An efficient derivative-free method for solving nonlinear equations
ACM Transactions on Mathematical Software (TOMS)
Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
ACM Transactions on Mathematical Software (TOMS)
Introduction to Robotics: Mechanics and Control
Introduction to Robotics: Mechanics and Control
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
IEEE Transactions on Robotics
IEEE Transactions on Robotics
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This paper addresses continuous collision-checking of a high-DOF robot trajectory in a completely unknown and unpredictable environment (i.e., obstacles are unknown and their motions are also unknown). In [1], the authors introduced how to discover, if a robot at configuration q at a future time t is guaranteed collision-free or not using the novel concept of the dynamic envelope and atomic obstacles based on sensing in such an unknown and unpredictable environment. In this paper, we further show that if a point (q, t) in the robot's configuration-time space (CT-space) is discovered collision-free, a neighborhood (CT-region) of (q, t) is also guaranteed collision-free. Based on that, given a continuous robot trajectory, we present a method to compute a set of discrete CT-points such that, if these points are discovered to be guaranteed collision-free, their associated collision-free neighborhood CT-regions contains the continuous trajectory, i.e., the trajectory is guaranteed continuously collision-free.