Inverse Kinematics Solution Research Articles

A Combined Planning Method Based on Biarc Curve and Bézier Curve for Concentric Cable-Driven Manipulators Working in Confined Environments

The concentric cable-driven manipulator is becoming increasingly important in minimally invasive surgery. Obviously, one of the basic requirements is to track trajectory and avoid collision at the same time. However, the unavoidable difficulty is to choose an inverse kinematics solution that fits inside the confined environment from infinitely many solutions due to its redundancy. This article proposes a combined planning method based on biarc curve and Bézier curve for the concentric cable-driven manipulator tracking desired trajectory in confined 2-D and 3-D. First, the new proposed structure and the nomenclature are introduced. Then, the kinematic modeling of the concentric cable-driven manipulator in actuator space, configuration space, and task space is detailed. Thereafter, using the proposed biarc curve, the relationship between the end direction and bending angles is comprehensively analyzed. The Bézier curve is then adopted to plan the desired path for the concentric cable-driven manipulator moving in confined 2-D and 3-D environments. Finally, the proposed combined planning method based on biarc curve and Bézier curve is experimentally verified in a trajectory tracking task simulating a large intestine examination in both the typical “C” configuration (2-D environment) and the “S” configuration (3-D environment). The results prove that the combined planning method based on biarc curve and Bézier curve can be applied to generate a reasonable solution for concentric cable-driven manipulators that are confined both 2-D and 3-D environments.

Hyper-Redundant Manipulators for Operations in Confined Space: Typical Applications, Key Technologies, and Grand Challenges

In this article, we review the state of the art in hyper-redundant manipulators for applications in confined space such as <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> -orbit services. With their multiple degrees of freedom and slender links, hyper-redundant manipulators can offer superior dexterity and excellent operability. They can traverse freely, manipulate objects flexibly, and conform to curvilinear paths accurately in confined spaces. The by-design separation of the mechanical and electrical parts in these manipulators also offers inherent structural compliance and miniaturization. Due to the elastic characteristics of driving cables, hyper-redundant manipulators have both stiffness and flexibility. In this article, the overviews of the current state of the art in this field are provided from the perspectives of both typical applications and key technologies. We detailed the relevant studies on the configuration, obstacle avoidance, path planning, and control technologies for hyper-redundant manipulators and highlight the use of these studies in the development of practical applications. Furthermore, we propose several aspects that need to be further studied, namely efficient inverse kinematics solution, strong coupled dynamics modeling, variable stiffness control, and multiobjective trajectory optimization. Breakthroughs in these areas will provide valuable solutions for complex path planning and control of hyper-redundant manipulators. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>

Singularity Analysis and Complete Methods to Compute the Inverse Kinematics for a 6-DOF UR/TM-Type Robot

Improving the strategies employed to control robotic arms is of great importance because of the increase in their use in advanced supervisory control strategies, such as digital twins. The inverse kinematic (IK) control of manipulators requires an IK solution and an awareness of the singular configurations. This work presents a complete IK calculation system with singularity analysis for the UR5 robotic arm created by Universal Robots. For a specific robot pose, different angle solution sets are obtained, and one of these solution sets has to be selected to achieve movement continuity and avoid singularities. Two methods for this double purpose are proposed: one calculates all the solution possibilities, and the other obtains only one solution set by following a sequence of decisions and calculations clearly stated by a finite state machine (FSM). Both methods are effective in managing singularities. The FSM-based method complements the IK solution procedure with advantages in the number of computations and performance by producing results that would not lead the joints to move abruptly. The results prove that the presented methods select an IK solution that does not result in a singular configuration, and that most of the time, they lead to the same valid IK solution.

A cable-driven highly compact single port laparoscopic surgical robot with sequentially inserted arms.

The single port surgical robot causes only one incision and brings many benefits to patients. It is very challenging to design a single port surgical robot that causes a smaller incision than current products. This paper presents a highly compact single port laparoscopy surgical robot, which makes full use of the space of the port and only needs a 15 mm-diameter port. The robot is composed of a camera manipulator and two operating manipulators. The non-fully cylindrical manipulators enter the port sequentially, and the equivalent diameter of each operating manipulator is 12mm. An additional 9 mm-diameter channel is left for other surgical tools to pass through after all manipulators entering the port. The kinematics model of the robot is established, including detailed forward kinematics model and inverse kinematics solution based on geometric iteration method. The teleoperation experiment shows that the manipulator can complete the object-grasping, object-transfer and weight-lifting tasks. The proposed single port surgical robot design concept can also be extended to the field of natural orifice transluminal endoscopic surgical robots.

