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58
Incremental Samplingbased Algorithms for Optimal Motion Planning
, 2006
"... During the last decade, incremental samplingbased motion planning algorithms, such as the Rapidlyexploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the s ..."
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Cited by 66 (4 self)
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During the last decade, incremental samplingbased motion planning algorithms, such as the Rapidlyexploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been established so far. The purpose of this paper is to fill this gap, by designing efficient incremental samplingbased algorithms with provable optimality properties. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path returned by RRT converges almost surely to a nonoptimal value, as the number of samples increases. Second, a new algorithm is considered, called the Rapidlyexploring Random Graph (RRG), and it is shown that the cost of the best path returned by RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called RRT ∗ , which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between samplingbased motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT ∗ algorithms is asymptotically within a constant factor of that required by RRT.
Systematic simulation using sensitivity analysis
 IN HSCC
, 2007
"... In this paper we propose a new technique for verification by simulation of continuous and hybrid dynamical systems with uncertain initial conditions. We provide an algorithmic methodology that can, in most cases, verify that the system avoids a set of bad states by conducting a finite number of sim ..."
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Cited by 37 (4 self)
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In this paper we propose a new technique for verification by simulation of continuous and hybrid dynamical systems with uncertain initial conditions. We provide an algorithmic methodology that can, in most cases, verify that the system avoids a set of bad states by conducting a finite number of simulation runs starting from a finite subset of the set of possible initial conditions. The novelty of our approach consists in the use of sensitivity analysis, developed and implemented in the context of numerical integration, to efficiently characterize the coverage of sampling trajectories.
An rrtbased algorithm for testing and validating multirobot controllers
 In Robotics: Science and Systems
, 2005
"... Abstract — We address the problem of testing complex reactive control systems and validating the effectiveness of multiagent controllers. Testing and validation involve searching for conditions that lead to system failure by exploring all adversarial inputs and disturbances for errant trajectories. ..."
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Cited by 28 (1 self)
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Abstract — We address the problem of testing complex reactive control systems and validating the effectiveness of multiagent controllers. Testing and validation involve searching for conditions that lead to system failure by exploring all adversarial inputs and disturbances for errant trajectories. This problem of testing is related to motion planning, with one main difference. Unlike motion planning problems, systems are typically not controllable with respect to disturbances or adversarial inputs and therefore, the reachable set of states is a small subset of the entire state space. In both cases however, there is a goal or specification set consisting of a set of points in state space that is of interest, either for demonstrating failure or for validation. In this paper we consider the application of the Rapidlyexploring Random Tree algorithm to the testing and validation problem. Because of the differences between testing and motion planning, we propose three modifications to the original RRT algorithm. First, we introduce a new distance function which incorporates information about the system’s dynamics to select nodes for extension. Second, we introduce a weighting to penalize nodes which are repeatedly selected but fail to extend. Third, we propose a scheme for adaptively modifying the sampling probability distribution based on tree growth. We demonstrate the application of the algorithm via three simple and one large scale example and provide computational statistics. Our algorithms are applicable beyond the testing problem to motion planning for systems that are not small time locally controllable. I.
Anytime motion planning using the RRT
 in IEEE International Conference on Robotics and Automation
, 2011
"... Abstract — The Rapidlyexploring Random Tree (RRT) algorithm, based on incremental sampling, efficiently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor “anytime ..."
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Cited by 28 (2 self)
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Abstract — The Rapidlyexploring Random Tree (RRT) algorithm, based on incremental sampling, efficiently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor “anytime” algorithms that quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. This paper describes an anytime algorithm based on the RRT ∗ which (like the RRT) finds an initial feasible solution quickly, but (unlike the RRT) almost surely converges to an optimal solution. We present two key extensions to the RRT ∗ , committed trajectories and branchandbound tree adaptation, that together enable the algorithm to make more efficient use of computation time online, resulting in an anytime algorithm for realtime implementation. We evaluate the method using a series of Monte Carlo runs in a highfidelity simulation environment, and compare the operation of the RRT and RRT ∗ methods. We also demonstrate experimental results for an outdoor wheeled robotic vehicle. I.
Montecarlo techniques for falsification of temporal properties of nonlinear hybrid systems
 In Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control
, 2010
"... We present a MonteCarlo optimization technique for finding inputs to a system that falsify a given Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of inputs guided by a robustness metric defined by the MTL property. Robustness can be used to guide our search ..."
