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Sampling-Based Approximation Algorithms for Reachability Analysis with Provable Guarantees

Lucas Liebenwein, Cenk Baykal, Igor Gilitschenski, Sertac Karaman, Daniela Rus
2018 Robotics: Science and Systems XIV  
In this work, we present a simple-to-implement, sampling-based algorithm for reachability analysis that is provably optimal up to any desired approximation accuracy.  ...  We prove that the reachable set generated by our algorithm approximates the ground-truth reachable set for any user-specified approximation accuracy.  ...  These computational challenges in conjunction with the need to obtain provably valid results motivate the development of approximation schemes with provable guarantees for reachability analysis.  ... 
doi:10.15607/rss.2018.xiv.014 dblp:conf/rss/LiebenweinBGKR18 fatcat:sxdla25b5rfi3eher5xgumjsdy

Interpretable Trade-offs Between Robot Task Accuracy and Compute Efficiency [article]

Bineet Ghosh, Sandeep Chinchali, Parasara Sridhar Duggirala
2021 arXiv   pre-print
A robot can invoke heterogeneous computation resources such as CPUs, cloud GPU servers, or even human computation for achieving a high-level goal.  ...  We show that such cost-benefit analysis can be performed by leveraging the statistical correlation between the accuracy of fast and slow compute models.  ...  Third, we show strong experimental performance of our algorithm on diverse domains ranging from robotic perception to sampling-based reachability analysis for a simulated rover navigating Martian terrain  ... 
arXiv:2108.01235v1 fatcat:7llg7dtfojanlmewzt62abscoi

Formal Certification Methods for Automated Vehicle Safety Assessment [article]

Tong Zhao, Ekim Yurtsever, Joel Paulson, Giorgio Rizzoni
2022 arXiv   pre-print
A majority of approaches used in providing safety guarantees for AV motion control originate from formal methods, especially reachability analysis (RA), which relies on mathematical models for the dynamic  ...  We also propose a unified scenario coverage framework that can provide either a formal or sample-based estimate of safety verification for full AVs.  ...  “Sampling-based approximation algorithms for reachability analysis with In 2019 he worked as a control algorithm intern provable guarantees,” Proceedings of Robotics  ... 
arXiv:2202.02818v2 fatcat:spgyrglbwjhshl2n43kyx722fa

Provably Safe Reinforcement Learning: A Theoretical and Experimental Comparison [article]

Hanna Krasowski, Jakob Thumm, Marlon Müller, Xiao Wang, Matthias Althoff
2022 arXiv   pre-print
Ensuring safety of reinforcement learning (RL) algorithms is crucial for many real-world tasks. However, vanilla RL does not guarantee safety for an agent.  ...  In recent years, several methods have been proposed to provide safety guarantees for RL. To the best of our knowledge, there is no comprehensive comparison of these provably safe RL methods.  ...  Shao et al. (2021) use a continuous reachability-based trajectory safeguard to evaluate the safety of actions based on reachability analysis.  ... 
arXiv:2205.06750v1 fatcat:6mkf42ygxzgfnl25e26jfusk64

Real-Time Reachability for Verified Simplex Design

Taylor T. Johnson, Stanley Bak, Marco Caccamo, Lui Sha
2016 ACM Transactions on Embedded Computing Systems  
In this work, we prove that a combined online/offline approach, which uses aspects of the two earlier methods along with a real-time reachability computation, also maintains safety, but with significantly  ...  This architecture enables the safe use of high-performance, untrusted, and complex control algorithms without requiring them to be formally verified.  ...  The algorithm will always return an over-approximation of the reachable set, with better accuracy as more computation time is given.  ... 
doi:10.1145/2723871 fatcat:aomr5vi5hnh25bd5633l26zwkq

Real-Time Reachability for Verified Simplex Design

Stanley Bak, Taylor T. Johnson, Marco Caccamo, Lui Sha
2014 2014 IEEE Real-Time Systems Symposium  
In this work, we prove that a combined online/offline approach, which uses aspects of the two earlier methods along with a real-time reachability computation, also maintains safety, but with significantly  ...  This architecture enables the safe use of high-performance, untrusted, and complex control algorithms without requiring them to be formally verified.  ...  The algorithm will always return an over-approximation of the reachable set, with better accuracy as more computation time is given.  ... 
doi:10.1109/rtss.2014.21 dblp:conf/rtss/BakJCS14 fatcat:dvoeivikknhm3bpeaq6xpwwqfy

Point-Based POMDP Algorithms: Improved Analysis and Implementation [article]

Trey Smith, Reid Simmons
2012 arXiv   pre-print
Existing complexity bounds for point-based POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history.  ...  We also discuss recent improvements to our (point-based) heuristic search value iteration algorithm.  ...  Acknowledgments Thanks to Geoff Gordon and Pascal Poupart for helpful discussions. This work was funded in part by a NASA GSRP Fellowship with Ames Research Center. cation.  ... 
arXiv:1207.1412v1 fatcat:7hkplw5wmrapvmfexrxqcjo4dm

