# LSTM-Based Absolute Position Estimation of a 2-DOF Planar Delta Robot Using Time-Series Data

## TL;DR

This paper uses LSTM networks to estimate the position of a robot based on time-series force data, achieving high accuracy in predicting its movements.

## Contribution

A novel LSTM-based method for absolute position estimation of a delta robot using time-series force signals is proposed.

## Key findings

- The LSTM model achieved RMSE values of 3.81 mm (X) and 2.94 mm (Y) in position prediction.
- Approximately 83.73% of test sequences had an error below 5 mm.
- The model effectively learned posture-dependent dynamics and force-manipulability relationships.

## Abstract

Accurately estimating the absolute position of robots under external loads is challenging due to nonlinear dynamics, posture-dependent manipulability, and structural sensitivities. This study investigates a data-driven approach for absolute position prediction of a 2-DOF planar delta robot by learning time-series force signals generated during manipulability-driven free motion. Constant torques of opposite directions were applied to the robot without any position or trajectory control, allowing the mechanism to move naturally according to its configuration-dependent manipulability. Reaction forces measured at the end-effector and relative encoder variations were collected across a grid of workspace locations and used to construct a 12-channel time-series input. A hybrid deep learning architecture combining 1D convolutional layers and a bidirectional LSTM network was trained to regress the robot’s absolute X–Y position. Experimental results demonstrate that the predicted trajectories closely match the measured paths in the workspace, yielding overall RMSE values of 3.81 mm(X) and 2.94 mm(Y). Statistical evaluation using RMSE shows that approximately 83.73% of all test sequences achieve an error below 5 mm. The findings confirm that LSTM models can effectively learn posture-dependent dynamic behavior and force-manipulability relationships.