# Detection of robustly collision-free trajectories in unpredictable environments in real-time

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## Abstract

One of the ultimate goals in robotics is to make robots of high degrees of freedom (DOF) work autonomously in real world environments. However, real world environments are unpredictable, i.e., how the objects move are usually not known beforehand. Thus, whether a robot trajectory is collision-free or not has to be checked on-line based on sensing as the robot moves. Moreover, in order to guarantee safe motion, the motion uncertainty of the robot has to be taken into account. This paper introduces a general approach to detect if a high-DOF robot trajectory is continuously collision-free even in the presence of robot motion uncertainty in an unpredictable environment in real time. Our method is based on the novel concept of *dynamic envelope*, which takes advantage of progressive sensing over time without predicting motions of objects in an environment or assuming specific object motion patterns. The introduced approach can be used by general real-time motion planners to check if a candidate robot trajectory is continuously and robustly collision-free (i.e., in spite of uncertainty in the robot motion).

## Keywords

Continuously collision-free trajectory High DOF robot Unpredictable environment Motion uncertainty## Notes

### Acknowledgments

This work was supported under the U.S. National Science Foundation grant IIS-0742610.

## Supplementary material

Supplementary material 1 (WMV 693 KB)

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