Closed-form Solution Of Inverse Kinematics Research Articles

Kinematic Modeling and Motion Planning of the Mobile Manipulator Agri.Q for Precision Agriculture

In recent years, the study of robotic systems for agriculture, a modern research field often shortened as “precision agriculture”, has become highly relevant, especially for those repetitive actions that can be automated thanks to innovative robotic solutions. This paper presents the kinematic model and a motion planning pipeline for a mobile manipulator specifically designed for precision agriculture applications, such as crop sampling and monitoring, formed by a novel articulated mobile base and a commercial collaborative manipulator with seven degrees of freedom. Starting from the models of the two subsystems, characterized by an adjustable position and orientation of the manipulator with respect to the mobile base, the linear mapping that describes the differential kinematics of the whole custom system is expressed as a function of the input commands. To perform pick–and–place tasks, a motion planning algorithm, based on the manipulator manipulability index mapping and a closed form inverse kinematics solution is presented. The motion of the system is based on the decoupling of the base and the arm mobility, and the paper discusses how the base can be properly used for manipulator positioning purposes. The closed form inverse kinematics solution is also provided as an open-source Matlab code.

Inverse Kinematics and Dexterous Workspace Formulation for 2-Segment Continuum Robots With Inextensible Segments

The inverse kinematics (IK) problem of continuum robots has been investigated in depth in the past decades. Under the constant-curvature bending assumption, closed-form IK solution has been obtained for continuum robots with variable segment lengths. Attempting to close the gap towards a complete solution, this paper presents an efficient solution for the IK problem of 2-segment continuum robots with one or two inextensible segments (a.k.a, constant segment lengths). Via representing the robots shape as piecewise line segments, the configuration variables are separated from the IK formulation such that solving a one-variable nonlinear equation leads to the solution of the entire IK problem. Furthermore, an in-depth investigation of the boundaries of the dexterous workspace of the end effector caused by the configuration variables limits as well as the angular velocity singularities of the continuum robots was established. This dexterous workspace formulation, which is derived for the first time to the best of the authors knowledge, is particularly useful to find the closest orientation to a target pose when the target orientation is out of the dexterous workspace. In the comparative simulation studies between the proposed method and the Jacobian-based IK method involving 500,000 cases, the proposed variable separation method solved 100% of the IK problems with much higher computational efficiency.

A Closed-Form Solution for the Inverse Kinematics of the 2n-DOF Hyper-Redundant Manipulator Based on General Spherical Joint

This paper presents a closed-form inverse kinematics solution for the 2n-degree of freedom (DOF) hyper-redundant serial manipulator with n identical universal joints (UJs). The proposed algorithm is based on a novel concept named as general spherical joint (GSJ). In this work, these universal joints are modeled as general spherical joints through introducing a virtual revolution between two adjacent universal joints. This virtual revolution acts as the third revolute DOF of the general spherical joint. Remarkably, the proposed general spherical joint can also realize the decoupling of position and orientation just as the spherical wrist. Further, based on this, the universal joint angles can be solved if all of the positions of the general spherical joints are known. The position of a general spherical joint can be determined by using three distances between this unknown general spherical joint and another three known ones. Finally, a closed-form solution for the whole manipulator is solved by applying the inverse kinematics of single general spherical joint section using these positions. Simulations are developed to verify the validity of the proposed closed-form inverse kinematics model.

A Real-Time-Capable Closed-Form Multi-Objective Redundancy Resolution Scheme for Seven-DoF Serial Manipulators

Using a closed-form inverse kinematics solution for motion planning has many advantages compared to traditional numerical approaches, most notably much faster computation times and better suitability for real-time applications. Steady progress has been made to develop an analytic inverse kinematics solution for seven degrees of freedom (DoF) manipulators without joint offsets. Redundancy resolutions have been proposed to push the individual joint angles away from their limits. However, no further objectives are considered in these closed-form solutions. We propose a multi-objective real-time optimization approach that is able to minimize joint velocities and accelerations, while still avoiding joint limits. A closed-form solution to the optimization is derived, which only requires a single intuitive tuning parameter. We provide a free and open-source software implementation of the full kinematics algorithm that covers the complete solution space. The null-space motion resulting from our method is evaluated, achieving faster motion times and smoother arm motions along Cartesian paths in comparison to the state-of-the-art approach. Finally, experimental results with a KUKA iiwa robot are reported.