A Review of Cuspidal Serial and Parallel Manipulators

Abstract Cuspidal robots can move from one inverse or direct kinematic solution to another without ever passing through a singularity. These robots have remained unknown because almost all industrial robots do not have this feature. However, in fact, industrial robots are the exceptions. Some robots appeared recently in the industrial market can be shown to be cuspidal, but, surprisingly, almost nobody knows it and robot users meet difficulties in planning trajectories with these robots. This article proposes a review on the fundamental and application aspects of cuspidal robots. It addresses the important issues raised by these robots for the design and planning of trajectories. The identification of all cuspidal robots is still an open issue. This article recalls in details the case of serial robots with three joints, but it also addresses robots with more complex architectures such as 6-revolute-jointed robot and parallel robots. We hope that this article will help disseminate more wide knowledge on cuspidal robots.

Inverse kinematics solution of CMOR short carrier manipulator

CMOR is a heavy-duty manipulator system applied to the maintenance of fusion reactor components. On the basis of fully considering the configuration characteristics of the manipulator, the geometric solution based on coordinate transformation combined with the analytical method is used to solve the inverse kinematics of the manipulator. First, the modified D-H method is used to establish the link coordinate system model of the CMOR carrier manipulator, and the forward kinematics is deduced. Then, based on the end pose 0T7 and the geometric structure of the manipulator, the movement range of the redundant degree of freedom d1 is deduced, and the remaining joint angles are obtained through the mapping solution and verified in MATLAB. The simulation results show that the method has high precision, reduces the overall calculation amount, and is conducive to the real-time and accurate maintenance movement of the carrier manipulator, which is of great significance for the maintenance of fusion reactors.

DESIGN, KINEMATICS AND MANIPULABILITY ANALYSES OF A SERIAL-LINK ROBOT FOR MINIMALLY INVASIVE TREATMENT IN FEMORAL SHAFT FRACTURES

The application of robot in orthopedic clinical surgery is more and more accepted. A femoral fracture reduction robot is described in the paper. The mechanism of the manipulator comprises a six-DOF serial-link robot, referred to as a 3P3R robot, with three prismatic joints and three rotational joints (including one for the knee). The manipulability of the system was analyzed, and its operability over the entire whole work space was verified. In addition, the existence of an inverse kinematic solution of the system was established, and the same was analytically implemented with physical meaningfulness. The kinematic analysis and investigation of the workspace confirmed the feasibility of the mechanism for the given design parameters. The joint displacements and rotation angles required to achieve the desired posture of the end-effector of the mechanism were also determined. The results of simulation substantiated the effectiveness of the developed robotic system, and its prospect for practical application through further research.

A novel method for computing self-motion manifolds

For kinematically redundant robots, self-motion manifolds that represent all the inverse kinematic solutions for a given end-effector location play a significant role in global motion planning. However, the efficient computation of self-motion manifolds, especially the computation of high-dimensional manifolds, is still a problem that needs to be solved. In this paper, the grid elements modeling criteria are formulated, and the specific modeling method of a grid element in the configuration space is developed. Based on the idea of cellular automata, the problem of computing self-motion manifolds is transformed into a dynamic model searching problem, and an evolution strategy is proposed to realize the efficient computation of self-motion manifolds. Finally, two examples are used to verify the effectiveness of the proposed method in computing high-dimensional self-motion manifolds. The results show that compared to the conventional methods, the proposed method can correctly identify all the self-motion manifolds with 94% reduced computational time on average.

Forward and inverse kinematics solution of a robotic manipulator using a multilayer feedforward neural network

In this paper, a multilayer feedforward neural network (MLFFNN) is proposed for solving the problem of forward and inverse kinematics of the manipulator. For forward kinematics solution, two cases are presented. The first case is that one MLFFNN is designed and trained to find only the position of the robot end-effector. In the second case, another MLFFNN is designed and trained to find both the position and the orientation of the robot end-effector. Both MLFFNNs are designed considering the joints’ positions as the inputs. For inverse kinematics solution, a MLFFNN is designed and trained to find the joints’ positions considering the position and the orientation of the robot end-effector as the inputs. For training any of the proposed MLFFNNs, data are generated in MATLAB using two different cases. The first case is considering incremental motion of the robot joints, whereas the second case is considering a sinusoidal motion. This method is designed to be generalized to any DOF manipulator. For simplicity, it is applied using a 2-DOF planar robot. The results show that the approximation error between the desired and estimated output is very low and approximately zero. The MLFFNN is efficient to solve the forward and inverse kinematics problems.

