Inverse Kinematics Problem Research Articles

Modelling of aircraft trajectories for emergency landing using kinematoid chains

Most methods that compute trajectories for un- or low-powered flight operate under simplifying assumptions such as constant curve radii and wind conditions. Likewise, changes of air density with altitude that lead to significant differences between equivalent airspeed (EAS) und true airspeed (TAS) are often not considered. Some approaches are based on Dubins paths, which are introduced in Dubins LE (Am J Math 79: 497, 1957). They combine three sections to form a trajectory, which is the shortest from a given start to an end position (In the original work, the position extended by the heading, is referred to as configuration. Since configuration has a different connotation in our context, we use the term state, which can contain other parameters in addition to the position and the heading, e.g. orientation, configuration of landing flaps, landing gear, etc.). A maximum distant landing spot can be reached this way. Often, the targeted landing spot is closer to the aircraft. If it is approached using a Dubins Path, the excess height must be dealt with. Here, we present a method addressing the problem directly, namely finding a trajectory which reduces the excess height over its entire length. Furthermore, it takes spatial and temporal changes of wind and air density into account. Several conditions influence the final shape of the trajectory. For example, avoidance of obstacles and predefined areas is easily achieved. Our method is motivated by kinematic chains, which are used in robotics and computer animation. We extend and modify this principle by incrementally transferring start and end states of the trajectory, modelled as state vectors, into each other. The resulting intermediate states form ends of chain links. To connect initial and final states through the resulting chain, we solve the inverse kinematic problem known from robotics. We extend it by several conditions, which are derived from the flight mechanical characteristics of the modeled aircraft on the one hand and from the desired properties of the trajectory on the other. Using practical examples, we will show the performance of this method, which we have efficiently implemented on off-the-shelf hardware. The method is suitable for systems that assist in the event of engine failures as well as for modeling planned un- or low-powered flights like continuous descent approaches or return flights of space gliders.

Inverse Kinematics of Robot Manipulator Based on BODE-CS Algorithm

Differential evolution is a popular algorithm for solving global optimization problems. When tested, it has reportedly outperformed both robotic problems and benchmarks. However, it may have issues with local optima or premature convergence. In this paper, we present a novel BODE-CS (Bidirectional Opposite Differential Evolution–Cuckoo Search) algorithm to solve the inverse kinematics problem of a six-DOF EOD (Explosive Ordnance Disposal) robot manipulator. The hybrid algorithm was based on the differential evolution algorithm and Cuckoo Search algorithm. To avoid any local optimum and accelerate the convergence of the swarm, various strategies were introduced. Firstly, a forward-kinematics model was established, and the objective function was formulated according to the structural characteristics of the robot manipulator. Secondly, a Halton sequence and an opposite search strategy were used to initialize the individuals in the swarm. Thirdly, the optimization algorithms applied to the swarm were dynamically allocated to the Differential Evolution algorithm or the Cuckoo algorithm. Fourthly, a composite differential algorithm, which consisted of a dynamically opposite differential strategy, a bidirectional search strategy, and two other typically used differential strategies were introduced to maintain the diversity of the swarm. Finally, two adaptive parameters were introduced to optimize the amplification factor F and cross-over probability Cr. To verify the performance of the BODE-CS algorithm, two different tasks were tested. The experimental results of the simulation showed that the BODE-CS algorithm had high accuracy and a fast convergence rate, which met the requirements of an inverse solution for the manipulator.

Kinematics of the Hybrid 6-Axis (H6A) manipulator

AbstractThis 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.

An Analytical Solution for Inverse Kinematics of SSRMS-Type Redundant Manipulators

Compared with non-redundant manipulators, the self-motion of 7-DOF redundant manipulators results in an infinite number of inverse kinematics solutions for a desired end-effector pose. This paper proposes an efficient and accurate analytical solution for inverse kinematics of SSRMS-type redundant manipulators. This solution is applicable to SRS-type manipulators with the same configuration. The proposed method involves introducing an alignment constraint to restrain the self-motion and to decompose the spatial inverse kinematics problem into three independent planar subproblems simultaneously. The resulting geometric equations depend on the part of the joint angles, respectively. These equations are then computed recursively and efficiently using the sequences of (θ1,θ7), (θ2,θ6), and (θ3,θ4,θ5), generating up to sixteen sets of solutions for a given desired end-effector pose. Additionally, two complementary methods are proposed for overcoming the possible singular configuration and judging unsolvable poses. Finally, numerical simulations are conducted to investigate the performance of the proposed approach in terms of average calculation time, success rate, average position error, and the ability to plan a trajectory with singular configurations.