Scanning The Issue

2014 IEEE Transactions on Automatic Control  
This hierarchy provides an explicit sequence of outer approximations to the ROA with a guaranteed set-wise convergence. Stability Analysis Of Systems With Generalized Frequency Variables S.  ...  For a particular choice of link weights, it is shown that this problem can be solved using supermodular optimization techniques, leading to efficient algorithms with provable bounds.  ... 
doi:10.1109/tac.2014.2298118 fatcat:4uh5u3p66rewphv7zzdf3s6yua

Provably Safe Deep Reinforcement Learning for Robotic Manipulation in Human Environments [article]

Jakob Thumm, Matthias Althoff
2022 arXiv   pre-print
We utilize a fast reachability analysis of humans and manipulators to guarantee that the manipulator comes to a complete stop before a human is within its range.  ...  However, no method guarantees the safety of highly dynamic obstacles, such as humans, in RL-based manipulator control.  ...  Part of our code is based on the open source reachability analysis tool SaRA (available at https://github.com/Sven-Schepp/SaRA) [32] . 3 Run on a ThinkPad P15 Gen 1 with an Intel(R) Core(TM) i7-10750H  ... 
arXiv:2205.06311v1 fatcat:4i7crcuehvasvl3xdydnuuzyoq

A Sample-Based Algorithm for Approximately Testing r-Robustness of a Digraph [article]

Yuhao Yi, Yuan Wang, Xingkang He, Stacy Patterson, Karl H. Johansson
2022 arXiv   pre-print
In this paper, we propose a sample-based algorithm to approximately test r-robustness of a digraph with n vertices and m edges.  ...  For a digraph with a moderate assumption on the minimum in-degree, and an error parameter 0<ϵ≤ 1, the proposed algorithm distinguishes (r+ϵ n)-robust graphs from graphs which are not r-robust with probability  ...  The main contribution of this paper is an algorithm for approximately testing r-robustness with provable guarantees.  ... 
arXiv:2207.12110v1 fatcat:vyvwg6saijbxhfbopazx6fnbbq

Communication coverage for independently moving robots

Stephanie Gil, Dan Feldman, Daniela Rus
2012 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems  
We provide a formal framework and design provable exact and approximate (faster) algorithms for finding optimal router vehicle locations that are updated according to sensor movement.  ...  The expiration time is compared against computation time required to update positions as a decision variable for choosing either the exact or approximate solution for maintaining connectivity with the  ...  Exact Algorithm for Reachable k-Connected Centers We combine the results from the previous two subsections on k-connected centers and reachability analysis to provide an algorithm for returning communication  ... 
doi:10.1109/iros.2012.6386226 dblp:conf/iros/GilFR12 fatcat:wji2fmwuovg2hfynevz7vosnju

Influence Maximization with Priority in Online Social Networks

Canh V. Pham, Dung K. T. Ha, Quang C. Vu, Anh N. Su, Huan X. Hoang
2020 Algorithms  
To find the solution, we propose two efficient algorithms, called Integrated Greedy (IG) and Integrated Greedy Sampling (IGS) with provable theoretical guarantees.  ...  In addition, IGS is an efficient randomized approximation algorithm based on sampling method that provides a 1−(1−1k)t−ϵ-approximation solution with probability at least 1−δ with ϵ>0,δ∈(0,1) as input parameters  ...  To overcome this challenge, we propose a randomize algorithm with provable approximation guarantee based on combining IG with a sampling technique.  ... 
doi:10.3390/a13080183 fatcat:3lg5u2qmergedlnwvbvz5sdchm

Provable Indefinite-Horizon Real-Time Planning for Repetitive Tasks [article]

Fahad Islam, Oren Salzman, Maxim Likhachev
2019 arXiv   pre-print
To this end, we propose a preprocessing-based method that provides provable bounds on the query time while incurring only a small amount of memory overhead in the query phase.  ...  While there are planners that guarantee real-time performance by limiting the planning horizon, we are not aware of general-purpose planners capable of doing it for indefinite horizon (i.e., planning to  ...  We can preprocess our planner with only static obstacles and in the query time we can do a validity check of the computed path; if the path intersects any non-static obstacle, we can fall back to the conventional  ... 
arXiv:1901.07698v2 fatcat:v4yqm75ptfci3jkj2njzvfdo3u

Reachability of Linear Uncertain Systems: Sampling Based Approaches [article]

Bineet Ghosh, Parasara Sridhar Duggirala
2021 arXiv   pre-print
In this work, we perform safety analysis of linear dynamical systems with uncertainties.  ...  As a result, the guarantees provided by our method are probabilistic in nature. In this paper, we provide two different techniques to compute statistical approximate reachable set.  ...  We now present a sampling based reachable set computation technique that computes a provable overapproximation of the uncertain systems considered in [22] .  ... 
arXiv:2109.07638v1 fatcat:xphwrq2mkfcuvezesxzis63lfe

Data-Driven Reachability Analysis from Noisy Data [article]

Amr Alanwar, Anne Koch, Frank Allgöwer, Karl Henrik Johansson
2022 arXiv   pre-print
First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems.  ...  Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set.  ...  Sampling-based reachability analysis that utilizes random set theory is presented in [9] .  ... 
arXiv:2105.07229v2 fatcat:6pia6vo4fve4fll7zqpargjnpu
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