An Optimization Based Inverse Kinematics of Redundant Robots Avoiding Obstacles and Singularities

This article presents a solution of the inverse kinematics problem of 7-degrees-of-freedom serial redundant manipulators. A 7-degrees-of-freedom (7-DoF) redundant manipulator can avoid obstacles and thus improve operational performance. However, its inverse kinematics is difficult to solve since it has one more DoF than that necessary for reaching the whole workspace, which causes infinite solutions. In this article, Gröbner bases theory is proposed to solve the inverse kinematics. First, the Denavit–Hartenberg model for the manipulator is established. Second, different joint configurations are obtained using Gröbner bases theory. All solutions are confirmed with the aid of algebraic computing software, confirming that this method is accurate and easy to be implemented.

In this paper, high-index norm approach towards inverse kinematic problem of redundant manipulators is investigated. It is well known that the inverse kinematics problem of redundant manipulator has infinite solutions. Out of these infinite solutions, only those solutions are preferred which fulfill some optimization criterion e.g joint toque minimization, obstacle avoidance, singularity avoidance etc. To calculate the joint velocities, the commonly practiced optimization criterion utilize Euclidean or infinity-norm of vectors in the joint space. This paper investigates the use of high-index norm and its comparison with other norm solutions, in formulating the optimization problem towards inverse kinematic solution of redundant manipulators. Several cases studies are reported to demonstrate the effectiveness of this approach to obtain the inverse kinematic solution, while optimizing secondary criteria like avoiding the joint limits, obstacle avoidance etc.

This paper presents analysis on kinematics and statics of redundant serial link manipulator and redundant parallel link manipulator with passive joints. Passive joint is a joint that the joint torque depends on the joint angle. Redundant manipulator is a manipulator that has actuated joints more than dimension of the task space. We study the theme not to be defined well the fundamental theory of the manipulator with passive joints. First, we study the redundant serial link manipulator with passive joints. We propose a solution method of kinematics and statics and a control method in a limited condition. Moreover, we can show a better performance of the serial link manipulator with additional passive joint, so-called semi-active joint, if we can control the equilibrium positions of passive joints by using numerical example. Secondary, we study the redundant parallel link manipulator with passive joints. We proposed a solution method of kinematics and statics. We can show the performance in each parallel link manipulator mode with semi-active joints by using numerical example.

We propose a new approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. It is inspired by recent motion planning research and explicitly takes into account constraints due to joint limits and self-collisions. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the configuration space of a manipulator in a finite graph like structure. The standard formulation of inverse kinematics problem is then solved using this roadmap. Our current implementation, based on Ariadne's clew algorithm, is composed of two sub-algorithms: EXPLORE, a simple algorithm that builds the kinematic roadmap by placing landmarks in the configuration space; and SEARCH, a local planner that uses this roadmap to reach the desired end-effector configuration. Our implementation of SEARCH is an extremely efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.

We propose a geometric method to solve inverse kinematics (IK) problems of 7-DoF manipulators with joint offsets at shoulder, elbow, and wrist. Traditionally, inverse position kinematics for redundant manipulators are solved by using an iterative method based on the pseudo-inverse of the manipulator Jacobian. This provides a single solution among the infinitely many possible solutions for the IK problem of redundant manipulators. There are no closed-form IK solutions for redundant manipulators with multiple joint offsets. Using our method we can compute multiple IK solutions using two-parameter search by exploiting geometry of the structure of a redundant manipulator. Our proposed IK algorithm can handle multiple joint offsets and is mathematically simple to implement in a few lines of code. We apply our algorithm to compute IK solutions for 7-DoF redundant Baxter robot (that has joint offsets at shoulder, wrist, and elbow joints) for end-effector configurations where existing geometry-based IK solvers fail to find solutions. We also demonstrate the use of our algorithm in an application where we want to compute an IK solution (among the infinitely many possible solutions) that has minimum error bound in end-effector position, in the presence of random joint actuation and sensing uncertainties.

Redundant robot manipulator is a kind of robot arm having more degrees-of-freedom (DOF) than required for a given task. Due to the extra DOF, it can be used to accomplish many complicated tasks, such as dexterous manipulation, obstacle avoidance, singularity avoidance, collision free, etc. However, modeling the inverse kinematics of such kind of robot manipulator remains challenging due to its property of null space motion. In this paper, support vector regression (SVR) is implemented to solve the inverse kinematics problem of redundant robotic manipulators. To further improve the prediction accuracy of SVR, a special machine learning technique called blending is used in this work. The proposed approach is verified in MATLAB with a seven DOF Mitsubishi PA-10 robot and the simulation results have proved its high accuracy and effectiveness.

