Hyper-redundant manipulators are produced by cascading several mechanisms on top of each other as modules. The discrete actuation makes their control easier because discrete actuators usually do not need any feedback to control. So far, several methods have been proposed to solve the inverse kinematic problem of discretely actuated, hyper-redundant manipulators. The two-by-two searching method is better than the other methods in terms of CPU time and error. In this article, the mentioned method is generalized by choosing an arbitrary number of modules as pending modules in each step of the solution instead of the necessary two. For validation, the proposed method is compared with nine meta-heuristic searching algorithms: simulated annealing, genetic algorithm, particle swarm optimization, ant colony optimization, gray wolf optimizer, stochastic fractal search, whale optimization algorithm, Giza pyramid construction, and flying fox optimization. Furthermore, the effect of the number of pending modules on CPU time and error is investigated. All the numerical problems have been solved for two case studies, one is planar and the other is spatial.

Inverse kinematics of robot is the basis of robot assembly, which directly determines the pose of robot. Because the traditional inverse solution algorithm is limited by the robot topology structure, singular pose and inverse solution accuracy, it affects the use of robots. In order to solve the above problems, an improved particle swarm optimization (PSO) algorithm is proposed to solve the inverse problem of robot. This algorithm initializes the particle population based on joint angle limitations, accelerating the convergence speed of the algorithm. In order to avoid falling into local optima and premature convergence, we have proposed a nonlinear weight strategy to update the speed and position of particles, enhancing the algorithm’s search ability, in addition introducing a penalty function to eliminate particles exceeding joint limits. Finally, the positions of common points and singular points are selected on PUMA 560 robot and redundant robot for inverse kinematics simulation verification. The results show that, compared with other algorithms, the improved PSO algorithm has higher convergence accuracy and better convergence speed in solving the inverse solution, and the algorithm has certain universality, which provides a new solution for the inverse kinematics solution of the assembly robot.

This paper proposes a new type of hybrid manipulator that can be of extensive use in industries where translational motion is required while maintaining an arbitrary end-effector orientation. It consists of two serially connected parallel mechanisms, each having three degrees of freedom, of which the upper platform performs a pure translational motion with respect to the mid-platform. Closed-form forward and inverse kinematic analysis of the proposed manipulator has been carried out. It is followed by the determination of all of its singular configurations. The theoretical results have been verified numerically, and the 3D modeling and simulation of the manipulator have also been performed. A simple optimal design is presented based on optimizing the kinematic manipulability, which further demonstrates the potential of the proposed hybrid manipulator.

In order to resolve redundancy and path planning of a high DOF mobile manipulator using conventional approaches like Jacobian and a pseudoinverse method, researchers face the limitation of computational load and delay in response. If such kind of mobile manipulator is traversing the rough terrain, then conventional methods become too costly to implement due to the handling of redundant joints, obstacles, and wheel-terrain interaction. A few optimization-based redundancy resolution approaches try incorporating wheel-terrain interaction but fail in real-time response. This paper describes a 14 DOF Rover Manipulator System’s end-effector path-tracking approach using CG-Space framework to incorporate wheel-terrain interaction. CG-Space means the center of gravity (CG) locus of the Rover. The Rover’s CG is calculated while traversing over 3D terrain using a multivariable optimization method and a 3D point cloud image of the actual terrain and stored as CG-Space over the given terrain. First of all, we decide which part of the system moves to track the path, that is, arm or Rover, depending upon the manipulator’s work volume and manipulability measure restrictions. The next task is to obtain the Rover pose according to the end-effector path using a simple arm’s inverse kinematic solution between the CG-Space and end-effector task space without resolving redundancy. Meanwhile, obstacles and non-traversable regions are avoided in CG-Space. On diverse 3D terrains, simulation and experimental results support the suggested CG-Space framework for end-effector tracking.

Hyper-redundant robots have good prospects for applications in confined space due to their high flexibility and slim body size. However, the super-redundant structure brings great challenges for its inverse kinematics with shape constraints. Unfortunately, traditional Jacobian pseudo-inverse-based inverse kinematics method and forward and backward reaching inverse kinematics (FABRIK) method are difficult to constrain the arm shape and realize trajectory tracking in confined spaces. To solve this problem, we propose a shape-controllable FABRIK method to satisfy the given path and shape constraints. Firstly, the kinematic model of the hyper-redundant robot is established, and the canonical FABRIK method is introduced. Based on the preliminary works, the single-layer improved FABRIK method is developed to solve the position and pointing inverse kinematics considering path environment and joint angle constraints instead of two-layer geometric iterations. For tracking the desired end roll angles, the polygonal virtual arm is designed. The real arm roll angle is achieved by controlling its winding on the virtual arm. In this way, the shape can be controlled. Finally, we compare the proposed method with other three approaches by simulations. Results show that the proposed method is more efficient and the arm shape is controllable.

