Computation Of Inverse Kinematics Research Articles

Collaborative Continuum Robots for Remote Engineering Operations

In situ repair and maintenance of high-value industrial equipment is critical if they are to maintain the ability to continue vital operations. Conventional single-arm continuum robots have been proven numerous times to be successful tools for use in repair operations. However, often more than one arm is needed to ensure successful operation within several scenarios; thus, the collaborative operation of multiple arms is required. Here, we present the design and operating principles of a dual-arm continuum robot system designed to perform critical tasks within industrial settings. Here, presented are the design principle of the robotic system, the optimization-based inverse kinematic calculation of the 6-DoF continuum arms, and the collaborative operation strategy. The collaborative principle and algorithms used have been evaluated by a set of experiments to demonstrate the ability of the system to perform in situ machining operations. With the developed prototype and controller, the average error between planned and real toolpaths can be within 2.5 mm.

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.

Extensively Explored and Evaluated Actor-Critic With Expert-Guided Policy Learning and Fuzzy Feedback Reward for Robotic Trajectory Generation

Trajectory generation for redundant manipulators based on inverse kinematics (IK) still faces some restraints, as it lacks universal IK calculation or specific trajectory generation methods that are suitable for robots with arbitrary degrees of freedom. In this article, the IK-free trajectory generation for robot manipulators is formulated as a Markov decision process and implemented by a general method based on deep reinforcement learning. First, an extensively explored and evaluated actor-critic (E3AC) algorithm that can make diverse action explorations and comprehensive evaluations is designed to solve the trajectory generation problem. Second, a dual-memory structure with expert-guided policy learning strategy is proposed to further enhance the performance of the algorithm in the early training period by additional successful experiences and performing an increasingly unbiased data sampling. Third, a fuzzy feedback reward mechanism that can directly establish a mapping from the abundant state variables to the self-tuning reward is constructed, instead of puzzling out an explicit function to feature the complex relations among the control objects. Finally, the comparative experimental results show that, the proposed approach is more efficient in algorithm convergence and reward calculation, and is more qualified for complex tasks with strong randomness.

Trajectory Control of An Articulated Robot Based on Direct Reinforcement Learning

Reinforcement Learning (RL) is gaining much research attention because it allows the system to learn from interacting with the environment. Yet, with all these successful applications, the application of RL in direct joint torque control without the help of an underlining dynamic model is not reported in the literature. This study presents a split network structure that enables successful training of RL to learn the direct torque control for trajectory following a six-axis articulated robot without prior knowledge of the dynamic robot model. The training took a very long time to converge. However, we were able to show the successful control of four different trajectories without needing an accurate dynamics model and complex inverse kinematics computation. To show the RL-based control’s effectiveness, we also compare the RL control with the Model Predictive Control (MPC), another popular trajectory control method. Our results show that while the MPC achieves smoother and more accurate control, it does not automatically treat the singularity. In addition, it requires complex inverse dynamics calculations. On the other hand, the RL controller instinctively avoided the violent action around the singularities.

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.

Projected frontal area and its components during front crawl depend on lung volume.

We examined the influence of lung volume on the vertical body position, trunk inclination, and projected frontal area (PFA) during swimming and the inter-relationships among these factors. Twelve highly trained male swimmers performed a 15 m front crawl with sustained maximal inspiration (INSP), maximal expiration (EXP), and intermediate (MID) at a target velocity of 1.20 m·s-1 . Using our developed digital human model, which allows inverse kinematics calculations by fitting individual body shapes measured with a three-dimensional photonic image scanner to individually measured underwater motion capture data, vertical center of mass (CoM) position, trunk inclination, and PFA were calculated for each complete stroke cycle. In particular, the PFA was calculated by automatic processing of a series of parallel frontal images obtained from a reconstructed digital human model. The vertical CoM position was higher with a larger lung-volume level (p < 0.01). The trunk inclination was smaller in INSP and MID than in EXP (p < 0.01). PFA was smaller with a larger lung-volume level (p < 0.01). Additionally, there was a significant interaction of vertical CoM position and trunk inclination with PFA (p=0.006). There was a negative association between PFA and vertical CoM position, and a positive association between PFA and trunk inclination less than the moderate vertical CoM position (each p < 0.05). These results obtained using our methodology indicate that PFA decreases with increasing lung volume due to an increase in vertical CoM position, and additionally due to a decrease in trunk inclination at low-to-moderate lung-volume levels.

