Inverse Kinematics Method Research Articles

A Novel Analytical Inverse Kinematics Method for SSRMS-Type Space Manipulators Based on the POE Formula and the Paden-Kahan Subproblem

Space manipulators which have a similar symmetrical structure with seven revolute joints, such as the space station remote manipulator system (SSRMS), can be called SSRMS-type space manipulators. The analytical inverse kinematics of an SSRMS-type manipulator can be solved by locking a single joint; the locked joint (joint 1, 2, 6, or 7) can be determined by configuration analysis. Although widely used in establishing the kinematics of SSRMS-type manipulators, the Denavit-Hartenberg (DH) method has a singular problem when two adjacent joint axes are nearly parallel. To avoid this problem, this paper proposes a novel analytical inverse kinematics method for SSRMS-type manipulators based on the product of exponentials (POE) formula and the Paden-Kahan subproblem. Because of the symmetrical structure, an SSRMS-type manipulator degrades to two kinds of 6-degree-of-freedom (DOF) manipulators when locking a single joint (joint 1, 2, 6, or 7). The analytical inverse kinematics of these two kinds of 6-DOF manipulators is solved by combining the Paden-Kahan subproblems and geometric and algebraic methods, respectively. The proposed approach is not only singularity free compared with the traditional DH-based methods but also more accurate than the POE-based numerical solution. The simulation results verify the efficiency of the proposed approach.

Inverse kinematics based on backbone curve for a hyper-redundant tensegrity bird-neck robotic mechanism

In this paper, we propose a hyper-redundant tensegrity bird-neck robotic mechanism. To study the inverse kinematics of this mechanism, we propose a method with two steps. Firstly, the backbone curve for the bird neck is used to describe the macroscopic shape of the mechanism. Secondly, by coordinating the internal forces of the cables when the bird-neck tensegrity model is in equilibrium, we can get all cable lengths of the bird neck at a certain shape which is the inverse kinematics solution. Simulations are conducted to verify the validity of the proposed inverse kinematics method.

Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

A grid gradient approximation method of energy-efficient gait planning for biped robots

In this article, an energy-efficient gait planning algorithm that utilizes both 3D body motion and an allowable zero moment point region (AZR) is presented for biped robots based on a five-mass inverted pendulum model. The product of the load torque and angular velocity of all joint motors is used as an energy index function (EIF) to evaluate the energy consumption during walking. The algorithm takes the coefficients of the finite-order Fourier series to represent the motion space of the robot body centroid, and the motion space is gridded by discretizing these coefficients. Based on the geometric structure of the leg joints, an inverse kinematics method for calculating grid intersection points is designed. Of the points that satisfy the AZR constraints, the point with the lowest EIF value in each network line is selected as the seed. In the neighborhood of the seed, the point with the minimum EIF value in the motion space is successively approximated by the gradient descent method, and the corresponding joint angle sequence is stored in the database. Given a distance to be traveled, our algorithm plans a complete walking trajectory, including two starting steps, multiple cyclic steps, and two stopping steps, while minimizing the energy consumption. According to the preset AZR, the joint angle sequences of the robot are read from the database, and these sequences are adjusted for each step according to the zero-moment-point feedback during walking. To determine the effectiveness of the proposed algorithm, both dynamic simulation and walking experiment in the real environment were carried out. The experimental results show that compared with algorithms based on the fixed body height or vertical body motion, our gait algorithm has a significant energy-saving effect.

Design and Implementation of 6 DOF ROTARIC Robot Using Inverse Kinematics Method

This paper will discuss the calculation of inverse kinematic which will be used to control the 6-DOF articulated robot. This robot consists of 6 Dynamixel MX-28 smart servo with OpenCM 9.04 microcontroller. The articulated robot has been simplified to 4-DOF because there are no obstacles in the work area and no special movements are required. The calculation method uses the intersection point equation between the ball and the line, so that it can make it easier to determine the point in calculating the kinematic inverse. The experiment is carried out using the desired position as input for the kinematic inverse to produce the angle of each joint. From the angle of each joint obtained, it will be entered into forward kinematic so that the end-effector position will be obtained. The desired position will be compared with the end-effector position, and then how much difference will be calculated. From the experimental results, it was found that the inverse kinematic method which has been inverted by the forward kinematic produces the same final position.
 Keywords: 6-DOF manipulator, Articulated robot, inverse kinematics and forward kinematics, Dynamixel MX-28, OpenCM 9

Self‐feeding assistive 7‐DOF robotic arm simulator using solving method of inverse kinematics

AbstractIn order to help people with disabilities of the upper extremities drink and eat, a simulator for self‐feeding assistive robotic arm using solving method of inverse kinematics has been developed in this paper. Using inverse kinematics equations of 7 degrees of freedom (DOF) with an arm angle parameter, the robotic arm model was implemented in the simulator and its controller with mouse device was also designed. The arm angle parameter defined the angle between the arm plane and a reference plane was used to resolve the robotic arm redundancy. Three able‐bodied persons participated in simulation experiments. They manipulated the robotic arm model in a virtual space using mouse device. It was found from the simulation results they successfully performed the drinking and eating tasks in our simulator.