This paper presents a comprehensive study of the forward and inverse kinematics of a six-degrees-of-freedom (DoF) spatial manipulator with a novel architecture. Developed by Systemantics India Pvt. Ltd., Bangalore, and designated as the H6A (i.e., Hybrid 6-Axis), this manipulator consists of two arm-like branches, which are attached to a rigid waist at the proximal end and are coupled together via a wrist assembly at the other. Kinematics of the manipulator is challenging due to the presence of two multi-DoF passive joints: a spherical joint in the right arm and a universal in the left. The forward kinematic problem has eight solutions, which are derived analytically in the closed form. The inverse kinematic problem leads to $160$ solutions and involves the derivation of a $40$-degree polynomial equation, whose coefficients are obtained as closed-form symbolic expressions of the pose parameters of the end-effector, thus ensuring the generality of the results over all possible inputs. Furthermore, the analyses performed lead naturally to the conditions for various singularities involved, including certain non-trivial architecture singularities. The results are illustrated via numerical examples which are validated extensively.

Thanks to recent developments in service robotics technologies, precision agriculture (PA) is becoming an increasingly prominent research field, and several studies were made to present and outline how the use of mobile robotic systems can help and improve farm production. In this paper, the integration of a custom-designed mobile base with a commercial robotic arm is presented, showing the functionality and features of the overall system for crop monitoring and sampling. To this aim, the motion planning problem is addressed, developing a tailored algorithm based on the so-called manipulability index, that treats the base and robotic arm mobility as two independent degrees of motion; also developing an open source closed-form inverse kinematics algorithm for the kinematically redundant manipulator. The presented methods and sub-system, even though strictly related to a specific mobile manipulator system, can be adapted not only to PA applications where a mobile manipulator is involved but also to the wider field of assistive robotics.

This paper, based on the idea of redundancy angle discretisation, proposes an obstacle avoidance method for the fixed tip pose trajectory of a seven degrees-of-freedom (7-DOF) modular manipulator. First, for the case in which a specific redundancy angle is given, the analytical solutions of the redundant manipulator left 6-DOF subchain are found. Then, through the discretisation of the redundancy angle, the concept of the self-motion space of the tip pose is proposed and is extended to the concept of the self-motion space of the trajectory. Based on this discrete space, a path-planning algorithm is proposed to help select the appropriate redundancy angles to obtain the collision-free solution set of the fixed Cartesian trajectory. However, due to the large fluctuation of the obtained path, a path optimisation method based on the path cost is proposed to smooth the path, and the continuous and collision-free solution set of the manipulator tip’s trajectory is obtained. The method proposed in this paper provides a new thought for the problem of collision-free solution set planning for the Cartesian trajectory of a 7-DOF manipulator and it has great application potential in working environments with high accuracy requirements for the trajectory.

The repetitive motion planning movements of the redundant manipulator will cause oscillations and unintended swings of joints, which increase the risk of collisions between the manipulator and its surroundings. Motivated by this phenomenon, this paper presents an inverse kinematics algorithm for the spherical-revolute-spherical manipulator to solve the paradox raised by joint-drift and control the pose with no swing of the elbow. This algorithm takes the joint Cartesian positions set as the intermediary and divides the inverse solution process into two mapping processes within joint limits. Simulations are executed to evaluate this algorithm, and the results show this algorithm is applicable to repetitive motion planning and is capable of producing superior configurations based on its real-time ability and stable solve rate. Experiments using the 7-degree-of-freedom spherical-revolute-spherical manipulator demonstrate the effectiveness of this algorithm to remedy the joint-drift and elbow swing compared to Kinematics and Dynamics Library and TRAC-IK.

This paper presents an investigation of the effectiveness of different inverse kinematics strategies in a context of physical human-robot interaction in which passive articulated shells are mounted on the links of a serial robot for manual guidance. The concept of passive link shells is first recalled. Then, inverse kinematics strategies that are designed to plan the trajectory of the robot according to the motion sensed at the link shells are presented and formulated. The different approaches presented all aim at interpreting the motion of the shells and provide an intuitive interaction to the human user. Damped Jacobian based methods are introduced in order to alleviate singularities. A serial 5-dof robot used in previous work is briefly introduced and is used as a test case for the proposed inverse kinematics schemes. The robot includes two link shells for interaction. Simulation results based on the different inverse kinematic strategies are then presented and compared. Finally, general observations and recommendations are discussed.

Due to the merits of high rigidity and good dynamics, hybrid machine tools have been gradually applied to efficient machining of thin-walled workpiece with complex geometries. However, the discontinuity of tangential component of toolpath in hybrid machine tools may cause velocity fluctuations, leading to poor surface quality of workpiece. In this paper, a novel 5-axis hybrid machine tool is taken as an example to demonstrate a smooth toolpath interpolation method. First, an adaptive acceleration and deceleration control algorithm is presented to realize the smooth transition between two constrained velocity points. Second, a spline curve-based interpolation algorithm is proposed to realize the smoothness of the trajectory. Meanwhile, a parameter synchronization method is proposed to ensure the synchronization of the interpolated tool-axis vector and the interpolated tool tip. Thirdly, an inverse kinematic analysis is conducted based on an inverse position solution model and a velocity mapping model. Finally, a set of machining tests on S-shape workpiece in line with the ISO standard is carried out to verify the effectiveness of the proposed smooth toolpath interpolation method.

