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Robotics and Autonomous Systems

Quantum neural network-based inverse kinematics of a six-jointed industrial robotic arm

Mehdi Fazilat, Nadjet Zioui

Published Jul 6, 2025• 16 citations
Publisher

Abstract

This research examines the potential of quantum-inspired neural networks (QNNs) for solving the inverse kinematics of robotic arms, focusing on the six-degree-of-freedom ABB IRB140 robot. Traditional inverse kinematics approaches face challenges such as non-unique solutions and computational complexity, especially with increasing degrees of freedom. While artificial neural networks (ANNs) have shown promise, they require further improvements, particularly in terms of quantum computing integration. This study introduces a quantum-inspired activation function to multi-layer perceptron neural networks. We compared ANNs and QNNs with and without singularity avoidance, finding that QNNs significantly outperformed ANNs in mean absolute error (MAE), achieving a 15.60% lower MAE in singularity-free models and a 16.67% lower MAE in singularity-avoidance models. The QNNs demonstrated superior precision, with a position error of 1.64 mm and an orientation error of 0.00179 radians when avoiding singularities. These results highlight the potential of QNNs to enhance the precision, efficiency, and performance of robotic arm manipulation. Quantum computing offers advantages including parallelism, quantum entanglement, and quantum annealing, which contribute to the QNNs’ superior performance. Overall, this study represents a practical contribution to robotics and quantum computing, paving the way for future research into applying quantum principles to neural network models for robotics.

