Session: 07-10-03: Medical Robotics, Rehabilitation, and Surgery III

Paper Number: 166471

Neural Network-Based Forward Kinematics for a 6-DOF 3-RRPS Parallel Robot: A Comparative Study of MLP and RBF Models 

Introduction:

The forward kinematics (FK) problem for the 6-DOF UPS surgical robot with a 3-arm mechanism, Robossis, is formulated using geometric constraints, leading to nonlinear algebraic equations. Each equation defines the relationship between the joint lengths, joint angles, and the end-effector’s position and orientation. This robot has 16 possible FK solutions, with four real solutions and twelve imaginary solutions. In real-world applications, due to workspace and mechanical constraints, the end-effector can only assume one of these four real solutions [1, 2].

Solving FK equations analytically allows for obtaining all possible solutions of the mechanism, but the derivation process is complex [3, 4]. Numerical methods offer high computational efficiency but require extensive calculations and are sensitive to initial values, potentially leading to divergence or incorrect solutions [2, 4, 5]. To address these challenges, various alternative algorithms have been proposed [3, 7]; however, these algorithms suffer from poor convergence if the initialization is inaccurate.

To overcome these limitations, machine learning (ML) approaches have been proposed to solve FK by learning the FK mapping from joint variables to the end-effector pose. This method enables direct FK prediction, faster computation, improved efficiency, enhanced suitability for real-time control, and the elimination of the need for initial guesses [7, 8, 9, 10].

For robots with multiple FK solutions, neural networks (NNs) can directly learn the FK mapping and efficiently predict the most likely solution based on the inputs. A feedforward neural network (FNN) was used in [8], while MLP, RBF, and ANFIS neural networks with various optimization techniques were employed in [8] to improve neural network training for the 6-UPS Stewart Platform. In [10], an MLP-based approach was used to solve the FK problem for Cable-Driven Parallel Robots (CDPRs). Additionally, in [12], different training optimizers (Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG)) were applied to improve MLP performance for a 4-DOF SCARA robot.

In this paper, we focus on solving the FK problem for the Robossis robot using two different neural network models. Our approach aims to find the only desired FK solution directly, improve efficiency, and facilitate real-time control.

Methodology:

Inverse kinematics

The inverse kinematics (IK) problem for the 6-DOF UPS parallel robot was solved to obtain the end-effector position and orientation. Actuator lengths were calculated using the Euclidean norm, while joint angles were derived from trigonometric equations. These equations allowed the precise computation of joint parameters necessary to achieve the desired pose.

Random Sampling

A dataset was generated using the rand function, where random values were used to calculate the joint lengths and angles based on IK equations. Each data point in the dataset contained three positional values (Px, Py, Pz) and three Euler angles (α, β, γ) following the x-y-z convention. The IK dataset was then inverted to train artificial neural network (ANN) models for predicting FK solutions.

Using MLP and RBF for FK Solutions

ANNs are widely used for nonlinear statistical modeling due to their ability to capture complex relationships between inputs and outputs. The most commonly used NNs for FK are the Multilayer Perceptron (MLP) and Radial Basis Function (RBF) networks. To improve model performance, different activation functions and optimizers were explored. The MLP model contained more than two hidden layers, while the RBF network employed a single hidden layer with radial basis neurons. For both NN models, the input layer received six inputs (joint angles and actuator values), while the output layer predicted six outputs representing the end-effector’s position and orientation.

Results and Conclusions:

Obtaining the dataset through IK ensured that only one valid FK solution was considered. The MLP model demonstrated a lower Mean Squared Error (MSE), while the RBF model achieved a lower Mean Absolute Error (MAE). Furthermore, by optimizing activation functions, adjusting the number of layers, and tuning neuron configurations, both the accuracy and computational speed of the models were improved.
 

References:

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2. M. H. Abedinnasab, et al. Robotica, vol. 35, no. 12, pp. 2257–2277, 2017

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7. A. Mahmoodi, et al, Adv. Robot., vol. 28, no. 1, pp. 27–37, Jan. 2014

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11. C. Liu, et al, Saf. Sci., vol. 117, pp. 243–249, 2019

12. R. Bouzid, et al, Eng. Res. Express, vol. 6, no. 4, p. 045209, 2024

 

Presenting Author: Hosna Rezapour-Shafigh Rowan University

Presenting Author Biography: Hosna Rezapour-Shafigh is a Graduate Research Assistant in the Department of Biomedical Engineering at Rowan University. Her research focuses on surgical robot kinematics and machine learning-based modeling of parallel mechanisms, particularly Robossis, for long bone fracture alignment.

Authors:

Hosna Rezapour-Shafigh Rowan University
Marzieh S. Saeedi-Hosseiny Rowan University
Mohammad H. Abedin-Nasab Rowan University