Quaternion-Based Feedforward Stabilization for Hexapod Robots: Experimental Evidence and Engineering Insights

Hexapod robots are designed to operate on uneven terrain, but changes in body orientation can create uneven load distribution and reduce stability. The reviewed study examines a quaternion-based feedforward stabilization method that calculates posture correction directly from absolute orientation data obtained from an inertial measurement unit (IMU). Unlike approaches that depend on rule-based inference, learning processes, or iterative error correction, the proposed method applies quaternion operations before inverse kinematics. Experimental testing was conducted at platform tilt angles of 0°, 5°, 10°, 15°, 20°, and 25°, with five replications at each condition. The reported results show very small stabilization residuals at low-to-moderate tilt angles, while larger residuals at 20–25° were associated with femur–tibia workspace saturation.

Bibliographic Information

Item	Information
Article Title	Quaternion-based feedforward attitude stabilization for hexapod robots: An experimental study
Authors	Habib Khairy; Yudhi Diputra; Arwizet K; Delima Yanti Sari
Journal	Innovation in Engineering
Volume	3
Issue	2
Publication Year	2026
Pages	133–148
DOI	https://doi.org/10.58712/ie.v3i2.54
ISSN	3047-5473
License	Creative Commons Attribution 4.0 International (CC BY 4.0)
Keywords	feedforward control; hexapod robot; inverse kinematics; quaternion

Introduction

Hexapod robots provide omnidirectional mobility and are suitable for environments where wheeled or tracked robots may encounter difficulties. The manuscript identifies applications including Search and Rescue (SAR), hazardous-area inspection, and extreme environments. However, operation on inclined surfaces introduces stability challenges because changes in body orientation can alter load distribution among the legs and increase servo loading. Maintaining accurate body posture therefore becomes an important control requirement for hexapod systems operating on inclined terrain.

The study focuses on the use of quaternion orientation representation for direct posture compensation. The manuscript discusses several existing control approaches, including Model Predictive Control (MPC), fuzzy logic, reinforcement learning, impedance control, and PID-based methods. According to the authors, these approaches may involve prediction, rule-based inference, learning processes, or error-based correction. The proposed approach instead uses the absolute body orientation obtained from the IMU to generate posture compensation directly before inverse kinematics.

The authors explicitly identify the main novelty as the direct application of quaternion-based orientation compensation as a feedforward mechanism for hexapod posture stabilization without a prediction horizon or learning process. The study also examines system behavior near the leg workspace limits to investigate the relationship between residual tilt, joint configuration, and workspace saturation.

Research Background

The research addresses a control problem in which a hexapod robot must maintain body orientation while its supporting platform is inclined. The manuscript emphasizes that body orientation changes can produce uneven leg loading, servo loading, body oscillation, and potential loss of stability. IMUs provide real-time orientation information that can be used for posture correction. Quaternion representation is used because it avoids gimbal lock and can be applied directly to rotation transformations.

The research gap identified by the authors concerns the use of direct quaternion-based feedforward compensation for hexapod posture stabilization. The authors distinguish this approach from predictive and learning-based methods by calculating posture correction directly from absolute orientation information and passing the correction to the inverse kinematics calculation. The study therefore focuses not only on stabilization performance but also on determining the operational boundary associated with the robot's mechanical workspace.

Research Objectives

To evaluate quaternion-based feedforward stabilization for maintaining hexapod body orientation under different platform tilt conditions.
To determine stabilization performance using residual tilt and settling time.
To examine system behavior across platform tilt angles of 0°, 5°, 10°, 15°, 20°, and 25°.
To investigate whether increasing residual tilt at high platform angles is associated with control performance or mechanical workspace limitations.
To analyze the relationship between pitch and roll stabilization under the tested conditions.

The experimental design used platform tilt angle as the independent variable, residual tilt and settling time as dependent variables, and several fixed control parameters including integral trim, gyro damping, loop frequency, robot geometry, power supply voltage, and IMU baseline calibration.

