Modeling the Reachability Space of Robotic Manipulators through Ellipsoid Equations

Accurate modeling of the reachability space of robotic manipulators is crucial for tasks such as robot positioning, trajectory planning, and human-robot collaboration. Traditional methods based on reachability and capability maps often rely on the workspace discretization, which can be computationally expensive and less adaptable to real-time applications. To address these limitations, this paper introduces a new approach to estimate and model the reachability space of manipulators using a single ellipsoid equation. By generating a point cloud from the robot kinematic model, the proposed method avoids the complexity of forward and inverse kinematics calculations to generate the set of reachable points. The ellipsoid parameters are computed by exploiting two techniques: an optimization-based process and a machine learning approach that leverages the PointNet model. Different optimization algorithms and variants of the PointNet model are tested and compared in terms of computational efficiency and accuracy. Experimental results demonstrate the effectiveness of the proposed method in capturing and modeling an accurate representation of the reaching capabilities of a robotic manipulator.