In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for achieving both efficiency and global convergence. In local search, it exploits derivatives for efficient computation. Unlike other methods for falsification of hybrid systems with deterministic evolution, we do not restrict our search to trajectories of a certain bounded length but search for error trajectories of arbitrary length.
The usage of abstractions for guiding local search for error trajectories has been proposed earlier @cite_21 , in combination with the usage of derivative-free algorithms for local search.
@cite_21
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Guided policy search algorithms can be used to optimize complex nonlinear policies, such as deep neural networks, without directly computing policy gradients in the high-dimensional parameter space. Instead, these methods use supervised learning to train the policy to mimic a “teacher” algorithm, such as a trajectory optimizer or a trajectory-centric reinforcement learning method. Guided policy search methods provide asymptotic local convergence guarantees by construction, but it is not clear how much the policy improves within a small, finite number of iterations. We show that guided policy search algorithms can be interpreted as an approximate variant of mirror descent, where the projection onto the constraint manifold is not exact. We derive a new guided policy search algorithm that is simpler and provides appealing improvement and convergence guarantees in simplified convex and linear settings, and show that in the more general nonlinear setting, the error in the projection step can be bounded. We provide empirical results on several simulated robotic manipulation tasks that show that our method is stable and achieves similar or better performance when compared to prior guided policy search methods, with a simpler formulation and fewer hyperparameters. We present a study which investigated how and why users of Mozilla Firefox use multiple tabs and windows during web browsing. The detailed web browsing usage of 21 participants was logged over a period of 13 to 21 days each, and was supplemented by qualitative data from diary entries and interviews. Through an examination of several measures of their tab usage, we show that our participants had a strong preference for the use of tabs rather than multiple windows. We report the reasons they cited for using tabs, and the advantages over multiple windows. We identify several common tab usage patterns which browsers could explicitly support. Finally, we look at how tab usage affects web page revisitation. Most of our participants switched tabs more often than they used the back button, making tab switching the second most important navigation mechanism in the browser, after link clicking. Direct policy search can effectively scale to high-dimensional systems, but complex policies with hundreds of parameters often present a challenge for such methods, requiring numerous samples and often falling into poor local optima. We present a guided policy search algorithm that uses trajectory optimization to direct policy learning and avoid poor local optima. We show how differential dynamic programming can be used to generate suitable guiding samples, and describe a regularized importance sampled policy optimization that incorporates these samples into the policy search. We evaluate the method by learning neural network controllers for planar swimming, hopping, and walking, as well as simulated 3D humanoid running. In this paper, a new method is presented for motion planning in dynamic environments, that is, finding a trajectory for a robot in a scene consisting of both static and dynamic, moving obstacles. We propose a practical algorithm based on a roadmap that is created for the static part of the scene. On this roadmap, an approximately time-optimal trajectory from a start to a goal configuration is computed, such that the robot does not collide with any moving obstacle. The trajectory is found by performing a two-level search for a shortest path. On the local level, trajectories on single edges of the roadmap are found using a depth-first search on an implicit grid in state-time space. On the global level, these local trajectories are coordinated using an A sup * -search to find a global trajectory to the goal configuration. The approach is applicable to any robot type in configuration spaces with any dimension, and the motions of the dynamic obstacles are unconstrained, as long as they are known beforehand. The approach has been implemented for both free-flying and articulated robots in three-dimensional workspaces, and it has been applied to multirobot motion planning, as well. Experiments show that the method achieves interactive performance in complex environments.