Optimization-Based Constrained Trajectory Generation for Robot-Assisted Stitching in Endonasal Surgery

The reduced workspace in endonasal endoscopic surgery (EES) hinders the execution of complex surgical tasks such as suturing. Typically, surgeons need to manipulate non-dexterous long surgical instruments with an endoscopic view that makes it difficult to estimate the distances and angles required for precise suturing motion. Recently, robot-assisted surgical systems have been used in laparoscopic surgery with promising results. Although robotic systems can provide enhanced dexterity, robot-assisted suturing is still highly challenging. In this paper, we propose a robot-assisted stitching method based on an online optimization-based trajectory generation for curved needle stitching and a constrained motion planning framework to ensure safe surgical instrument motion. The needle trajectory is generated online by using a sequential convex optimization algorithm subject to stitching kinematic constraints. The constrained motion planner is designed to reduce surrounding damages to the nasal cavity by setting a remote center of motion over the nostril. A dual concurrent inverse kinematics (IK) solver is proposed to achieve convergence of the solution and optimal time execution, in which two constrained IK methods are performed simultaneously; a task-priority based IK and a nonlinear optimization-based IK. We evaluate the performance of the proposed method in a stitching experiment with our surgical robotic system in a robot-assisted mode and an autonomous mode in comparison to the use of a conventional surgical tool. Our results demonstrate a noticeable improvement in the stitching success ratio in the robot-assisted mode and the shortest completion time for the autonomous mode. In addition, the force interaction with the tissue was highly reduced when using the robotic system.

Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

For both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

Small-scale Robot Arm Design with Pick and Place Mission Based on Inverse Kinematics

Robot arm is often used in industry with various tasks, one of which is a pick and place. Rapid prototyping of robot arms is needed to facilitate the development of many industrial tasks, especially on a laboratory scale. This study aims to design a small-scale three degree of freedom (3-DoF) robot arm for pick and place mission using the inverse kinematics method. The mechanical robotic arm system is designed using Solidworks with four servo motors as the actuator. Arduino Mega 2560 is used as a microcontroller in which the inverse kinematic method is embedded. This method is used to move the robot based on the coordinates of the destination pick and place. The test results show that the robot arm can carry out the pick and place mission according to the target coordinates given with the largest average error of about 5 cm. While the error generated between the calculation and computation results is around 3%.

Small-scale Robot Arm Design with Pick and Place Mission Based on Inverse Kinematics

Robot arm is often used in industry with various tasks, one of which is a pick and place. Rapid prototyping of robot arms is needed to facilitate the development of many industrial tasks, especially on a laboratory scale. This study aims to design a small-scale three degree of freedom (3-DoF) robot arm for pick and place mission using the inverse kinematics method. The mechanical robotic arm system is designed using Solidworks with four servo motors as the actuator. Arduino Mega 2560 is used as a microcontroller in which the inverse kinematic method is embedded. This method is used to move the robot based on the coordinates of the destination pick and place. The test results show that the robot arm can carry out the pick and place mission according to the target coordinates given with the largest average error of about 5 cm. While the error generated between the calculation and computation results is around 3%.

MB-RRT: An Inverse Kinematics Solver of Reduced Dimension

The evolution of manipulator robots has increased the complexity of their models and applications, requiring that the inverse kinematics (IK) methods integrated into their control systems to have features such as fast convergence, completeness, low computational cost, and the ability to avoid local minima and singularities. We propose in this paper a new probabilistic IK solver based on the probabilistic search method known as Rapidly-Exploring Random Tree (RRT), the Workspace-RRT. The technique grows the tree as a spatial representation of the manipulator on the workspace instead of the configuration space, which reduces the search space up to 3 dimensions. Based on this new representation we also present the Manipulator-Based Rapidly Random Tree (MB-RRT) by incorporating to the Workspace-RRT a new probability model and a new metric for the closest node. We evaluate the presented methods through simulated experiments in the Matlab software. First, we evaluate the impact of the proposed aspects through a comparison between the RRT-based IK solvers, which emphasizes the proposed changes as a key to make the method suitable for the IK problem. At last, we show the use of the MB-RRT for precision tasks and obstructed environments.