General inverse kinematics method for 7-DOF offset manipulators based on arm angle parameterization

This paper proposes a general numerical methodology of inverse kinematics computation for 7-degree-of-freedom offset manipulators based on arm angle parameterization. First, analytical inverse kinematics solutions for two types of Spherical-Revolute-Spherical manipulators are derived based on arm angle parameterization. Then, the inverse kinematics of the offset manipulator is solved using a simplified manipulator. In each iteration of the algorithm, the inverse solution of the simplified manipulator is used to calculate the position and arm angle error between the actual manipulator and desired value. The error is utilized to compensate the position and arm angle of the simplified manipulator so that the inverse solution of the simplified manipulator gradually approaches the desired solution of the actual manipulator. Moreover, the problems of workspace reduction due to structure simplification and the placement of the iteration point outside of the workspace of the simplified manipulator are optimized. Additionally, the algorithm singularity problem of the offset manipulator is solved via the dual arm angle parameterization method. Finally, the method is validated by numerical simulation and physical experiments.

Learning-Based Approach to Inverse Kinematics of Wheeled Mobile Continuum Manipulators

Continuum manipulators have been the subject of intensive research due to their inherent flexibility, allowing them to have a dexterous positioning, even in restricted environments. However, while research abounds on static continuum manipulators, a few are interested in wheeled mobile continuum manipulators (WMCMs), where the workspace is extended, and additional degrees of freedom can be used to perform more complex tasks. This article proposes a learning framework for solving the inverse kinematics (IK) of the WMCM while maintaining multiple IK solutions. The configuration space of the WMCM is discretized to reduce the infinite number of IK solutions to a finite number. Besides, the WMCM’s IK problem is transformed into a single-section IK problem of the continuum manipulator by parameterizing the mobile platform’s variables and the actuating variables of the first <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(N-1)$</tex-math></inline-formula> sections, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> being the number of sections. The parameterization is carried out by clustering the WMCM workspace using the growing neural gas algorithm. The proposed approach is validated by performing simulations and experiments on a WMCM named Robotino XT.

Human-like redundancy resolution: An integrated inverse kinematics scheme for anthropomorphic manipulators with radial elbow offset

As a mimic of the human arm structure, anthropomorphic manipulators with radial elbow offset (AMREO) are often deployed on humanoid service robots. However, the unique offset leads to difficulties in solving the analytical inverse kinematics (IK), which poses a challenge for further anthropomorphic control. This paper presents an integrated scheme for solving the path-wise IK problem of a 7-DoF AMREO in the position domain. Unlike other approaches, special attention is paid to the naturalness of the arm configuration, with the aim of making AMREO exhibit human-like behavior in human-centered environments. First, an analytical IK solution of AMREO for a single end-effector pose is derived based on the arm angle parameterization. Then, inspired by the habitual arm configurations in human reaching movements, the natural arm configuration mapped to wrist position is proposed for AMREO. To learn the patterns implied therein, a LSTM-based natural arm angle prediction network (NAPN) is designed and trained based on a human demonstration dataset. Finally, a redundancy resolution framework embedded with NAPN is built to generate smooth and natural joint configurations in the path-wise IK tasks. Comparative experiments show that the proposed analytical IK algorithm has better computational efficiency and precision than conventional methods, and can give complete results for one IK call within 4 μs. In addition, continuous path tracking experiments on a real robot validate the effectiveness and anthropomorphism of the redundancy resolution scheme based on NAPN.

Wild Geese Migration Optimization Algorithm: A New Meta-Heuristic Algorithm for Solving Inverse Kinematics of Robot.

This paper proposes a new meta-heuristic algorithm, named wild geese migration optimization (GMO) algorithm. It is inspired by the social behavior of wild geese swarming in nature. They maintain a special formation for long-distance migration in small groups for survival and reproduction. The mathematical model is established based on these social behaviors to solve optimization problems. Meanwhile, the performance of the GMO algorithm is tested on the stable benchmark function of CEC2017, and its potential for dealing with practical problems is studied in five engineering design problems and the inverse kinematics solution of robot. The test results show that the GMO algorithm has excellent computational performance compared to other algorithms. The practical application results show that the GMO algorithm has strong applicability, more accurate optimization results, and more competitiveness in challenging problems with unknown search space, compared with well-known algorithms in the literature. The proposal of GMO algorithm enriches the team of swarm intelligence optimization algorithms and also provides a new solution for solving engineering design problems and inverse kinematics of robots.

