Analytical Inverse Kinematic Solution Research Articles

An Analytical Inverse Kinematics Solution with the Avoidance of Joint Limits, Singularity and the Simulation of 7-DOF Anthropomorphic Manipulators

An Analytical Inverse Kinematics Solution with the Avoidance of Joint Limits, Singularity and the Simulation of 7-DOF Anthropomorphic Manipulators

Development of the LSTM Model and Universal Polynomial Equation for All the Sub-Phases of Human Gait

Human gait can be measured using a change in the joint angles value of the lower limb joints during walking. Inverse kinematics (IK) of a human leg refers to calculating joint angle values from different leg positions during locomotion. This paper calculates a real-time IK for a 3-link kinematic leg using a musculoskeletal model in OpenSim. The model provides the analytical solution of IK, which is quick and accurate. But, the model-based approach is very much dependent on the morphology of the bipedal robot. The existing bipedal robots are mainly planned for walking on flat terrain and unconstrained environment. So, these limitations lead to the developing of a generalised polynomial equation for generating walking trajectories. The model-based approaches rely on the degree of similarity between the virtual human model and the actual human body, which does not fully describe the human body. Due to the difference in real and virtual models, the model-based approaches suffer during the optimisation process of the boundary conditions and the mass-inertial parameters, leading to an unstable numerical solution. The learning-based method using long short-term memory (LSTM) model for gait generation is proposed to overcome the limitation of model-based approaches.

An improved inverse kinematics solution for 6-DOF robot manipulators with offset wrists

AbstractEfficiently solving inverse kinematics (IK) of robot manipulators with offset wrists remains a challenge in robotics due to noncompliance with Pieper criteria. In this paper, an improved method to solve the IK for 6-DOF robot manipulators with offset wrists is proposed. This method is based on the Newton iteration technique, but it does not require a selection of initial estimation of joint variables. The solution is divided into two parts: the first part is to reconstruct a simplified structure with analytical IK solution, and the second part is to obtain a numerical solution by iteration. Further, a robot manipulator HSR-BR606 with an offset wrist is used as an example to specifically elaborate the mathematical procedure of the method and to investigate the algorithm in terms of accuracy, efficiency, and application of motion planning. A comparative experiment is conducted with a typical IK algorithm, which demonstrates a higher accuracy and shorter calculation time of the proposed method. The mean calculation time for a single IK solution required for this algorithm is only 4% of the comparison algorithm.

Parameter Calibration on Replacement Manipulator for UHV Valve-Side Bushing Based on Spinor Theory

In this paper, a structure design scheme of intelligent replacement device for the ultrahigh voltage (UHV) converter transformer valve-side bushing is put forward, and its size is determined according to the actual size of domestic converter station valve hall and UHV converter transformer valve-side bushing. Moreover, the weak links in its working state are analyzed by finite element method to ensure the safety and reliability of the structure. Based on the spinor theory, the forward kinematics and Jacobian matrix model of the manipulator are established, and the analytical solution of inverse kinematics is derived. In order to analyze the accuracy of the intelligent replacement manipulator for the UHV converter transformer valve-side bushing, considering that the end actuator of the robot arm is under heavy load, the absolute positioning accuracy and repeated positioning accuracy are analyzed. In addition, the corresponding error model is established, the least square method is proposed to identify the error model, and the influence of the error caused by the load on the repetition accuracy is analyzed. Finally, the whole process simulation in ROS provides data support for the calculation of repetitive precision and verifies the feasibility of the intelligent replacement device for the UHV converter valve-side bushing.

Development of a redundant anthropomorphic hydraulically actuated manipulator with a roll-pitch-yaw spherical wrist

The demand for redundant hydraulic manipulators that can implement complex heavy-duty tasks in unstructured areas is increasing; however, current manipulator layouts that remarkably differ from human arms make intuitive kinematic operation challenging to achieve. This study proposes a seven-degree-of-freedom (7-DOF) redundant anthropomorphic hydraulically actuated manipulator with a novel roll-pitch-yaw spherical wrist. A hybrid series-parallel mechanism is presented to achieve the spherical wrist design, which consists of two parallel linear hydraulic cylinders to drive the yaw/pitch 2-DOF wrist plate connected serially to the roll structure. Designed as a 1RPRRR-1SPU mechanism (“R”, “P”, “S”, and “U” denote revolute, prismatic, spherical, and universal joints, respectively; the underlined letter indicates the active joint), the 2-DOF parallel structure is partially decoupled to obtain simple forward/inverse kinematic solutions in which a closed-loop subchain “RPRR” is included. The 7-DOF manipulator is then designed, and its third joint axis goes through the spherical center to obtain closed-form inverse kinematic computation. The analytical inverse kinematic solution is drawn by constructing self-motion manifolds. Finally, a physical prototype is developed, and the kinematic analysis is validated via numerical simulation and test results.