Protein secondary structure motifs: A kinematic construction.

The kinematic geometry of protein backbone structures, constrained by either single or multiple hydrogen bonds (H-bonds), possibly in a periodic array, is discussed. These structures include regular secondary structure elements α-helices and β-sheets but also include other short H-bond stabilized irregular structural elements like β-turns. The work here shows that the variations observed in such structures have simple geometrical correlations consistent with constrained motion kinematics. A new classification of the ideal helices is given, in terms of the parameter α, the angle at a Cα atom to its two neighboring Cα 's along the helix, and shown how it can be generalized to include nonideal helices. Specifically, we derive an analytical expression of the backbone dihedrals, (ϕ, ψ), in terms of the parameter α subject to the constraint that the peptide planes are parallel to the helical axis. Helices constructed in this way exhibit near-vertical alignment of the C = O and N - H units and are the canonical objects of this study. These expressions are easily modifiable to include perturbations of parameters relevant to nonplanar peptide units and noncanonical angles. The addition of a second parameter, ε0 , inclination of successive peptide planes along a helix with respect to the helical axis leads to a generalization of the previous expression and provides an efficient parametrization of such structures in terms of coordinates consistent with H-bond parameters. An analogs parametrization of β-turns, using inverse kinematic methods, is also given. Besides offering a unifying viewpoint, our results may find useful applications to protein and peptide design.

A novel inverse kinematics method for 6-DOF robots with non-spherical wrist

A novel numerical method is proposed to solve the inverse kinematics for 6-DOF robots with non-spherical wrist in this paper, which firstly simplifies the non-spherical wrist structure to a spherical one. In each iteration of the algorithm, the inverse solution of simplified robot is firstly used to calculate the end pose of actual robot to estimate the end position error between the calculated end pose and the target pose. And then the inverse solution of simplified robot gradually approaches the desired solution by compensating for the end position error. Additionally, the failure of proposed method caused by the reduction of robot workspace due to structure simplification is analyzed and then the offsetting of known end pose is introduced to improve the robustness of algorithm. Finally, numerical experiments for two typical robots prove the effectiveness of proposed method; a comparative study shows the advantages of proposed algorithm over Newton-Raphson (NR) algorithm; and the performance in processing continuous trajectories demonstrates its good practicability.

Deep-learning damped least squares method for inverse kinematics of redundant robots

In the robot field, it has always been a hard issue of solving inverse kinematics (IK) problems of redundant robot. Although many researchers have come up with solutions for redundant robots with different configurations, there is still an issue of computational efficiency for redundant robot with complex configuration. In this paper, we proposed a novel optimization method which solves redundant robot IK with ultra-high speed and accuracy. On the basis of damped least square (DLS) method with a good stability, we introduced an optimal enhanced coefficient for the first time to achieve faster iteration and more accurate convergence. This is also due to the good performance of the deep neural network we designed in coefficient prediction. 106 data points were selected from the robot working space as the original data training network. The simulation result showed that, unlike other algorithms which take hundreds of iterations to achieve convergence, through the optimized method proposed in this paper, the average number of iteration was just less than 10 and the solving speed was greatly improved on the basis of ensuring stability. In addition, the convergence of the algorithm was greatly improved and when the error threshold was 0.01 mm, the convergence reached 95.47%, which is better than most existing algorithms. In this paper, we evaluated the common IK methods, and the results showed that this method performed better in convergence, accuracy and speed.

Impedance Model-Based Optimal Regulation on Force and Position of Bimanual Robots to Hold an Object

Bimanual robots have been studied for decades and regulation on internal force of the being held object by two manipulators becomes a research interest in recent years. In this paper, based on impedance model, a method to obtain the optimal target position for bimanual robots to hold an object is proposed. We introduce a cost function combining the errors of the force and the position and manage to minimize its value to gain the optimal coordinates for the robot end effectors (EE). To implement this method, two necessary algorithms are presented, which are the closed-loop inverse kinematics (CLIK) method to work out joint positions from desired EE pose and the generalized-momentum-based external force observer to measure the subjected force acting on the EE so as to properly compensate for the joint torques. To verify the effectiveness, practicality, and adaptivity of the proposed scheme, in the simulation, a bimanual robot system with three degrees of freedom (DOF) in every manipulator was constructed and employed to hold an object, where the results are satisfactory.