A New Solving Method Based on Simulated Annealing Particle Swarm Optimization for the Forward Kinematic Problem of the Stewart–Gough Platform

The forward kinematics of the Stewart–Gough platform is vital for high-precision positioning and sensing in six degrees of freedom. In this paper, the solving of forward kinematics is converted to searching for the best posture corresponding to the input outrigger length vectors by inverse kinematic calculation. The simulated annealing (SA) process is embedded into particle swarm optimization (PSO) to improve the convergence speed and overcome the local convergence. The proposed SA–PSO algorithm not only accelerates the convergence speed but also improves the reliability and success rate. After the optimization of algorithm parameters, the success rate of the SA–PSO for random outrigger length vector input is steadily above 99.9% while the results of PSO is between 93% and 100%. In the workspace simulation, the average iteration number of the proposed algorithm is reduced from 146.6 to 122.7, meanwhile, the success rate of SA–PSO is 99.992%, much higher than the 93.805% of PSO. Compared with the traditional Newton–Raphson method, the SA–PSO method has a higher success rate and is less time consuming. Finally, a physical experiment is conducted on a six-degree-of-freedom platform, revealing that the given algorithm is reliable and accurate.

Forward kinematics of body posture perception using an improved BP neural network based on a quantum genetic algorithm

Forward kinematics analysis of body posture perception is the basis for studying other performance of 6-degree of freedom parallel robot. Because forward kinematics involves many sets of nonlinear equations, it is usually difficult to solve. In this paper, an improved BP neural network (BPNN) based on a quantum genetic algorithm (GA) is designed to solve the forward kinematics problem. Additionally, we use the characteristics of easy calculation of inverse kinematics to generate a dataset for training and testing. Finally, through a large number of experiments, we show that the improved strategy of BPNN by quantum GA is effective, and the accuracy of the model we designed is high enough to solve the forward kinematics of body posture perception.

A novel end-effector upper limb rehabilitation robot: Kinematics modeling based on dual quaternion and low-speed spiral motion tracking control

For patients with upper limb dysfunction after stroke, robot-assisted rehabilitation training plays an important role in functional recovery. The existing upper limb rehabilitation robots have some problems, such as complex mechanisms, insufficient compliance, and can only realize the rehabilitation training of shoulder and elbow joints in the horizontal plane. This research proposes a novel end-effector upper limb rehabilitation robot with three degrees of freedom. Two horizontal rotation freedoms are driven by motors and one vertical translation freedom is driven by a pneumatic cylinder. So it can realize the spatial rehabilitation training of shoulder and elbow joints. The rotation and translation transformation of the robot can be represented by a dual quaternion, which is concise in form and clear in the physical meaning. Therefore, this article adopts dual quaternions to complete the robot’s kinematics modeling, inverse kinematics calculation, and terminal spiral motion trajectory planning. To improve the low-speed moving performance of the spiral motion, a sliding mode control strategy plus feedforward compensation is employed to control the displacement of the cylinder. Experiments show that the robot can realize proximal joints training and has good position tracking accuracy (tracking error is within 2 mm) with smoothness under the proposed control strategy, which can guarantee the accuracy and comfort of passive rehabilitation training, contributing to restoring the function of the impairment upper limbs.

FORWARD &amp; INVERSE KINEMATICS SOLUTION OF 6-DOF ROBOTS THOSE HAVE OFFSET &amp; SPHERICAL WRISTS

One of the critical design decisions that arise during the design of an industrial robot is the function of the joints to be used and their location. Of course, for the designed robot to provide the expected performance, the selection of the motors and gear reducers that will create these joints will primarily affect the determination of these joints. However, both the examination of the existing industrial robots and the fact that the motor and gear reducer information that can be supplied can be easily obtained with today’s technology, these joints can be determined quickly as a result of a short investigation. Along with the mechanical design, robot control unit design also has stages that progress in parallel and depend on or affect the mechanical design decisions. One of the most important of these is that especially inverse kinematics calculations can be performed analytically, enabling the robot control unit to make decisions and give commands in real-time.&#x0D; This article aims to publish the geometric calculation of inverse kinematics of commonly used exampled configuration of 6-DOF industrial robot that has offset and spherical joint along with interactive calculation tables and sheets. There are numerous articles published on the same subject but none of them has provided any verification supplement so far. Thus, it is also aimed to confirm and verify the calculations given in this article by providing convenient tables and sheets and to create a solid foundation for future studies.