Real Time Control Application of the Robotic Arm Using Neural Network Based Inverse Kinematics Solution

Robotic arms are widely used in many industrial applications at present. The control of robotic arms involves position coordination Cartesian space by a forward/inverse kinematics solution method. The inverse kinematics is difficult for real-time control applications, computational requirements are intensive and the run-time is high. The traditional solution methods used geometric, algebraic, and numerical iterative techniques are inadequate and slow in the inverse kinematics solution. Recently, alternative solution methods based on artificial intelligence techniques have been developed to solve the inverse kinematics problem. In this study, a multi-layered feed-forward Artificial Neural Network model was developed to solve the inverse kinematics of the 5 degrees of freedom robotic arm. Using the Proportional-Integral control algorithm combined with this Artificial Neural Network model, the real-time position control of the robotic arm was accomplished. The obtained results were compared with the PI control supported by an analytical inverse kinematics solution in real-time. The results showed that the PI control combined with Artificial Neural Network has superior tracking ability, smaller control error, and better absolute fit to the reference.

Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

Seven-degree-of-freedom redundant manipulators with link offset have many advantages, including obvious geometric significance and suitability for configuration control. Their configuration is similar to that of the experimental module manipulator (EMM) in the Chinese Space Station Remote Manipulator System. However, finding the analytical solution of an EMM on the basis of arm angle parameterization is difficult. This study proposes a high-precision, semi-analytical inverse method for EMMs. Firstly, the analytical inverse kinematic solution is established based on joint angle parameterization. Secondly, the analytical inverse kinematic solution for a non-offset spherical-roll-spherical (SRS) redundant manipulator is derived based on arm angle parameterization. The approximate solution of the EMM is calculated in accordance with the relationship between the joint angles of the EMM and the SRS manipulator. Thirdly, the error is corrected using a numerical method through the analytical inverse solution based on joint angle parameterization. After selecting the stride and termination condition, the precise inverse solution is computed for the EMM based on arm angle parameterization. Lastly, case solutions confirm that this method has high precision, and the arm angle parameterization method is superior to the joint angle parameterization method in terms of parameter selection.

An analytical inverse kinematics solution with joint limits avoidance of 7-DOF anthropomorphic manipulators without offset

The inverse solution calculation speed and the configuration control are very important for anthropomorphic manipulators with 7 degree-of-freedom (DOF). In order to realize the combined control of global arm configuration manifolds and local self-motion of 7-DOF anthropomorphic manipulators without offset, an analytical inverse kinematics solution method is proposed in this paper. By defining a new arm reference plane for 7-DOF anthropomorphic manipulators, it uses arm angle to deal with local self-motion and orientation control to deal with global arm configuration manifolds. All possible inverse kinematics solutions for target pose can be intuitively expressed with the assistance of the parameters of arm angle and orientation control. Meanwhile, the corresponding singularity is also taken into account and a detection metric is provided. Furthermore, the problem of joint limits avoidance is mapped to the selection of arm angle in null space, and the Self-Adaptive Particle Swarm Optimization algorithm is introduced to obtain the optimal arm angle that can maximize the avoidance of joint limits. Simulation results show the proposed method has such advantages as fast calculation speed, high precision and high stability.

Analytical inverse kinematic computation for 7-DOF redundant sliding manipulators

The shape and movement irregularities of rail-type redundant sliding manipulators lead to structural uncertainty, which results in inverse kinematics computations that are considerably more complicated than those of the traditional redundant manipulator currently studied. In this paper, an analytical inverse kinematic parameterized method is proposed for the redundant sliding manipulators, which solves the inverse kinematics analytically and adopts the Newton–Raphson algorithm for secondary adjustment. This paper is the first time to propose a general analytical inverse kinematics solution for all types of rail-type redundant sliding manipulators. Furthermore, the special structural characteristics of the rail-type redundant sliding manipulator are analyzed in this paper. The proposed method takes the redundant circular-sliding manipulator as the research object, and extends to all types of rail-type redundant sliding manipulators. It has the advantages of simplicity, practicability, obvious geometric meaning and universality, which can solve the real-time motion planning and control issues of all types of redundant sliding manipulators. Simulation illustrations and physical experiments are performed to verify the effectiveness and universality of the method.