Axis manipulation to solve Inverse Kinematics of Hyper-Redundant Robot in 3D Space

A solution based on inverse kinematics is required for the robot's end effector, also known as its tip, to reach a target. Current methods for solving the inverse kinematics solution for a hyper-redundant robot in three 3D are generally complex, difficult to visualize, and time-intensive. This requires the development of new algorithms for solving inverse kinematics in a quicker and more efficient manner. In this study, an axis manipulation using a geometrical approach is used. Initially, a general algorithm for a 2 m-link hyper-redundant robot in 3D is generated. The method employed a repetitive basic inverse kinematics solution of a two-link robot on virtual links. The virtual links are generated using a specific geometric proposition. Finally, the 3D solution is generated by rotating about the global z-axis. This method reduces the mathematical complexity required to solve the inverse kinematics solution for a 2-m-link robot. In addition, this method can manage variable link manipulators, thereby eliminating singularity. To demonstrate the effectiveness of the model, numerical simulations of hyper redundant models in 3D are presented. This new geometric approach is anticipated to enhance the performance of hyper-redundant robots, enabling them to be of greater assistance in fields such as medicine, the military, and search and rescue.

A Novel Inverse Kinematic Solution of a Six-DOF Robot Using Neural Networks Based on the Taguchi Optimization Technique

The choice of structural parameters in the design of artificial neural networks is generally based on trial-and-error procedures. They are regularly estimated based on the previous experience of the researcher, investing large amounts of time and processing resources during network training, which are usually limited and do not guarantee the optimal selection of parameters. This paper presents a procedure for the optimization of the training dataset and the optimization of the structural parameters of a neural network through the application of a robust neural network design methodology based on the design philosophy proposed by Genichi Taguchi, applied to the solution of inverse kinematics in an open source, six-degrees-of-freedom robotic manipulator. The results obtained during the optimization process of the structural parameters of the network show an improvement in the accuracy of the results, reaching a high prediction percentage and maintaining a margin of error of less than 5%.

An Inverse Kinematics Solution for a Series-Parallel Hybrid Banana-Harvesting Robot Based on Deep Reinforcement Learning

A series-parallel hybrid banana-harvesting robot was previously developed to pick bananas, with inverse kinematics intractable to an address. This paper investigates a deep reinforcement learning-based inverse kinematics solution to guide the banana-harvesting robot toward a specified target. Because deep reinforcement learning algorithms always struggle to explore huge robot workspaces, a practical technique called automatic goal generation is first developed. This draws random targets from a dynamic uniform distribution with increasing randomness to facilitate deep reinforcement learning algorithms to explore the entire robot workspace. Then, automatic goal generation is applied to a state-of-the-art deep reinforcement learning algorithm, the twin-delayed deep deterministic policy gradient, to learn an effective inverse kinematics solution. Simulation experiments show that with automatic goal generation, the twin-delayed deep deterministic policy gradient solved the inverse kinematics problem with a success rate of 96.1% and an average running time of 23.8 milliseconds; without automatic goal generation, the success rate was just 81.2%. Field experiments show that the proposed method successfully guided the robot to approach all targets. These demonstrate that automatic goal generation enables deep reinforcement learning to effectively explore the robot workspace and to learn a robust and efficient inverse kinematics policy, which can, therefore, be applied to the developed series-parallel hybrid banana-harvesting robot.

A PI Control Method with HGSO Parameter Regulator for Trajectory Planning of 9-DOF Redundant Manipulator.

In order to solve the tracking accuracy problem of the redundant manipulator, a PI control method with Henry gas solubility optimization parameter regulator (PI-HGSO) is proposed in this paper. This method consists of the controller and the parameter regulator. The characteristic is that the position deviation of a manipulator is equivalent to a specific function; namely, the proportional-integral (PI) controller is used to adjust the deviation input. The error can be better corrected by the processing of the PI controller so that the inverse kinematics solution of the minimum error can be realized. At the same time, the parameter selection of PI controllers has always been a difficulty in controller design. To address the problem, Henry gas solubility optimization (HGSO) is selected as a parameter regulator to optimize the parameters and obtain the optimal controller, thereby achieving high-precision trajectory tracking. Experiments on 9-DOF redundant manipulator show that our method achieves competitive tracking accuracy in contrast with others. Meanwhile, the efficiency and accuracy of the PI controller are greatly guaranteed by using HGSO to automatically optimize controller parameters instead of making approximate adjustments through infinite manual trial and error. Therefore, the feasibility and competitive superiority of PI-HGSO is fully proved in trajectory planning of redundant manipulators.

