Approximating robot reachable space using convex polytopes

TL;DR

This paper introduces a convex polytope-based method to approximate a robot's reachable space, accounting for actuation, kinematic constraints, and environment, with promising accuracy and real-time performance for control applications.

Contribution

It extends existing methods by integrating environmental constraints and link geometry into convex polytope approximations for robot reachability.

Findings

Accurately approximates reachable space up to 250ms horizon

Maintains good volume approximation with low computational cost

Enables real-time reachability analysis for 7 DOF robots

Abstract

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.