Approximating robot reachable space using convex polytopes
Résumé
This paper presents an approach for approximating the reachable space of robotic manipulators based on convex polytopes. The proposed approach predicts the reachable space over a given time horizon based on the robot's actuation limits and kinematic constraints. The approach is furthermore extended to integrate the robot's environment, if one can be expressed in a form of linear constraints. The accuracy of the proposed method is evaluated using dynamic simulations of the robot with respect to the non-linear robot simulation and is compared to results obtained using the cartesian space limits, usually provided by manufacturers in their standard datasheet. The accuracy analysis results show that the polytope based method has good performance for the time horizons up to t h ≤250ms, encapsulating most of the simulated robot's reachable space while maintaining comparable volume. For a 7 dof robot, the method has an average execution time of 50ms, independent of the horizon time, potentially enabling realtime applications.
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