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This paper presents an approach for approximating the reachable space ofrobotic manipulators based on convex polytopes. The proposed approach predictsthe reachable space over a given time horizon based on the robot's actuationlimits and kinematic constraints. The approach is furthermore extended tointegrate the robot's environment, assuming it can be expressed in a form oflinear constraints, and to account for the robot's link geometry.The accuracyof the proposed method is evaluated using simulations of robot's nonlineardynamics and it is compared against the cartesian space limits, usuallyprovided by manufacturers in standard datasheets.The accuracy analysis resultsshow that the proposed method has good performance for the time horizons up to250ms, encapsulating most of the simulated robot's reachable space whilemaintaining comparable volume. For a 7 dof robot, the method has an averageexecution time of 50ms, independent of the horizon time, potentially enablingreal-time applications.

Approximating robot reachable space using convex polytopes