Why This Research Matters

Addresses hexapod stability on inclined surfaces. The study focuses on maintaining body orientation when the robot operates under controlled platform inclination.
Uses direct orientation-based compensation. The proposed control mechanism generates posture correction from absolute quaternion orientation rather than relying on rule-based inference or an iterative error-convergence process.
Examines the mechanical boundary of stabilization. Testing extends to 25° to identify the point at which joint workspace limitations begin to influence stabilization residuals.
Combines control and kinematic analysis. The study relates orientation stabilization performance to the inverse-kinematic workspace of the femur and tibia joints.

Research Methodology

The study used an experimental approach involving a physical hexapod robot equipped with a BNO08x IMU and touch sensors. The control system consists of user-interface, communication, and motion-control layers. A DualShock 4 controller communicates with an ESP32, which transmits commands to an OpenRB-150 through UART. The OpenRB-150 executes inverse kinematics, reads the IMU and leg-contact sensors, calculates stabilization corrections, and sends joint commands to 18 Dynamixel AX-18A servos.

Experimental Design

The robot was tested at six platform tilt angles: 0°, 5°, 10°, 15°, 20°, and 25°. Each condition was repeated five times. Each experimental session lasted 30 seconds. The robot remained upright during the initial phase, the platform was tilted between 2 and 5 seconds, the target angle was maintained until 15 seconds, and the platform was subsequently returned to the flat position for recovery observation until 30 seconds. Onset residual was calculated over 5–15 seconds, while recovery residual was calculated over 20–30 seconds.

Robot Configuration

The robot employs a symmetric hexagonal configuration with a uniform leg-base radius of 81.33 mm and an inter-leg angle of 60°. Each leg consists of three segments: coxa, femur, and tibia, with lengths of 52 mm, 83 mm, and 153 mm, respectively. The robot therefore has 18 degrees of freedom, with three degrees of freedom per leg.

Quaternion-Based Feedforward Control

The stabilization method uses quaternion orientation information from the BNO08x IMU. The quaternion is used to calculate posture compensation through rotation operations, and the resulting correction is applied to the body control point before inverse kinematics. The method therefore directly converts measured orientation into a posture correction without requiring fuzzy-rule inference, prediction-horizon optimization, or a learning process.

Experimental Measurement

Residual tilt and settling time were used to evaluate stabilization performance. The experimental data were recorded through a CSV debug log at approximately 50 Hz, including relative quaternion components and calculated tilt magnitude. The control loop operated at 125 Hz.

Key Findings

Low Residual Tilt at Low-to-Moderate Angles

The experimental results show that onset residual remained below 0.1° at tilt angles of 0–10° for both pitch and roll. At 15°, the residual increased to approximately 0.29° for both orientations. At 20–25°, substantially larger residuals were observed. For pitch, the mean onset residual reached 2.497° at 20° and 4.402° at 25°, while roll reached 2.093° at 20° and 5.687° at 25°.

Recovery Returned the Robot to Near-Upright Orientation

The recovery experiments produced considerably smaller residuals than the onset phase. The manuscript reports recovery residuals below 0.12° even at the 20° and 25° conditions that produced larger onset residuals. This indicates that, after the platform was returned to the flat position, the robot was able to return close to its upright configuration under all tested conditions.

Workspace Saturation Became the Dominant Limitation

The manuscript attributes the increase in residual tilt above 15° primarily to femur and tibia joint workspace saturation. Joint-angle observations showed that the increase in residual occurred while these joints approached their motion limits. The authors therefore distinguish between the accuracy of the orientation calculation and the physical ability of the robot to generate sufficient corrective motion.

Pitch and Roll Performance Was Similar Within the Lower Tilt Range

The statistical analysis found no significant difference between pitch and roll up to 20° (p > 0.05), whereas a significant difference was observed at 25° (p = 0.021). The authors relate this behavior to the symmetric hexagonal geometry and the increasing influence of joint workspace limitations at the higher tilt condition.