Closed-Form Solution of Inverse Kinematics for a Minimally Invasive Surgical Robot Slave Manipulator Similar to Da Vinci Robot System

Abstract Closed-form solution inverse kinematics has a unique advantage in robot control; it is quite difficult to be obtained through traditional methods as no effective analytic method has been identified so far, when the robot's joint configuration does not conform to the “Pieper Criterion.” In this paper, a new modeling method named extended Denavit-Hartenberg (DH) method was presented for solving this problem. And the conditions of robots' configuration that conform to the method have been given for different joints combinations. The precise closed-form solution to a minimally invasive surgical robot slave manipulator was obtained through this new method. The correctness of the new method was verified through simulation analyses; this study enriched robot kinematic modeling and the closed-form solution to inverse kinematics of Da Vinci surgical robot, and will help to obtain a fast, accurate, and general method of closed-form solution for the same kind of robots and provide the precondition for robot control and trajectory planning.

Forward and inverse kinematics of a 5-DOF hybrid robot for composite material machining

Abstract Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.

Kinematics-based end-effector path control of a mobile manipulator system on an uneven terrain using a two-stage Support Vector Machine

SUMMARYA mobile manipulator system (MMS) consists of a robotic arm mounted on a mobile platform that is used in rescue and relief, space exploration, warehouse automation, etc. As the total system has 14 Degrees of Freedom (DOF), it does not have a closed-form inverse kinematics (IK) solution. A learning-based method is proposed, which uses the forward kinematics data to learn the IK relation for motion of an MMS on a rough terrain, using a one-class support vector machine (SVM) framework. Once trained, the model estimates the joint probability distribution of the MMS configuration and end-effector position. This distribution is used to find the MMS configuration for a given desired end-effector path. Past research using a Kohonen Self organizing map (KSOM) neural network-based open-loop control method has shown that the MMS deviates from its desired path while moving on an uneven terrain due to unknown disturbances such as wheel slip, slide, and terrain deformation. Therefore, a new sequential two-stage SVM-based end-effector path-tracking control scheme is proposed to control the end-effector path. In this scheme, the error in the end-effector path is continuously tracked with the help of a Microsoft Kinect 2.0 (Microsoft Regional Sales, Singapore 119968) and is sent as a feedback to the controller. Once the error reaches a threshold value, the error correction step of the controller gets activated to correct the error until the desired accuracy is reached. The effectiveness of the proposed approach is proved through extensive simulations and experiments conducted on 3D terrain in which it is shown that the end effector can follow the desired path with an average experimental error of around 2 cm between the desired and final corrected path.

Existence Conditions and General Solutions of Closed-form Inverse Kinematics for Revolute Serial Robots

This study proposes a method for judging the existence of closed-form inverse kinematics solutions based on the Denavit–Hartenberg (DH) model. In this method, serial robots with closed-form solutions are described using three types of sub-problems from the viewpoint of solving algebraic equations. If a serial robot can be described using these three types of sub-problems, i.e., if the inverse kinematics problems can be solved by several basic problems, then there is a closed-form solution. Based on the above method, we design a set of universal closed-form inverse kinematics solving algorithms. Since there is a definite formula solution for the three types of sub-problems, the joint angles can be rapidly determined. In addition, because the DH parameters can directly reflect the linkage of the robot, the judgment of the sub-problems is also quick and accurate. More importantly, the algorithm can be applied to serial robots with low degrees of freedom. This enables the algorithm to not only quickly and accurately solve inverse kinematics problems but also to exhibit high universality. This proposed theory improves the existence conditions for closed-form reverse solutions and further promotes the development of motion control techniques for serial robots.

