# Trajectory Learning Using HMM: Towards Surgical Robotics Implementation

## TL;DR

This paper introduces a new method for surgical robotics that improves trajectory learning by combining motion and force data using HMMs.

## Contribution

The novel extension of the Douglas–Peucker algorithm incorporates both kinematic and dynamic data for better trajectory representation.

## Key findings

- Including force interaction data improves trajectory reconstruction accuracy with an RMSE of 0.29 mm.
- Motion-only models achieved an RMSE of 0.44 mm, showing the benefit of dynamic data.
- The method provides a clearer and more generalizable representation of surgical trajectories.

## Abstract

Autonomy represents one of the most promising directions in the future development of surgical robotics, and Learning from Demonstration (LfD) is a key methodology for advancing technologies in this field. The proposed approach extends the classical Douglas–Peucker algorithm by incorporating multidimensional trajectory data, including both kinematic and dynamic information. This enhancement enables a more comprehensive representation of demonstrated trajectories, improving generalization in high-dimensional spaces. This representation allows clearer codification and interpretation of the information used in the learning process. A series of experiments were designed to validate this methodology. Motion data and force interaction data were collected, preprocessed, and used to train a hidden Markov model (HMM). Different experimental conditions were analyzed, comparing training using only motion data versus incorporating force interaction data. The results demonstrate that including interaction forces improves trajectory reconstruction accuracy, achieving a lower root mean squared error (RMSE) of 0.29 mm, compared to 0.44 mm for the model trained solely on motion data. These findings support the proposed method as an effective strategy for encoding, simplifying, and learning robotic trajectories in surgical applications.