Body posture determination methods have many applications, including product design, ergonomic workplace design, human body simulation, virtual reality, and animation industry. Initiated in robotics, inverse kinematic (IK) method has been widely applied to proactive human body posture estimation. The analytic inverse kinematic (AIK) method is a convenient and time-saving type of IK methods. It is also indicated that, based on AIK methods, a specific body posture can be determined by the optimization of an arbitrary objective function. The objective of this paper is to predict the postures of human arms during reaching tasks. In this research, a human body model is established in MATLAB, where the middle rotation axis analytic kinematic method is accomplished, based on this model. The joint displacement function and joint discomfort function are selected to be initially applied in this AIK method. Results show that neither the joint displacement function nor the joint discomfort function predicts postures that are close enough to natural upper limb postures of human being, during reaching tasks. Therefore, a bi-criterion objective function is proposed by integrating the joint displacement function and joint discomfort function. The accuracy of the arm postures, predicted by the proposed objective function, is the most satisfactory, while the optimal value of the coefficient, in the proposed objective function, is determined by golden section search.

Efficiently 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.

In this paper, the inverse kinematics (IK) of redundant manipulators is presented and studied, where the performance of end-effector path planning is guaranteed. A new Jacobian pseudoinverse (JP)-based IK method is proposed and studied using a typical numerical difference rule to discretize the existing IK method based on JP. The proposed method is depicted in a discrete-time form and is theoretically proven to exhibit great performance in the IK of redundant manipulators. A discrete-time repetitive path planning (DTRPP) scheme and a discrete-time obstacle avoidance (DTOA) scheme are developed for redundant manipulators using the proposed method. Comparative simulations are conducted on a universal robot manipulator and a PA10 robot manipulator to validate the effectiveness and superior performance of the DTRPP scheme, the DTOA scheme, and the proposed JP-based IK method.

The 7 degrees of freedom (DOF) redundant manipulator greatly improves obstacle/singularity avoidance capability and operational flexibility. However, the inverse kinematics problem of this manipulator is very difficult to solve because it has an infinite number of solutions. This paper uses a new numerical sequence processing method with a closed-loop framework to solve the inverse kinematics of the 7-DOF redundant manipulator. Simulation and experiment show that this method has high commonality. No special structure of the robot is required, and this method has improved computational efficiency and reliability.

The Inverse Kinematics (IK) problem of manipulators can be divided into two distinct steps: (1) Problem formulation, where the problem is developed into a form which can then be solved using various methods. (2) Problem solution, where the IK problem is actually solved by producing the values of different joint space variables (joint angles, joint velocities or joint accelerations). The main focus of this paper is concentrated on the discussion of the IK problem of redundant manipulators, formulated as a quadratic programming optimization problem solved by different kinds of recurrent neural networks.

A 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.

This paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

This paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a novel spherical robot that is called a 3(RPSP)-S parallel manipulator. The proposed manipulator provides high rotational displacement of the moving platform for low angular displacement of the motors. The advised robot is suitable for repetitive oscillatory applications (for example, wrist and ankle rehabilitation and table of autopilot and gyroscope life test, etc.). First, we describe the structure of the proposed manipulator and solve the inverse kinematics problem of the manipulator. Next, based on the principle of virtual work, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated and verified by a special dynamics modeling commercial software (MSC ADAMS).

The cyclic coordinate descent (CCD) method is a popular loop closure method in protein structure modeling. It is a robotics algorithm originally developed for inverse kinematic applications. We demonstrate an effective method of building the backbone of protein structure models using the principle of CCD and a guiding trace. For medium-resolution 3-dimensional (3D) images derived using cryo-electron microscopy (cryo-EM), it is possible to obtain guiding traces of secondary structures and their skeleton connections. Our new method, constrained cyclic coordinate descent (CCCD), builds α-helices, β-strands, and loops quickly and fairly accurately along predefined traces. We show that it is possible to build the entire backbone of a protein fairly accurately when the guiding traces are accurate. In a test of 10 proteins, the models constructed using CCCD show an average of 3.91 Å of backbone root mean square deviation (RMSD). When the CCCD method is incorporated in a simulated annealing framework to sample possible shift, translation, and rotation freedom, the models built with the true topology were ranked high on the list, with an average backbone RMSD100 of 3.76 Å. CCCD is an effective method for modeling atomic structures after secondary structure traces and skeletons are extracted from 3D cryo-EM images.