An Improved Inverse Kinematics Solution for a Robot Arm Trajectory Using Multiple Adaptive Neuro-Fuzzy Inference Systems

Inverse kinematics of robots is a critical topic in the robotics field. Although there are conventional ways of solving inverse kinematics, soft computing is an important technology that has lately gained prominence due to its ability to reduce the complexity of the inverse kinematics problem. This paper presents an inverse kinematics solution using multiple adaptive neuro-fuzzy inference systems (MANFIS). Different models were established by employing various methods of identification. Subtractive Clustering (SCM), Fuzzy C-Means Clustering (FCM), and Grid Partitioning (GP) are the three methods used in this study. This work is being carried out on a 5-DOF articulated robot arm, which is commonly used in industry. A mathematical model is built based on the Denavit-Hartenberg (DH) approach. Following confirmation that the kinematic findings of the mathematical model match the actual observed values of the robot arm, two types of data sets are generated: a random data set and a systematic data set based on a trajectory. The data sets are then utilized to train and evaluate ANFIS models and choose the optimal models to develop MANFIS model. Thus, the prediction and experimental data are compared to assess the performance of the MANFIS model.

A Cable-Driven Hyperredundant Manipulator: Obstacle-Avoidance Path Planning and Tension Optimization

Manipulators with a hyperredundant and large aspect ratio are becoming more commonly used to detect complex and narrow spaces. The hyperredundant feature confers advantages for such manipulator types in comparison to traditional manipulators. However, they also introduce path-planning challenges. Due to the characteristics of hyperredundancy, there are countless inverse kinematics solutions, and the path-planning method that is used for traditional manipulators cannot be directly applied to these hyperredundancy manipulators in terms of the number of calculations or adaptability of the algorithm.

The Wearable Lower Limb Rehabilitation Exoskeleton Kinematic Analysis and Simulation.

In recent years, due to the increase in the incidence of traffic accidents, the number of people with limb injuries has also increased. At the same time, among the aging population, neurological diseases or cardiovascular and cerebrovascular diseases have caused many people to have limb hemiplegia. It has been clinically proven that the use of rehabilitation equipment can help patients with limb injuries to restore limb motor function. This paper takes wearable lower limb rehabilitation exoskeleton as the research object, and its main contents are mechanical structure design, kinematics analysis, gait planning, virtual prototype simulation, and experimental verification and analysis. Based on the physiological characteristics of human body and the principle of comfortable and reliable wearing, this paper designs wearable exoskeleton for lower limb rehabilitation. Firstly, the physiological structure characteristics and movement mechanism of human lower limbs were studied and analyzed. By referring to the rotation range and height and size of each joint of human lower limbs, the overall scheme of wearable lower limb rehabilitation exoskeleton was designed and the degree of freedom was allocated. At the same time, Solidworks was used to establish a three-dimensional model. On the basis of a 3D model, a kinematics model was established, and the forward kinematics solution was obtained by using homogeneous coordinate transformation. Since the inverse kinematics solution was relatively complicated, the inverse kinematics solution was conducted in this paper according to the geometric relations of the joints of the lower limbs. Kinematics analysis of the exoskeleton structure of wearable lower limb rehabilitation was carried out to lay a theoretical foundation for gait planning. The off-line gait planning was carried out by using the method based on ZMP stability criterion, and the gait planning was divided into five stages: squat, start, middle step, stop and rise, and the motion trajectory of the center of mass and ankle joint was planned. Based on the inverse kinematics formula, the function of the change of joint angle with time in walking process is derived. The virtual prototype is established in ADAMS, and the simulation of virtual prototype is carried out by using the function of gait planning's joint angle and time. The correctness of structural design and gait planning was verified by measuring the trajectories of the centroid and ankle joints in each gait stage and the functional relationship between the rotation angle of each joint and time. Then, using a 3D dynamic capture system to capture the human lower limb motion trajectory of each joint, each joint trajectory data output, using the MATLAB software to output data, gets the joint trajectory change over time function curve and is used to verify feasibility and applicability of human gait planning. Through the research and analysis of the joints of the lower limbs of the human body, it can be concluded that the hip joint and the knee joint have 3 degrees of freedom, respectively, and the knee joint has 1 degree of freedom.