Achieving Unit-Consistent Pseudo-Inverse-based Path-Planning for Redundant Incommensurate Robotic Manipulators

TL;DR

This paper emphasizes the importance of unit consistency in pseudo-inverse calculations for path planning in redundant incommensurate robotic manipulators, demonstrating that improper methods cause failures, and proposing a unit-consistent mixed inverse approach.

Contribution

The paper introduces a unit-consistent mixed inverse method for pseudo-inverse calculations, improving path planning robustness in incommensurate robotic manipulators.

Findings

Improper pseudo-inverse methods cause path planning failures.

The proposed mixed inverse improves robustness against noise.

Simulations confirm the effectiveness of the unit-consistent approach.

Abstract

In this paper, we review and compare several velocity-level and acceleration-level Pseudo-Inverse-based Path Planning (PPP) and Pseudo-Inverse-based Repetitive Motion Planning (PRMP) schemes based on the kinematic model of robotic manipulators. We show that without unit consistency in the pseudo-inverse computation, path planning of incommensurate robotic manipulators will fail. Also, we investigated the robustness and noise tolerance of six PPP and PRMP schemes in the literature against various noise types (i.e. zero, constant, time-varying and random noises). We compared the simulated results using two redundant robotic manipulators: a 3DoF (2RP), and a 7DoF (2RP4R). These experimental results demonstrate that the improper Generalized Inverse (GI) with arbitrary selection of unit and/or in the presence of noise can lead to unexpected behavior of the robot, while producing wrong instantaneous outputs in the task space, which results in distortions and/or failures in the execution of the planned path. Finally, we propose and demonstrate the efficacy of the Mixed Inverse (MX) as the proper GI to achieve unit-consistency in path planning.