Closed form inverse kinematics solution for a redundant anthropomorphic robot arm

An inverse kinematics solution of a redundant 7R serial chain that mimics the human arm is presented. Such manipulators are composed of two spherical wrists with one revolute joint in between. In the case of non-redundant manipulators the inverse kinematics yields a discrete set of solutions for the joint axes to reach a given end effector position and orientation. For redundant arms, however, the solution consists of a one parameter set. In contrast to other solutions to this problem herein a closed form solution is given without the need of specifying the design, task nor the redundant parameter in the solution process. That gives the possibility to use the degree of freedom provided by the additional joint for different applications, such as avoiding singularities, joint limits and collisions or to apply an optimization algorithm to achieve, for example, minimal joint velocities or joint movements.

3D Modeling and Closed-Form Inverse Kinematics Solution for 6dof Surgical Robot

Since robots began to inter the medical fields, more research efforts and more attention have been given to this kind of robots. In this paper six degrees of freedom surgical robot was studied. The Denavit-Hartenberg parameters of the robot have been computed and 3D model has been built by using open source robotics toolbox. The paper also discussed a closed form solution for the inverse kinematics problem by using inverse kinematic decoupling method.

Kinematic analysis of 7 degrees of freedom upper-limb exoskeleton robot with tilted shoulder abduction

An exoskeleton robot is a hybrid between human and robot where the two are mechanically integrated to function as one intelligent as well as powerful robot. This study presents a kinematic analysis of 7degrees of freedom (DOF) exoskeleton robot with its base rotational axis skewed to avoid singularity within workspace and to maximize ease of movement in all directions. The tilt of the base rotational axis configures the exoskeleton robot into an initial posture to which it is difficult to identify a geometric transformation from a kinematical model with all joint angels set to zero. When the limbs of the exoskeleton robot are configured either vertical or parallel to the ground, the resulting configuration can be initialized and then, ensuing kinematic analysis can be more conveniently performed from this nominal configuration. An analytical relationship defining a geometric transformation from the skewed configuration to the user-defined nominal configuration is developed and an explicit closed-form inverse kinematic solution for the 7 DOF exoskeleton robot is also presented.

Efficient closed-form solution of inverse kinematics for a specific six-DOF arm

Inverse kinematics solutions for multi-DOF arms can be classified as analytical or numerical. In general, analytical solutions are preferable to numerical solutions because analytical ones yield complete solutions and are computationally fast and reliable. However, analytical closed-form solutions for inverse kinematics of 6-DOF arms rarely exist for real-time control purposes of fast moving arms. In this paper, we propose a fast inverse kinematics algorithm with a closed-form solution for a specific 6-DOF arm. The proposed algorithm is verified using simulation modules developed by us for demonstrations.

A New Algorithm for a Spatial Serial Robot

In this paper a new algorithm to compute all the closed-form inverse kinematics solutions of a spatial serial robot. Based on the method, A 16th degree univariate polynomial of the spatial serial robot is obtained without factoring out or deriving the greatest common divisor. We also obtain all the closed-form solutions for the inverse kinematics of the robot. Finally a numerical example is given to demonstrate the algorithm process.

Freeing the Serial Mechanism Designer from Inverse Kinematic Solvability Constraints

This paper presents a fast numerical solution for the inverse kinematics of a serial manipulator. The method is implemented on the C-arm, a manipulator designed for use in robotic surgery. The inverse kinematics solution provides all possible solutions for any six degree-of-freedom serial manipulator, assuming that the forward kinematics are known and that it is possible to solve for the remaining joint angles if one joint angle’s value is known. With a fast numerical method and the current levels of computing power, designing a manipulator with closed-form inverse kinematics is no longer necessary. When designing the C-arm, we therefore chose to weigh other factors, such as actuator size and patient safety, more heavily than the ability to find a closed-form inverse kinematics solution.

