank my dad, in particular, for being the greatest example of perseverance and strength during hard times that I have ever had. I also want to thank my mentor and advisor, Professor Eric Aaron. He reached out to me when I first came to Wesleyan with no idea of how to reach my full potential in a new, strange academic environment. Whatever comes next in my professional career, it will be greatly due to his hands-on guidance in my Wesleyan years. I want to thank my housemates Becca, Reilly, and Shannon, for giving me a great living experience this year and for lending me their support, especially during the last stages of my thesis experience. Finally, I want to thank the Wesleyan Hughes Program for supporting this work and giving me the opportunity to dedicate to it all the time it needs. The work presented here is the product of an ongoing collaboration between Prof. Aaron and me; several of the ideas in this paper are his, and several of my ideas are a direct result of our conversations. i Contents List of Figures iv List of Tables vii Chapter 1. Introduction 5.3 The figure shows two agents of different sizes (0.2 and 0.6) reaching a path parallel to the wall. Each agent has a value of D = 4r R which causes the distance between the parallel path and the wall to be proportional to r R. 5.4 Scenarios on which DT navigation was tested, and their names as used throughout this paper. Only walls and targets (green) are shown in each scenario. Arrows represent wall rotation. 5.5 Example of a navigation path taken by an agent using DT navigation in the Hallways and Hallways2 scenario. Dotted circles indicate targets in the sequence, and numbers indicate the order in which they had to be reached. 5.6 Previously employed approaches to wall representation: (a) Multiple circle (MC); (b) Bounded, visible (BV); (c) Bounded, pre-computed (BP);

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