  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, assuming it can be expressed in a form of
linear constraints, and to account for the robot's link geometry.The accuracy
of the proposed method is evaluated using simulations of robot's nonlinear
dynamics and it is compared against the cartesian space limits, usually
provided by manufacturers in standard datasheets.The accuracy analysis results
show that the proposed method has good performance for the time horizons up to
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
real-time applications.