Conclusion or Illusion: Quantifying Uncertainty in Inverse Analyses From Marker-Based Motion Capture due to Errors in Marker Registration and Model Scaling.

Estimating kinematics from optical motion capture with skin-mounted markers, referred to as an inverse kinematic (IK) calculation, is the most common experimental technique in human motion analysis. Kinematics are often used to diagnose movement disorders and plan treatment strategies. In many such applications, small differences in joint angles can be clinically significant. Kinematics are also used to estimate joint powers, muscle forces, and other quantities of interest that cannot typically be measured directly. Thus, the accuracy and reproducibility of IK calculations are critical. In this work, we isolate and quantify the uncertainty in joint angles, moments, and powers due to two sources of error during IK analyses: errors in the placement of markers on the model (marker registration) and errors in the dimensions of the model’s body segments (model scaling). We demonstrate that IK solutions are best presented as a distribution of equally probable trajectories when these sources of modeling uncertainty are considered. Notably, a substantial amount of uncertainty exists in the computed kinematics and kinetics even if low marker tracking errors are achieved. For example, considering only 2 cm of marker registration uncertainty, peak ankle plantarflexion angle varied by 15.9°, peak ankle plantarflexion moment varied by 26.6 N⋅m, and peak ankle power at push off varied by 75.9 W during healthy gait. This uncertainty can directly impact the classification of patient movements and the evaluation of training or device effectiveness, such as calculations of push-off power. We provide scripts in OpenSim so that others can reproduce our results and quantify the effect of modeling uncertainty in their own studies.

Development of a redundant anthropomorphic hydraulically actuated manipulator with a roll-pitch-yaw spherical wrist

The demand for redundant hydraulic manipulators that can implement complex heavy-duty tasks in unstructured areas is increasing; however, current manipulator layouts that remarkably differ from human arms make intuitive kinematic operation challenging to achieve. This study proposes a seven-degree-of-freedom (7-DOF) redundant anthropomorphic hydraulically actuated manipulator with a novel roll-pitch-yaw spherical wrist. A hybrid series-parallel mechanism is presented to achieve the spherical wrist design, which consists of two parallel linear hydraulic cylinders to drive the yaw/pitch 2-DOF wrist plate connected serially to the roll structure. Designed as a 1RPRRR-1SPU mechanism (“R”, “P”, “S”, and “U” denote revolute, prismatic, spherical, and universal joints, respectively; the underlined letter indicates the active joint), the 2-DOF parallel structure is partially decoupled to obtain simple forward/inverse kinematic solutions in which a closed-loop subchain “RPRR” is included. The 7-DOF manipulator is then designed, and its third joint axis goes through the spherical center to obtain closed-form inverse kinematic computation. The analytical inverse kinematic solution is drawn by constructing self-motion manifolds. Finally, a physical prototype is developed, and the kinematic analysis is validated via numerical simulation and test results.

Design and implementation of computer aided resource management system for dance teaching

Traditional teaching methods are limited to time and place, and the performance of dance teaching resources management is poor. Design a computer-assisted dance teaching resource management system. The functional structure of the system includes core computer-assisted teaching and teaching management applications. The data management module is used to store the processed data in data files, and the dance teaching content release module retrieves requests and multimedia. The remote image resource location request of the management module responds to the feedback. In order to improve the management of computer-aided dance teaching resources, this article takes dance robots as the research object, takes dance video information as input, uses deep learning methods to estimate the human body posture in the video, and obtains the key point position coordinates of the human body; The inverse kinematics calculation of the robot obtains the angle values of each joint of the robot, and the angle values of the lower body joints are adjusted to maintain the balance of the robot. In addition, this paper also proposes a method to automatically generate robot dance sequence. Gated cyclic unit (GRU) network is used to learn the correlation between the global characteristics of music and dance gesture relationship characteristics, the correlation between music local characteristics and dance movement density characteristics, and then combine the dance movement graphs to sample and plan Robot dance moves synchronized with the beat. Experimental results show that whether it is robot dance movement imitation or dance movement generation, it can improve the computer-aided management of dance teaching.