Inverse Kinematics: An Alternative Solution Approach Applying Metaheuristics

The inverse kinematics problem (IKP) is fundamental in robotics, but it gets harder to solve as the complexity of the mechanisms increases. For that reason, several approaches have been applied to solve it, including metaheuristic algorithms. This work presents a proposal for solving the IKP of a doubly articulated kinematic chain by means of a modified differential evolution (DE) algorithm. The novelty of the proposal is both in the modeling of the problem and the modification to the DE for solving it. The modeling is inspired by a technique used in animation software to recreate movements by dividing the complete trajectory in a number of segments. Each segment represents a single optimization problem linked to the IKP as a sequence that is solved by the modified DE where the initial population for each single problem is biased by using the solution of the previous one. The approach produces solutions for positioning the end effector in a specific point within the work space while minimizing the angular displacement between the initial and final poses. The proposal was able to obtain solutions requiring a fewer total execution cycles compared to the usual approach of solving only one optimization problem related to the inverse kinematics. Different trajectories were used to test the solutions generated by the proposed approach, and the set of conditions that must be covered to apply it to solve the IKP of a particular mechanism are presented.

Development and Experimental Studies of a Method Based on a Reference Control Signal Generating System for Redundant Serial Manipulators

The paper presents the design and experimental study of a synthesis method based on reference signal generation systems. The method can be used for all actuators of redundant manipulators. The aforementioned systems aim to save the dynamic control accuracy of the working tools of serial manipulators when they move along arbitrary spatial trajectories, taking into account restrictions in all degrees of freedom and special cases of their link positions. The maintenance of the control accuracy could be ensured by eliminating the reach of all degrees of freedom of manipulators to their limits and to indicated special positions, characterized by an ambiguity when solving the inverse kinematic problems of various serial manipulators. This is in addition to preventing the reach of their working tools to the boundaries of the working area due to the use of a redundant degree of freedom when approaching the indicated undesirable positions. The experimental studies performed in this paper confirm the efficiency of the proposed method and allow accurate characteristics to be obtained.

A Review and Comparative Study of Differential Evolution Algorithms in Solving Inverse Kinematics of Mobile Manipulator

Mobile manipulator robots have become important pieces of equipment due to the high mobility of mobile subsystems and the high flexibility of manipulator subsystems. Considering the increasing degrees of freedom and the need to avoid singular locations, one of the most challenging problems is solving the inverse kinematics problem of mobile manipulator robots (IKMM). Of all the popular optimization algorithms, the differential evolution (DE) algorithm is the most effective method for quickly solving the IKMM problem with sufficient solutions. Currently, many strategies have been proposed for DE algorithms to improve the performance of solving mathematical problems; some symmetry strategies or symmetry functions have been introduced to DE algorithms. However, the effects of various DE algorithms on solving the actual IKMM lack a comprehensive explanation. Therefore, we divide various DE algorithms into three categories considering the control parameter selection and compare the specific optimization of various DE algorithms. Then, we compare the performance of various DE algorithms when solving the inverse kinematics problems of mobile manipulators with different degrees of freedom. Considering the effectiveness and the speed of the DE algorithm on the IKMM problem, we determine the best DE algorithm by comparing the error and time required to reach 100 random mission points and tracking the typical trajectories. Finally, the best-performing DE method is further improved by studying the selection of fundamental parameters in the best DE algorithm. Valuable conclusions are obtained from these experimental simulations, which can help with choosing an algorithm that is suitable for solving the inverse kinematics problem of mobile manipulator robots in practice.

Readjustment of a robot for educational purposes

AbstractDevelopment of control of a five degrees of freedom robot is discussed in this paper. Only two robots were made, and one of these is in the University of Miskolc. The robot was made in the 80s for educational purposes, the electronic components were obsolete and control software was missing, therefore it became necessary to perform hardware improvements, and develop a new control program. Inverse kinematics problem of the robot is solved by geometric approach to formulate the joint angles, which will form the basis of the control. A braking system containing electromagnets for the robot is constructed to balance it. A printed circuit board is designed to establish the control of the system, the central element is a Cypress PSoC 5LP platform. The development of the control program is performed in software PSoC Creator 4.4. The developed control system of the robot can receive instructions from a computer via a designed special purpose user program, which is written in Python programming language. Thanks to the improvements, the robot has become operational. Thus, the robot can serve educational purposes performing different manipulation tasks. By completing the developments, students can get to know the structure and programming of the robot, its inverse kinematics problem. This will require the development of practice-oriented tasks in the future.