DOI
10.1016/j.robot.2025.105123

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This research examines the potential of quantum-inspired neural networks (QNNs) for solving the inverse kinematics of robotic arms, focusing on the six-degree-of-freedom ABB IRB140 robot. Traditional inverse kinematics approaches face challenges such as non-unique solutions and computational complexity, especially with increasing degrees of freedom. While artificial neural networks (ANNs) have shown promise, they require further improvements, particularly in terms of quantum computing integration. This study introduces a quantum-inspired activation function to multi-layer perceptron neural networks. We compared ANNs and QNNs with and without singularity avoidance, finding that QNNs significantly outperformed ANNs in mean absolute error (MAE), achieving a 15.60% lower MAE in singularity-free models and a 16.67% lower MAE in singularity-avoidance models. The QNNs demonstrated superior precision, with a position error of 1.64 mm and an orientation error of 0.00179 radians when avoiding singularities. These results highlight the potential of QNNs to enhance the precision, efficiency, and performance of robotic arm manipulation. Quantum computing offers advantages including parallelism, quantum entanglement, and quantum annealing, which contribute to the QNNs’ superior performance. Overall, this study represents a practical contribution to robotics and quantum computing, paving the way for future research into applying quantum principles to neural network models for robotics.
This research explores the application of quantum-inspired neural networks (QNNs) to address the inverse kinematics problem in robotic arms, explicitly focusing on the ABB IRB140, an articulated robot arm with six degrees of freedom. The primary objective is to develop a quantum-inspired activation function for multilayer perceptron (MLP) neural networks. The study evaluates their performance in avoiding singularities by comparing artificial neural networks (ANNs) with quantum neural networks (QNNs). The findings demonstrate that QNNs outperform ANNs in terms of mean absolute error (MAE), achieving a 15.60% lower MAE in the model without singularities and a 16.67% reduction in the Jacobian-based MAE in the model designed to avoid singularities. The study demonstrates that QNNs offer superior accuracy in predicting the robot arm's inverse kinematics, achieving a position error of 1.64 mm and an orientation error of 0.00179 radians while effectively avoiding singularities. These outcomes underscore the potential of quantum-inspired neural networks to enhance robotic arm manipulations' precision, efficiency, and performance.
A novel quantum-based kinematic model for computing the position and the orientation of the six-jointed IRB 140 ABB robotic arm is presented. Position is determined through successive elementary translations and rotations from the end effector down to the base frame, whereas orientation is derived from quaternion representation. The model is based on the equivalence between quaternions and Pauli matrices or gates. Based on comparison to experimental results, the quantum kinematic model is valid. Its main advantage is that it uses only one qubit to model both position and orientation, which represents a major saving in terms of computing resources and time. This model could guide development of other quantum models and simulation software to be used in future quantum computers and could also inform classical computing theory for robotic arm kinematics modeling.
Accurate prediction of a robot’s dynamic parameters, including mass and moment of inertia, is essential for adequate motion planning and control in autonomous systems. Traditional methods often depend on manual computation or physics-based modelling, which can be time-consuming and approximate for intricate, real-world environments. Recent advances in machine learning, primarily through artificial neural networks (ANNs), offer profitable alternatives. However, the potential of quantum-inspired models in this context remains largely uncharted. The current research assesses the predictive performance of a classical artificial neural network (CANN) and a quantum-inspired artificial neural network (QANN) in estimating a car-like mobile robot’s mass and moment of inertia. The predictive accurateness of the models was considered by minimizing a cost function, which was characterized as the RMSE between the predicted and actual values. The outcomes indicate that while both models demonstrated commendable performance, QANN consistently surpassed CANN. On average, QANN achieved a 9.7% reduction in training RMSE, decreasing from 0.0031 to 0.0028, and an 84.4% reduction in validation RMSE, dropping from 0.125 to 0.0195 compared to CANN. These enhancements highlight QANN’s singular predictive accuracy and greater capacity for generalization to unseen data. In contrast, CANN displayed overfitting tendencies, especially during the training phase. These findings emphasize the significance of quantum-inspired neural networks in enhancing prediction precision for involved regression tasks. The QANN framework has the potential for wider applications in robotics, including autonomous vehicles, uncrewed aerial vehicles, and intelligent automation systems, where accurate dynamic modelling is necessary.
The increasing convergence of quantum computing (QC) and advanced robotic control is giving rise to a new class of intelligent automation systems. Utilizing quantum-inspired computational principles, contemporary robotic platforms demonstrate greater optimization efficiency, superior perceptual processing, and improved decision-making performance. This survey outlines the principal quantum-oriented control methodologies utilized in robotics, with particular emphasis on approaches that incorporate Quantum Neural Networks (QNN), Quantum Machine Learning (QML), and Quantum-behaved Particle Swarm Optimization (QPSO). The investigation systematically reviews recent advances in quantum-assisted adaptive control, trajectory planning, and optimization frameworks, spotlighting their contributions to improved robustness, precision, and energy efficiency. By analyzing research in quantum reinforcement learning, distributed Noisy Intermediate-Scale Quantum (NISQ) computing, and hybrid quantum-classical approaches, this review clarifies how quantum principles are transforming both theoretical and practical aspects of robotic control. Likewise, several real-world implementations ranging from industrial manipulators to autonomous and cognitive robotic systems demonstrate the growing feasibility of quantum-enhanced decision-making. The review concludes that while remarkable progress has been made in quantum-inspired control for robotics, most existing studies remain constrained to simulations with restricted experimental validation on physical platforms. Addressing this gap will be essential in future research to transition from theoretical and simulated models toward hardware-level implementations, enabling the realization of scalable, fault-tolerant quantum control architectures.
This study evaluates quantum-inspired control strategies on classical hardware, specifically Quantum Sliding Mode Control (QSMC), Quantum Genetic Algorithm (QGA), and a Grover-based quantum search controller, to improve control of a six-degree-of-freedom robotic arm with nonlinear dynamics. Building upon quantum-analogous probabilistic principles, these methods offer significant potential across industries. To clarify the basis of these approaches, the analysis centers on quantum-computation concepts, such as probabilistic amplitude encoding and superposition, which can enhance robustness, trajectory smoothness, and energy efficiency in classical control systems. Consistent, noise-free simulation conditions and multiple independent trials ensured fairness and reproducibility throughout the study. Performance assessment relied on Integrated Absolute Error (IAE), which measures total error over time, and Average Control Energy (Eavg\mathrm{E}_{\text{av}} \mathrm{g}Eav​g) for mean energy consumption. Compared with classical Sliding Mode Control (SMC), QSMC achieved an 11 % faster transient response. Additionally, QGA delivered 21 % lower IAE and 12.3 % lower average control energy, while the Grover-based controller provided balanced performance among convergence speed, tracking accuracy, and energy efficiency. Overall, these results suggest that quantum-inspired approaches can significantly advance trajectory precision, robustness, and energy efficiency, supporting the development of nextgeneration intelligent robotics.
The paper proposes a new method of quantum computing using control and systems theory as well as matrix-quantum computing. The algorithm developed on the basis of the PR-02 robot’s arm’s movement was implemented in using the Neural Network Toolbox. The application of the neural model instead of the analytic model allowed for obtaining the improvement of the trajectory of the PR-02 robot’s arm movement, while the application of the quantum artificial neural network for the assumed number of quasi-parallel computations equal 1000 did not result in the improvement of the model.