Forward and Inverse Kinematics Solution of A 3-DOF Articulated Robotic Manipulator Using Artificial Neural Network

In this research paper, the multilayer feedforward neural network (MLFFNN) is architected and described for solving the forward and inverse kinematics of the 3-DOF articulated robot. When designing the MLFFNN network for forward kinematics, the joints' variables are used as inputs to the network, and the positions and orientations of the robot end-effector are used as outputs. In the case of inverse kinematics, the MLFFNN network is designed using only the positions of the robot end-effector as the inputs, whereas the joints’ variables are the outputs. For both cases, the training of the proposed multilayer network is accomplished by Levenberg Marquardt (LM) method. A sinusoidal type of motion using variable frequencies is commanded to the three joints of the articulated manipulator, and then the data is collected for the training, testing, and validation processes. The experimental simulation results demonstrate that the proposed artificial neural network that is inspired by biological processes is trained very effectively, as indicated by the calculated mean squared error (MSE), which is approximately equal to zero. The resulted in smallest MSE in the case of the forward kinematics is 4.592×10^(-8) in the case of the inverse kinematics, is 9.071×10^(-7). This proves that the proposed MLFFNN artificial network is highly reliable and robust in minimizing error. The proposed method is applied to a 3-DOF manipulator and could be used in more complex types of robots like 6-DOF or 7-DOF robots

Sliding Mode Control of Cable-Driven Redundancy Parallel Robot with 6 DOF Based on Cable-Length Sensor Feedback

The sliding mode control of the cable-driven redundancy parallel robot with six degrees of freedom is studied based on the cable-length sensor feedback. Under the control scheme of task space coordinates, the cable length obtained by the cable-length sensor is used to solve the forward kinematics of the cable-driven redundancy parallel robot in real-time, which is treated as the feedback for the control system. First, the method of forward kinematics of the cable-driven redundancy parallel robot is proposed based on the tetrahedron method and Levenberg-Marquardt method. Then, an iterative initial value estimation method for the Levenberg-Marquardt method is proposed. Second, the sliding mode control method based on the exponential approach law is used to control the effector of the robot, and the influence of the sliding mode parameters on control performance is simulated. Finally, a six-degree-of-freedom position tracking experiment is carried out on the principle prototype of the cable-driven redundancy parallel robot. The experimental results show that the robot can accurately track the desired position in six directions, which indicates that the control method based on the cable-length sensor feedback for the cable-driven redundancy parallel robot is effective and feasible

Admittance Controller Complemented with Real-time Singularity Avoidance for Rehabilitation Parallel Robots

Rehabilitation tasks demand robust and accurate trajectory-tracking performance, mainly achieved with parallel robots. In this field, limiting the value of the force exerted on the patient is crucial, especially when an injured limb is involved. In human-robot interaction studies, the admittance controller modifies the location of the robot according to the user efforts driving the end-effector to an arbitrary location within the workspace. However, a parallel robot has singularities within the workspace, making implementing a conventional admittance controller unsafe. Thus, this study proposes an admittance controller that overcomes the limitations of singular configurations by using a real-time singularity avoidance algorithm. The singularity avoidance algorithm modifies the original trajectory based on the actual location of the parallel robot. The complemented admittance controller is applied to a 4 degrees of freedom parallel robot for knee rehabilitation. In this case, the actual location is measured by a 3D tracking system because the location calculated by the forward kinematics is inaccurate in the vicinity of a singularity. The experimental results verify the effectiveness of the proposed admittance controller for safe knee rehabilitation exercise

Type Synthesis and Performance Optimization of Parallel Manipulators

Parallel robots have been widely employed in industrial applications. There are still some challenging topics in the fundamental research, e.g., the primary problem mobility analysis has not been solved for about 150 years. A universal mobility equation for all kinds of parallel architectures has not been found. Another issue lies on the performance measurements for parallel manipulators. There are plenty of kinematic and dynamic performance indices. However, the various ranges and scales of these indicators make the optimal design considering multiple indices complicated. It is essential to search for a unified approach to normalize performance indicators. More dynamic performance measurement indicators should be raised to explore the dynamic features and complete the theory for parallel mechanisms. In this research, an improved mobility equation is designed to reveal the degrees of freedom for a special class of parallel robots. A novel methodology called the kinematic joint matrix is proposed. It possesses the mapping relations with parallel manipulators. A series of 2-6 degrees of freedom parallel architectures is denoted by the kinematic joint matrix. The theory of screw is employed to check the feasibility from several kinds of parallel structures. A special block diagram is introduced to distinguish various kinematic joint matrices. Since this family of parallel robots contains various motion characteristics, four parallel robots with distinct features are selected. Based on the kinematic models, three categories of singularities are explored. The operational and reachable workspaces of the pure-translational parallel robots are searched and the parametric analyses are reported. The linkage’s impacts for the reachable workspace of the mixed-motion parallel architectures are investigated. The novel performance level index is designed to unify the positive performance index and demonstrated the performance rank for any pose (position and orientation). The dexterity index is utilized as an example to verify the characteristics of the level index. The distributions and parametric analyses of two novel mass-related performances are studied. The dimension synthesis of a selected planar parallel robot is presented based on the non-dominated genetic algorithm II. The experiment results testify the correctness of the mobility and kinematic mathematical models of this mechanism