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Robotic kinematic models are associated with various mathematical functions to establish the relationship between joint angles and their respective positions. Generally, the joints are series-connected, which are controlled by the motors as actuators. Commonly, the series-connected links are attached with a gripper at the end. This defines the position of the robotic arm in the three-dimensional coordinate systems. The problem of estimation for robotic models can be widely categorized as 1) forward kinematics and 2) inverse kinematics. The equations derive relationships between the position of the gripper and joints, called forward kinematics (Saha, 2014). Similarly, estimating the joint angles from the end position information is termed inverse kinematics. Various Machine Learning (ML) approaches have been proposed in the past decade, addressing the generalization of robotic manipulators to predict the position of robots. The forward kinematics for a 6-3 Stewart Platform Mechanism (SPM) has been well established using the Neural Network (NN) (Yurt et al., 2007). Also, similar NN architecture helped to solve the forward kinematics problem for HEXA Parallel Robot (Dehghani et al., 2008). Further improvement is observed with integration of PSO to NN for a 6-DOF parallel robot (Li et al., 2007) to fine-tune the backpropagation learning. Also, an iterative approach to NN strategy proved to be efficient for the parallel manipulators (Parikh & Lam, 2009). Multi-Layer Perception (MLP) based backpropagation approach has been implemented for 3D cable robot (Ghasemi et al., 2010), 7-DOF Sawyer Robotic Arm (Theofanidis et al., 2018), and Delta parallel robot (Liu et al., 2019) model. Another hybrid approach combining neural networks with interval arithmetic to solve the forward kinematics (Schmidt et al., 2014) is experimented for Cable-Driven Parallel Robots.
Recently, the deep learning models for image processing have been vastly exploited and validated its significance on large-scale databases. Such a Hybrid Deep Learning approach is implemented for 6-DOF Serial Manipulator (Mohamed et al., 2020). The improved Newton iterative method is validated on a 3-DOF parallel manipulator (Wu & Xie, 2019) for the forward kinematics estimation problem. Other than machine learning, the optimization approaches are also found helpful to estimate the position information for 2-DOF using genetic programming (Arellano & Rivera, 2019). Also, the Artificial Neural Networks (ANN) for a 6-DOF robot is experimented with forward kinematics for different pose and joint space representations (Grassmann & Burgner-Kahrs, 2019). Inverse kinematics solution of a 3R robotic manipulator is also analyzed for optimal ANN parameters like input data, sample size, training algorithm (Karkalos et al., 2017) etc. The Path planning of industrial robot based on Fuzzy control is also investigated (Sahu & Choudhury, 2018).
From the above framework, it seems that the NN architectures are vastly exploited for non-linear estimation of the position while incorporation of optimal training sample selection is limited in the literature. All machine learning algorithms need a set of training dataset to train the model, which is determined prior. However, such an initial selection of data plays a crucial role in the prediction accuracy. Active selection of data samples is necessary, which may reduce the memory and time requirement of the learning process. Such an approach is based on a sparse dictionary (Patro et al., 2019), which eliminates the redundancy of selected training samples. Also, refining the training data for ANN (Kavzoglu, 2009), (Chen et al., 2013) proved to be efficient in terms of classification accuracy. Recently data sampling has been applied for deep learning architectures for image processing (Van et al., 2016). However, such analysis is limited in the forward kinematics prediction problems. Hence, presently, a clustering-based active training sample selection is proposed, which is fed to the NN model for learning and for further prediction of the gripper position.