Proposing a Graphic Simulator for an Upper Limb Exoskeleton Robot

In this study, a graphic simulator that is used to simulate problems related to kinematics and dynamics for an exoskeleton robot arm with 5 degrees of freedom (DoF) was presented. The graphic simulator utilized the advantages of design software SolidWorks, Catia, and the computing and simulation power of SimMechanics Toolbox in Matlab. The core of the proposed graphic simulator is algorithm to solve the kinematics and dynamic problems of a developing upper-limb rehabilitation robot. The study used the proposed optimization-based algorithm to solve the inverse kinematics (IK) problem for the redundant robot model. Endpoint trajectories were imported from measurement data. The joints variable solutions obtained before entering the dynamics problem were smoothed to ensure feasibility in the later calculation process. A process to solve the inverse dynamics problem using physical model by combining the power of two software SolidWorks and SimMechanics was also proposed. This process ensured that the Robot’s design could be changed and updated to the kinematics calculation fast and easily. To evaluate this procedure, we also compared these dynamics results with results when applying the Lagrange–Euler formulation. All these calculation and simulation processes have been integrated into the graphic simulator software to show efficiency and user-friendliness.

Multi-objective optimization approach for Inverse Kinematics of redundant manipulator for welding applications

This article presents an optimization-based approach for determining the Inverse Kinematics (IK) of redundant robot manipulators for industrial welding applications. Nine degrees of freedom (DOF) kinematic configuration of a robot manipulator with one prismatic and eight revolute joints has been modelled to improve maneuverability in a welding environment. To perform welding operations at desired task space locations (TSLs), the IK are to be determined. The IK problem is solved using a constrained multi-objective optimization technique with the objective of a reachability manipulator with minimal positional and orientational errors. An obstacle avoidance algorithm is also implemented to avoid collisions during welding operations. IK Simulations of the redundant manipulator in different welding applications were performed in a MATLAB environment. The obtained results shows that the welding manipulator reached desired locations successfully and this approach is adaptable for various shapes of weld joints.

Analytical and deep learning approaches for solving the inverse kinematic problem of a high degrees of freedom robotic arm

Inverse kinematics is the basis for controlling the motion of robotic manipulators. It defines the required joint variables for the robotic end-effector accurately reach the desired location. Due to the derivation difficulty, computation complexity, singularity problem, and redundancy, analytical Inverse kinematics solutions pose numerous challenges to the operation of many robotic arms, especially for a manipulator with a high degree of freedom. This paper develops different Deep Learning networks for solving the Inverse kinematics problem of six- Degrees of Freedom robotic manipulators. The implemented neural architectures are Artificial Neural Network, Convolutional Neural Network, Long–Short Term Memory, Gated Recurrent Unit, and Bidirectional Long–Short Term Memory. In this context, we associate the proposed results with a specific tuning of Deep Learning network hyper-parameters (number of hidden layers, learning rate, Loss function, optimization algorithm, number of epochs, etc.). The Bidirectional Long–Short Term Memory network outperformed all proposed architectures. To be close as possible to the experimental results, we have included two types of noise in the training data set to validate which of the five proposed neural networks is more efficient. Furthermore, in this study, we compare the performance of analytical and soft computing solutions in generating robots’ trajectories. We include this scenario, focusing on the advantage of implementing neural networks in avoiding the singularity problem that can occur using the analytical approach. In addition, we used the RoboDK simulator to show simulation results with real-world meaning. The performance of Deep Learning models depends on the complexity of the posed problem. Moreover, the complexity of the Inverse Kinematics problem is related to the number of Degrees of Freedom. At the end of this work, we evaluate the influence of the complexity of robotic manipulators on the proposed Deep Learning networks’ performance. The results show that the implemented Deep Learning mechanisms performed well in reaching the desired pose of the end-effector. The proposed inverse kinematics strategies apply to other manipulators with different numbers of Degrees of Freedom.

Investigation of the limitations and applicability of the method of homogeneous functions for solving the inverse kinematic problem of seismic exploration

The results of the application of the variational ray tracing algorithm to study the possibilities and limitations of one of the methods for solving the inverse kinematic problem of seismic exploration — the method of homogeneous functions developed at the Department of Seismometry and Geoacoustics of Moscow State University are presented. As a result of the calculations carried out on synthetic models and field material, conclusions were drawn about the exploration possibilities and areas of application of the method of homogeneous functions. Model examples show that the method of homogeneous functions gives correct results only for simple media: vertically inhomogeneous or layered with slightly inclined boundaries, and folds or inclusions can be restored only at a qualitative level. When working with real field data, the method of homogeneous functions correctly restores the velocity structure of the section to a depth of 1/3-1/2 of the maximum depth of ray penetration. At the same time, it makes sense to interpret only large anomalies with contrasting velocity values on the obtained velocity sections.