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Cited by 24 (14 self)
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We present a MonteCarlo optimization technique for finding inputs to a system that falsify a given Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of inputs guided by a robustness metric defined by the MTL property. Robustness can be used to guide our search for a falsifying trajectory by exploring trajectories with smaller robustness values. We show that the notion of robustness can be generalized to consider hybrid system trajectories. The resulting testing framework can be applied to nonlinear hybrid systems with external inputs. We show through numerous experiments on complex systems that using our framework can help automatically falsify properties with more consistency as compared to other means such as uniform sampling.
Falsification of LTL Safety Properties in Hybrid Systems
"... This paper develops a novel computational method for the falsification of safety properties specified by syntactically safe linear temporal logic (LTL) formulas φ for hybrid systems with general nonlinear dynamics and input controls. The method is based on an effective combination of robot motion p ..."
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Cited by 21 (6 self)
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This paper develops a novel computational method for the falsification of safety properties specified by syntactically safe linear temporal logic (LTL) formulas φ for hybrid systems with general nonlinear dynamics and input controls. The method is based on an effective combination of robot motion planning and model checking. Experiments on a hybrid robotic system benchmark with nonlinear dynamics show significant speedup over related work. The experiments also indicate significant speedup when using minimized DFA instead of nonminimized NFA, as obtained by standard tools, for representing the violating prefixes of φ.
Test coverage for continuous and hybrid systems
 CAV 2007. LNCS
, 2007
"... We propose a novel test coverage measure for continuous and hybrid systems, which is defined using the star discrepancy notion. We also propose a test generation method guided by this coverage measure. This method was implemented in a prototype tool that can handle high dimensional systems (up to 1 ..."
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Cited by 18 (2 self)
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We propose a novel test coverage measure for continuous and hybrid systems, which is defined using the star discrepancy notion. We also propose a test generation method guided by this coverage measure. This method was implemented in a prototype tool that can handle high dimensional systems (up to 100 dimensions).
H.: Verification of automotive control applications using staliro
 In: Proceedings of the American Control Conference (2012
"... Abstract — STALIRO is a software toolbox that performs stochastic search for system trajectories that falsify realtime temporal logic specifications. STALIRO is founded on the notion of robustness of temporal logic specifications. In this paper, we present a dynamic programming algorithm for compu ..."
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Cited by 17 (10 self)
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Abstract — STALIRO is a software toolbox that performs stochastic search for system trajectories that falsify realtime temporal logic specifications. STALIRO is founded on the notion of robustness of temporal logic specifications. In this paper, we present a dynamic programming algorithm for computing the robustness of temporal logic specifications with respect to system trajectories. We also demonstrate that typical automotive functional requirements can be captured and falsified using temporal logics and STALIRO. I.
Probabilistic Temporal Logic Falsification of CyberPhysical Systems
"... We present a MonteCarlo optimization technique for finding system behaviors that falsify a Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a fals ..."
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Cited by 14 (12 self)
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We present a MonteCarlo optimization technique for finding system behaviors that falsify a Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a falsifying behavior by exploring trajectories with smaller robustness values. The resulting testing framework can be applied to a wide class of CyberPhysical Systems (CPS). We show through experiments on complex system models that using our framework can help automatically falsify properties with more consistency as compared to other means such as uniform sampling.
Samplingbased falsification and verification of controllers for continuous dynamic systems
 Workshop on Algorithmic Foundations of Robotics VII
, 2006
"... Summary. In this paper, we present a samplingbased verification algorithm for continuous dynamic systems with uncertainty due to unmodeled disturbance inputs, unknown parameters, or initial conditions. The algorithm attempts to find inputs (and resulting trajectories) that falsify the specification ..."
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Cited by 14 (4 self)
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Summary. In this paper, we present a samplingbased verification algorithm for continuous dynamic systems with uncertainty due to unmodeled disturbance inputs, unknown parameters, or initial conditions. The algorithm attempts to find inputs (and resulting trajectories) that falsify the specifications of the system thus providing examples of bad inputs to the system. The system is said to be verified if the algorithm cannot find falsifying inputs. The main contribution of the paper is the analysis of the effects of discretization of the state and input spaces that are inherent to samplingbased techniques. We derive conditions that guarantee resolution completeness. These provide sufficient, although conservative, conditions for verifying Lipschitz continuous (but possibly non smooth) dynamic systems without known analytical solutions. We analyze the effects of transformations of the input and state space on these conditions. The main results of this paper are illustrated with several simple examples. 1