Analytical Inverse Kinematic Solution for Original Robotic Manipulator Construction

Analytical Inverse Kinematic Solution for Original Robotic Manipulator Construction

Kinematics analysis and self - collision detection of Truss type multi-robot cooperative welding platform

A collaborative welding platform consists of a XYZ-mobile truss, a 3R (revolute joint) clamping robot and a dual-arm welding robot. Based on Denavit-Hartenberg (D-H) method, the analytical inverse kinematics solution of the platform is obtained. Dual-arm coordination is a technical difficulty in robot control field. Focusing on self-collision problem during dual-arm robot motion planning, this paper proposes a new obstacle avoidance algorithm based on Rapidly Exploring Random Tree (RRT) algorithm. Setting searching area founded on artificial potential field (APF) algorithm and adopting note-pruning strategy achieves high searching efficiency. Simulation results verify the correctness of kinematics analysis and self-collision detection algorithm.

Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints

It is a common belief that service robots shall move in a human-like manner to enable natural and convenient interaction with a human user or collaborator. In particular, this applies to anthropomorphic 7-DOF redundant robot manipulators that have a shoulder-elbow-wrist configuration. On the kinematic level, human-like movement then can be realized by means of selecting a redundancy resolution for the inverse kinematics (IK), which realizes human-like movement through respective nullspace preferences. In this paper, key positions are introduced and defined as Cartesian positions of the manipulator's elbow and wrist joints. The key positions are used as constraints on the inverse kinematics in addition to orientation constraints at the end-effector, such that the inverse kinematics can be calculated through an efficient analytical scheme and realizes human-like configurations. To obtain suitable key positions, a correspondence method named wrist-elbow-in-line is derived to map key positions of human demonstrations to the real robot for obtaining a valid analytical inverse kinematics solution. A human demonstration tracking experiment is conducted to evaluate the end-effector accuracy and human-likeness of the generated motion for a 7-DOF Kuka-LWR arm. The results are compared to a similar correspondance method that emphasizes only the wrist postion and show that the subtle differences between the two different correspondence methods may lead to significant performance differences. Furthermore, the wrist-elbow-in-line method is validated as more stable in practical application and extended for obstacle avoidance.

Practical analytical inverse kinematic approach for 7-DOF space manipulators with joint and attitude limits

In this study, we propose a practical approach for calculating the analytical inverse kinematic solution for a seven-degrees of freedom (7-DOF) space manipulator with joint and attitude limits. Instead of utilizing traditional velocity-based approaches that limit the ranges of joints by calculating the velocity-level Jacobian matrix, we propose a position-based approach for evaluating the ranges of feasible inverse kinematic solutions. We then search for the optimal solution, which is estimated based on the disturbance that acts on the base of the manipulator to obtain the final solution. First, the concept of the redundancy of manipulators is defined and each joint is parameterized by the redundancy. Second, how the joint limits affect this redundancy is discussed. Third, a practical approach (include the objective function that the author needs to minimize) is proposed for dealing with the inverse kinematic problem of 7-DOF manipulators. Finally, the validity of this approach is verified by numerical simulation.

Analityczne rozwiązanie zadania odwrotnego kinematyki dla manipulatora robota GMF S-420F

Analityczne rozwiązanie zadania odwrotnego kinematyki dla manipulatora robota GMF S-420F

Symbolic Singular Value Decomposition for a PUMA Robot and Its Application to a Robot Operation Near Singularities

Singular value decomposition has received considerable atten tion in robot control during the past several years because of the fact that it may be used in solving the problem of robot operation in singular configurations. However, its main draw back is its high computational complexity when compared with that of the Gaussian elimination or analytical inverse kinematic solution. In this article we have derived symbolic expressions for matrices of the decomposition for both a 2-DOF planar manipulator and a 6-DOF PUMA robot. This reduces the com putational burden by an order of magnitude and gives us more insight into the nature of the singularities. The symbolic ex pressions have been applied to obtain the damped least-squares solution for joint velocities. Some modifications of the damped least-squares solution are proposed, and the simulation results are included. The method can be applied to other robots when position and orientation problems can be separated.