This paper presents an algorithm for the solution of the inverse kinematics of a serial redundant manipulator with one (or more) locked joint(s). To this end, a general procedure is developed for the determination of the equivalent Denavit-Hartenberg parameters of a serial manipulator with locked joints. This procedure can be applied to any serial architecture. The solution of the inverse kinematic problem for the three cases which can arise is then addressed. An example of the application of the method to a SARCOS 7-DOF manipulator is also given.

The inverse kinematics (IK) problem is a fundamental problem in robotic manipulation. Traditional, Jacobian-based solutions to this problem are known to scale poorly with the number of degrees of freedom (DOF) in the manipulator, necessitating novel IK solutions for high-DOF manipulators. Metaheuristic optimization algorithms such as Particle Swarm Optimization (PSO) are a promising alternative approach to traditional IK techniques due to their strong performance on difficult and high-DOF problems in many diverse domains. Previous applications of PSO to the IK problem have focused on specific classes (e.g., planar) or models of manipulators or specific IK subproblems (e.g., position only IK). Furthermore, the experimental validation of these techniques has considered only manipulators with seven or fewer degrees of freedom and taken place almost exclusively in simulation. In this paper, we (1) generalize previous work to derive a fitness function that can be minimized to solve the full position and orientation IK problem for any serial manipulator while respecting joint limits and avoiding self-collisions, (2) present the first statistical analysis of PSO as a high-DOF IK solver on simulated manipulators with up to 180 DOF using this fitness function, and (3) present an important validation of PSO-based IK using this fitness function on real-world hardware on a difficult precision manipulation task.

Two potential fields fused adaptive path planning system for autonomous vehicle under different velocities

In this article an Artificial Neural Network (ANN) approach for the obstacle avoidance of redundant robot manipulators is presented. The approach is based on formulating an inverse kinematics problem under an inexact context. This procedure permits to deal with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudo inverse perturbation. Here the computation of the inverse kinematics problem is performed by a properly trained ANN and including a null space vector for obstacle avoidance which is also realized by another properly trained ANN. The approach is tested on the simulation of a planar redundant manipulator performing some obstacle avoidance tasks. From the results obtained, the approach compares favorably with the numerical approach.

In this study a five Degrees of Freedom (DOF) serial robot manipulator was designed and implemented. The inverse kinematics problem, which has not exact analytical solution (only one inverse kinematic solution for a predefined end effector position in three dimensional space), of the robot mechanism was solved by using the combination of the analytical method and a simple search method. In order to use the proposed method in real-time applications, the method is designed so that it can be used to solve the inverse kinematics problem for the next point of the end-effector while the mechanism is working. Moreover, so that to control the implemented mechanism, a user interface program was written by using Visual Basic programming language. Finally, the proposed inverse kinematic solution method was tested on two different trajectories, an arc shaped trajectory that composed of 58 points and a linear trajectory divided into 29 points. The obtained results revealed that the proposed method can be used successfully in solving the inverse kinematic problem of the designed mechanism.

A Learning Framework to Inverse Kinematics of Redundant Manipulators

The Inverse Kinematics (IK) problem is concerned with finding robot control parameters to bring the robot into a desired position under the kinematics and joint limit constraints. We present a globally optimal solution to the IK problem for a general serial 7DOF manipulator with revolute joints and a polynomial objective function. We show that the kinematic constraints due to rotations can be all generated by the second-degree polynomials. This is an important result since it significantly simplifies the further step where we find the optimal solution by Lasserre relaxations of nonconvex polynomial systems. We demonstrate that the second relaxation is sufficient to solve a general 7DOF IK problem. Our approach is certifiably globally optimal. We demonstrate the method on the 7DOF KUKA LBR IIWA manipulator and show that we are, in practice, able to compute the optimal IK or certify infeasibility in 99.9% tested poses. We also demonstrate that by the same approach, we are able to solve the IK problem for any generic (random) manipulator with seven revolute joints.

Closed form solutions applied to redundant serial link manipulators

In this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end‐effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor‐based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.