Feedforward Operation Was Effective Without Iterative Error Correction

The manuscript reports onset residuals of approximately 0.048–0.065° at 0–10°, which are below the stated ±1° target. The authors interpret these results as evidence that direct correction based on absolute IMU orientation can maintain posture under low-to-moderate tilt conditions without waiting for error accumulation.

Scientific Contribution

Quaternion-based feedforward stabilization. The study explicitly identifies the direct application of quaternion-based orientation compensation as its main novelty for hexapod posture stabilization.
Direct integration with inverse kinematics. Orientation information is converted into posture compensation and passed to the inverse kinematics calculation.
Experimental identification of operational boundaries. The study does not restrict evaluation to nominal stabilization conditions but investigates behavior near the robot's leg workspace limits.
Separation of algorithmic and mechanical limitations. The results distinguish increasing residual tilt caused by joint workspace saturation from a failure of the quaternion orientation calculation.

The contribution is therefore centered on the implementation and experimental evaluation of direct quaternion-based feedforward posture compensation and its relationship with the physical kinematic limits of the hexapod platform. :

Industrial Implications

The manuscript does not explicitly present a dedicated industrial-implementation analysis or commercialization assessment. Its stated engineering context includes hexapod applications in Search and Rescue, hazardous-area inspection, and extreme environments. Within the scope demonstrated experimentally, the results provide information about stabilization behavior and the relationship between control performance and mechanical workspace limits.

The authors also characterize the proposed approach as computationally lightweight for resource-constrained microcontrollers because the method relies on quaternion normalization, multiplication, SLERP, and coordinate transformations rather than the fuzzification, inference, and defuzzification stages of fuzzy logic. However, the manuscript explicitly states that the computational advantage has not yet been verified through head-to-head empirical testing under identical platform and test conditions.

Research Limitations

The experiments were performed under static standing conditions using a single geometric configuration.
Dynamic walking, gait transitions, and alternative mechanical configurations were not evaluated.
External disturbances such as lateral impacts, randomly uneven surfaces, coefficient-of-friction variations, and changes in load distribution were not considered.
The comparison with fuzzy logic and other approaches was based on literature findings and mechanistic comparison rather than head-to-head experimental testing on the same platform.
The authors note that the claim concerning computational advantages requires further empirical verification.

These limitations are explicitly acknowledged by the authors and define the conditions under which the reported stabilization results should be interpreted.

Future Research Opportunities

Dynamic walking stabilization. Future work should evaluate stabilization during walking by using leg-contact sensors and integrating human–robot command inputs.
Alternative standing configurations. A lower standing posture or alternative leg geometry should be investigated to address the workspace limitations observed at higher tilt angles.
Additional environmental sensing. Future research should consider force sensors or vision-based terrain estimation.
Communication latency. The authors recommend evaluating communication latency during walking as part of future system development.

These directions are explicitly proposed in the manuscript following the experimental observation that high-tilt performance is constrained by the available joint workspace and that the present study does not evaluate dynamic locomotion or external disturbances.

Policy Relevance

The manuscript does not explicitly discuss policy implications, regulatory implications, engineering standards, or public-policy applications. Its focus remains on experimental stabilization performance, robot kinematics, control implementation, and the operational limitations of the tested hexapod configuration.

Suggested Citation

Khairy, H., Diputra, Y., Arwizet K., & Sari, D. Y. (2026). Quaternion-based feedforward attitude stabilization for hexapod robots: An experimental study. Innovation in Engineering, 3(2), 133–148. https://doi.org/10.58712/ie.v3i2.54

Editorial Note

This article is an independent editorial review of the research published by Habib Khairy, Yudhi Diputra, Arwizet K, and Delima Yanti Sari in Innovation in Engineering. The review summarizes and explains the reported methodology, experimental results, scientific contribution, limitations, and future research directions based on the published article. It does not constitute the original research and should not be treated as a replacement for the source publication.

Readers who use the reported experimental results or scientific conclusions in academic or technical work should consult and cite the original research article. The original publication remains the authoritative source for the reported experimental data and scientific findings.

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