# An Adaptive External Torque Estimation Algorithm for Collision Detection in Robotic Arms

## TL;DR

This paper introduces a new algorithm to detect collisions in robotic arms by estimating external forces more accurately.

## Contribution

The novel contribution is a variational Bayesian Kalman filter that dynamically estimates process noise covariance to improve collision detection.

## Key findings

- The proposed algorithm dynamically estimates process noise covariance to avoid recursive error accumulation.
- The method integrates the robot's dynamic model without increasing system complexity.
- The approach improves external torque estimation for safer human–robot collaboration.

## Abstract

As robotic applications rapidly expand into increasingly complex and dynamic environments, greater emphasis is being placed on the intelligence and safety of human–robot collaboration at the task execution level. In shared human–robot workspaces, even the most precise motion planning cannot fully prevent collisions. To address this critical safety concern, we propose a variational Bayesian Kalman filtering-based external torque estimation algorithm that integrates the robot’s dynamic model while avoiding additional system complexity. We begin by reviewing the robot dynamics framework and the classical external torque estimation method based on generalized momentum. We then derive a Kalman filter-based approach for external torque estimation in robotic manipulators and analyze the adverse effects arising from mismatches in process noise covariance. Finally, we introduce a sliding window-based variational Bayesian Kalman filter, which dynamically estimates the current process noise covariance while simultaneously mitigating the accumulation of recursive errors.