Coordinated kinematic modelling for motion planning of heavy-duty manipulators in an integrated open-die forging centre

An integrated open-die forging centre can realize programmed incremental forging processes to improve safety and efficiency; the centre consists of a forging press and one or two heavy-duty manipulators. This paper focuses on the coordinated kinematic modelling of the integrated system. First a newly designed serial—parallel forging manipulator is presented and the closed-form inverse kinematic solution is derived based on homogeneous co-ordinate transformation. Then the deformation of the forged workpiece is investigated by the spread coefficient method of plastic deformation theory, and the relation between the motion of the holding end of the workpiece and the movement of the upper die is formulated. Finally, the coordinated kinematic modelling of the integrated system is established, where the press and the manipulator are coordinated in movement. Simulation of a typical open-die forging process shows that the gripper of the manipulator should have good compliance abilities in horizontal and vertical directions during forging; however, it should have high rotation stiffness with respect to the transverse axis. The automatic programmed forging plan and coordination control strategy can be pre-designed based on this model.

Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution

This paper proposes an analytical methodology of inverse kinematic computation for 7 DOF redundant manipulators with joint limits. Specifically, the paper focuses on how to obtain all feasible inverse kinematic solutions in the global configuration space where joint movable ranges are limited. First, a closed-form inverse kinematic solution is derived based on a parameterization method. Second, how the joint limits affect the feasibility of the inverse solution is investigated to develop an analytical method for computing feasible solutions under the joint limits. Third, how to apply the method to the redundancy resolution problem is discussed and analytical methods to avoid joint limits are developed in the position domain. Lastly, the validity of the methods is verified by kinematic simulations.

Closed-form inverse kinematic solution for fluoroscopic C-arms

This paper presents a closed-form solution to the inverse kinematic problem for general fluoroscopic C-arms. The resulting algorithm determines the necessary joint parameters for imaging a given point of interest p→ from a given direction z→. The existence and uniqueness of the solution is proven for all p→ and z→. The inverse kinematics lays the basis for a completely robotized C-arm. The paper describes some applications for such an automatized device and presents the first results.

The model-based dynamic hand posture identification using genetic algorithm

This paper proposes a new hand posture identification system which applies genetic algorithm to develop an efficient 3D hand-model-fitting method. The 3D hand-model-fitting method consists of (1) finding the closed-form inverse kinematics solution, (2) defining the alignment measure function for the wrist-fitting process, and (3) applying genetic algorithm to develop the dynamic hand posture identification process. In contrast to the conventional computationally intensive hand-model-fitting methods, we develop an off-line training process to find the closed-form inverse kinematics solution functions, and a fast model-based hand posture identification process. In the experiments, we will illustrate that our hand posture identification system is very effective.

Parallel manipulator kinematics learning using holographic neural network models

The forward kinematic problem of parallel manipulators is resolved using a holographic neural paradigm. In a holographic neural model, stimulus–response (input–output) associations are transformed from the domain of real numbers to the domain of complex vectors. An element of information within the holographic neural paradigm has a semantic content represented by phase information and a confidence level assigned in the magnitude of the complex scalar. Networks are trained on a database generated from the closed-form inverse kinematic solutions. After the learning phase, the networks are tested on trajectories which were not part of the training data. The simulation results, given for a planar three-degree-of-freedom parallel manipulator with revolute joints and for a spherical three-degree-of-freedom parallel manipulator, show that holographic neural network models are feasible to solve the forward kinematic problem of parallel manipulators.

Model-based articulated hand motion tracking for gesture recognition

Conventional model-based hand gesture analysis systems require high computation cost to solve the finger inverse kinematics that makes them very difficult for real-time implementation. In this paper, we propose a fast hand model fitting method for the tracking of hand motion. The model fitting method consists of (1) finding the closed-form inverse kinematics solution for the finger fitting process, and (2) defining the alignment measure for the wrist fitting process. In the experiments, we illustrate that our hand model fitting method is effective and real-time implementable.