Model-free kinematic control of redundant manipulators with simultaneous joint-physical-limit and joint-angular-drift handling

Model-free tracking control methods have been developed for redundant robotic manipulators with unknown kinematic or dynamic models. However, most existing works have not considered the problems of joint physical limits and joint angular drift. Joint angular drift refers to the phenomenon that the joint angles of a redundant manipulator are different from their initial state when the end-effector of the manipulator returns to its initial position. Therefore, this article proposes a model-free scheme for the tracking control of redundant manipulators as well as the avoidance of joint physical limits and joint angular drift. The proposed method aims to overcome these challenges by formulating the inverse kinematics problem as a constrained optimization problem, which incorporates the avoidance of joint angular drift into the optimization objective and takes the joint physical limits as a constraint. At the same time, an online Jacobian estimator is designed to observe the state of the manipulator. Specifically, it can estimate the Jacobian matrix of a redundant manipulator in real-time during the operation by fully exploiting the sensory data, without knowing the analytic robot model. Then, the optimization problem is integrated with the Jacobian estimator and solved by a discrete-time algorithm. Theoretical analysis is conducted to prove the stability and convergence of the proposed method. Moreover, the efficacy, practicability and superiority of the proposed method are supported by simulations and experiments based on different redundant manipulators.

Inverse Kinematics for Serial Robot Manipulators by Particle Swarm Optimization and POSIX Threads Implementation

Inverse kinematics is a fundamental problem in manipulator robotics: a set of joint angles must be calculated so that the robot arm can be manipulated to the corresponding desired end effector position and orientation (also known as “pose”). Traditional solution techniques include analytical kinematics solvers, which provide the closed-form expressions for the joint positions as functions of the end-effector pose. When analytical inverse kinematics solvers are not possible due to the manipulator structure, numerical methods such as Newton–Raphson or Jacobian inverse can be used to achieve the task, but at a much slower speed due, to the iterative nature of the computation. Recent swarm intelligence technology has also contributed to manipulator inverse kinematics solutions. In this paper, the use of the Particle Swarm Optimization (PSO) approach in solving the inverse kinematics problem is investigated for the general serial robotic manipulators. Many of the reviewed robotic manipulator inverse kinematics solvers using swarm intelligence only deal with end effector position and not its orientation. Our PSO approach provides the convergence of a complete end-effector pose and will be demonstrated using the Baxter Research Robot, which has two seven-joint arms, although the method is applicable to any general serial robotic manipulator. For computational efficiency, the inverse kinematic calculations were implemented in parallel using Portable Operating Interface (POSIX) threads to take advantage of the independent swarm particle dynamics.

An Atlas-Based Approach to Planar Variable-Structure Cable-Driven Parallel Robot Configuration-Space Representation

Variable-structure cable-driven parallel robots (VSCR) are a new class of cable robots that are able to cover nonconvex installation spaces by permitting collisions between cables and fixed objects in the environment. In this article, we show how the configuration space of a general planar VSCR can be represented as an organized set of partially overlapping regions of constant structure. The benefit of this representation, which we refer to as the “structure atlas,” is that it allows any techniques from the established cable-driven parallel robot literature to be applied locally, greatly simplifying the modeling complexity associated with VSCRs. A complete method for how such a representation can be constructed is provided, which includes identifying the set of reachable kinematic structures for a given VSCR and the area where each structure is active. We then give specific examples of how this new representation can be used for performing VSCR workspace analysis and directly solving the VSCR inverse kinematics problem. Our results are demonstrated with the aid of simulated and experimental results.

The Limitations and Applicability of the Method of Homogeneous Functions for Solving the Inverse Kinematic Problem of Seismic Exploration

The Limitations and Applicability of the Method of Homogeneous Functions for Solving the Inverse Kinematic Problem of Seismic Exploration

A Concurrent Framework for Constrained Inverse Kinematics of Minimally Invasive Surgical Robots.