Rancang Bangun Robot Lengan Pemindah Barang 3 DOF Menggunakan Metode Inverse Kinematics Berbasis Android

Moving object process from one place to another is usually done with the conventional way using human power, then it can certainly getting heavy objects and the farther the distance of displacement, manpower required objects are also getting bigger. It is judged ineffective considering the limitations of human capability in the shift of weight and time limitations of humans in the work. Based on these problems required a robot arm that is able to moving an object from one place to another. The robot arm was designed to have 3 DOF (Degree of Freedom) and the whole joint is revolute and implemented using servo dynamixel AX-12A. Input from this robot is initial coordinates and final coordinates are then computing by the method of inverse kinematics with an output in the form of large angle of each joint required in order for the robot arm reaches the point coordinates. Results from research that has been done, the robot is able to move the object from one point coordinate to another within an average period of 6 to 7 seconds as well as the level error that occurred in the achievement of the desired angle of 0.64%. Based on the results of the implementation system of the arm robot assessed transporter 3DOF using inverse kinematics method is very effective in carrying out its functions to move an object.

Nine Degree-of-Freedom Kinematic Modeling of the Upper-Limb Complex for Constrained Workspace Evaluation.

The design of rehabilitation devices for patients experiencing musculoskeletal disorders (MSDs) requires a great deal of attention. This article aims to develop a comprehensive model of the upper-limb complex to guide the design of robotic rehabilitation devices that prioritize patient safety, while targeting effective rehabilitative treatment. A 9 degree-of-freedom kinematic model of the upper-limb complex is derived to assess the workspace of a constrained arm as an evaluation method of such devices. Through a novel differential inverse kinematic method accounting for constraints on all joints1820, the model determines the workspaces in which a patient is able to perform rehabilitative tasks and those regions where the patient needs assistance due to joint range limitations resulting from an MSD. Constraints are imposed on each joint by mapping the joint angles to saturation functions, whose joint-space derivative near the physical limitation angles approaches zero. The model Jacobian is reevaluated based on the nonlinearly mapped joint angles, providing a means of compensating for redundancy while guaranteeing feasible inverse kinematic solutions. The method is validated in three scenarios with different constraints on the elbow and palm orientations. By measuring the lengths of arm segments and the range of motion for each joint, the total workspace of a patient experiencing an upper-limb MSD can be compared to a preinjured state. This method determines the locations in which a rehabilitation device must provide assistance to facilitate movement within reachable space that is limited by any joint restrictions resulting from MSDs.

Model-Based Real-Time Motion Tracking Using Dynamical Inverse Kinematics

This paper contributes towards the development of motion tracking algorithms for time-critical applications, proposing an infrastructure for dynamically solving the inverse kinematics of highly articulate systems such as humans. The method presented is model-based, it makes use of velocity correction and differential kinematics integration in order to compute the system configuration. The convergence of the model towards the measurements is proved using Lyapunov analysis. An experimental scenario, where the motion of a human subject is tracked in static and dynamic configurations, is used to validate the inverse kinematics method performance on human and humanoid models. Moreover, the method is tested on a human-humanoid retargeting scenario, verifying the usability of the computed solution in real-time robotics applications. Our approach is evaluated both in terms of accuracy and computational load, and compared to iterative optimization algorithms.

On Null Space-Based Inverse Kinematics Techniques for Fleet Management: Toward Time-Varying Task Activation

Multirobot fleets play an important role in industrial logistics, surveillance, and exploration applications. A wide literature exists on the topic, both resorting to reactive (i.e. collision avoidance) and to deliberative (i.e. motion planning) techniques. In this work, null space-based inverse kinematics (NSB-IK) methods are applied to the problem of fleet management. Several NSB-IK approaches existing in the literature are reviewed, and compared with a reverse priority approach, which originated in manipulator control, and is here applied for the first time to the considered problem. All NSB-IK approaches are here described in a unified formalism, which allows (i) to encode the property of each controller into a set of seven main key features, (ii) to study possible new control laws with an opportune choice of these parameters. Furthermore, motivated by the envisioned application scenario, we tackle the problem of task-switching activation. Leveraging on the iCAT TPC technique Simetti and Casalino, 2016, in this article, we propose a method to obtain continuity in the control in face of activation or deactivation of tasks, and subtasks by defining suitable damped projection operators. The proposed approaches are evaluated formally, and via simulations. Performances with respect to standard methods are compared considering a specific case study for multivehicles management.

Active Compensation Analysis Method of Inverse Kinematics of Hydraulic Transmission Through Passage Based on Fuzzy Algorithm

Active Compensation Analysis Method of Inverse Kinematics of Hydraulic Transmission Through Passage Based on Fuzzy Algorithm