Minimally invasive surgery has undergone significant advancements in recent years, transforming various surgical procedures by minimizing patient trauma, postoperative pain, and recovery time. However, the use of robotic systems in minimally invasive surgery introduces significant challenges related to the control of the robot's motion and the accuracy of its movements. In particular, the inverse kinematics (IK) problem is critical for robot-assisted minimally invasive surgery (RMIS), where satisfying the remote center of motion (RCM) constraint is essential to prevent tissue damage at the incision point. Several IK strategies have been proposed for RMIS, including classical inverse Jacobian IK and optimization-based approaches. However, these methods have limitations and perform differently depending on the kinematic configuration. To address these challenges, we propose a novel concurrent IK framework that combines the strengths of both approaches and explicitly incorporates RCM constraints and joint limits into the optimization process. In this paper, we present the design and implementation of concurrent inverse kinematics solvers, as well as experimental validation in both simulation and real-world scenarios. Concurrent IK solvers outperform single-method solvers, achieving a 100% solve rate and reducing the IK solving time by up to 85% for an endoscope positioning task and 37% for a tool pose control task. In particular, the combination of an iterative inverse Jacobian method with a hierarchical quadratic programming method showed the highest average solve rate and lowest computation time in real-world experiments. Our results demonstrate that concurrent IK solving provides a novel and effective solution to the constrained IK problem in RMIS applications.

Inverse Kinematic Solver Based on Bat Algorithm for Robotic Arm Path Planning

The bat algorithm (BA) is a nature inspired algorithm which is mimicking the bio-sensing characteristics of bats, known as echolocation. This paper suggests a Bat-based meta-heuristic for the inverse kinematics problem of a robotic arm. An intrinsically modified BA is proposed to find an inverse kinematics (IK) solution, respecting a minimum variation of the joints’ elongation from the initial configuration of the robot manipulator to the proposed new pause position. The proposed method is called IK-BA, it stands for a specific bat algorithm dedicated to robotic-arms’ inverse geometric solution, and where the elongation control mechanism is embedded in bat agents update equations. Performances analysis and comparatives to related state of art meta-heuristics solvers showed the effectiveness of the proposed IK bat solver for single point IK planning as well as for geometric path planning, which may have several industrial applications. IK-BA was also applied to a real robotic arm with a spherical wrist as a proof of concept and pertinence of the proposed approach.

Modelling and Simulation of a Redundant Agricultural Manipulator with Virtual Prototyping

The development of autonomous robots for agricultural applications includes motion planning, fruit picking, and collision avoidance with surrounding environments, and these become challenging tasks. For harvesting applications, robust control of the manipulator is needed for the effective motion of the robot. Several combinations of Proportional(P)- Integrative(I)- Derivative(D) controllers are modelled and a simulation study was performed for trajectory tracking of a redundant manipulator in virtual agricultural environments. The article presents a comprehensive study on kinematic modelling and dynamic control of redundant manipulator for fruit-picking applications in virtual environments. The collisions with surrounding environment were eliminated using ‘bounding box technique’. The joint variables are obtained by constructing Inverse Kinematics (IK) problem and are determined using a classical optimization technique. Different controllers are modelled in the ‘Simulink’ environment and are tuned to generate error-free trajectory tracking during harvesting. The task space locations (TSLs) are considered as via-points, and joint variables at each TSLs are obtained by Sequential Quadratic Programming (SQP) technique. Joint-level trajectories are generated using Quintic and B-spline polynomials. For effective trajectory tracking, torque variations are controlled using the PID and Feedforward (FF) controller. The dynamic simulations of the robot manipulator are performed in Simscape Multibody software. Results show that the during the trajectory tracking of the manipulator, the Feed-forward controller performs best with Quintic polynomial trajectory.

Kinematic Analysis of three degrees of freedom planar parallel continuum mechanisms

Parallel continuum mechanisms are a type of compliant mechanisms comprising a rigid end-effector connected to a fixed frame by flexible and slender elements in a closed-kinematic morphology, being their flexibility the source of mobility. Solving the position problem involves the static equilibrium of the whole device considering the nonlinear large deformations of slender elements. Numerical iterative solutions are already available to solve real-time simulations. However, an assembled solution, which meets both geometric conditions and static equilibrium, is needed to start the process. A comprehensive Kinematic Analysis in the classical sense is not fully established yet. The aim of the paper is to propose a procedure that solves the full inverse and forward kinematic problems for planar three degrees of freedom systems, hence obtaining the multiple solutions arising from the closed-loop structure and the multiplicity of the deformation mode of slender links. From those solutions, finding of the different aspects that comprise the workspace is possible, as well as determining singularities and instability loci.