Optimal Design of Continuum Robots With Reachability Constraints

While multi-joint continuum robots are highly dexterous and flexible, designing an optimal robot can be challenging due to its kinematics involving curvatures. Hence, the current work presents a computational method developed to find optimal designs of continuum robots, given reachability constraints. First, we leverage both forward and inverse kinematic computations to perform reachability analysis in an efficient yet accurate manner. While implementing inverse kinematics, we also integrate torque minimization at joints such that robot configurations with the minimum actuator torque required to reach a given workspace could be found. Lastly, we apply an estimation of distribution algorithm (EDA) to find optimal robot dimensions while considering reachability, where the objective function could be the total length of the robot or the actuator torque required to operate the robot. Through three application problems, we show that the EDA is superior to a genetic algorithm (GA) in finding better solutions within a given number of iterations, as the objective values of the best solutions found by the EDA are 4-15% lower than those found by the GA.

Strengthening the PSO algorithm with a new technique inspired by the golf game and solving the complex engineering problem

This study has been inspired by golf ball movements during the game to improve particle swarm optimization. Because, all movements from the first to the last move of the golf ball are the moves made by the player to win the game. Winning this game is also a result of successful implementation of the desired moves. Therefore, the movements of the golf ball are also an optimization, and this has a meaning in the scientific world. In this sense, the movements of the particles in the PSO algorithm have been associated with the movements of the golf ball in the game. Thus, the velocities of the particles have converted to parabolically descending structure as they approach the target. Based on this feature, this meta-heuristic technique is called RDV (random descending velocity) IW PSO. In this way, the result obtained is improved thousands of times with very small movements. For the application of the proposed new technique, the inverse kinematics calculation of the 7-joint robot arm has been performed and the obtained results have been compared with the traditional PSO, some IW techniques, artificial bee colony, firefly algorithm and quantum PSO.

Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

For both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

A design of stretcher with auxiliary functions of lateral positioning and transferring for immobilized patients

For now, many hospitals that require nurses to move patients by hand from stretchers to a hospital bed, so a design of stretcher with auxiliary functions of lateral positioning and transferring for immobilized patients, which is a mechanical mechanism consisted of rigid rods, joints and sliders, was designed to help the nurses to move patients between beds and reduce their workload. Driven by motors, the rigid rods can be rotated, stretched or shortened so that the entire stretcher bed board can archive to a proper posture and position. In this paper, the following objectives will be achieved: (i) Create a schematic of the mechanism and describe the principles and functions (ii) the calculation of inverse kinematics, forward kinematics, dynamics (including energy), and PD control in the mechanism (iii) The motion process of simulating the mechanism using MATLAB (iv) Using MATLAB to create the plots of angle, torque, and position state (v) Using SolidWorks to construct the prototype and to implement the motion simulation of the mechanism (vi) Describe the practical application and future Extensions of this mechanism.

Holonomic Implementation of Three Wheels Omnidirectional Mobile Robot using DC Motors

In the Indonesian Wheeled Football Robot Contest (KRSBI) wheeled division, the robot that is made must be able to complete a predetermined task, one of which is the robot for chasing the ball and catching it. Holonomic is one of the methods used in navigating the omnidirectional movement of mobile robot applications. Because the movement is designed without changing the position of the robot in the direction of the facing, the omnidirectional wheels are used which has the ability to move freely in two directions. The mobile robot has three omnidirectional wheels and DC motors each used for movement. DC motors controlled by EMS 30A H-Bridge as a driver and Arduino Mega 2560 as the main microcontroller. Holonomic and inverse kinematic calculations are conducted to control the mobile robot movement of x, y, and ω toward angular velocity and direction of s1, s2, and s3 for each wheel. The length of the wheel axis to the middle of the body of robot is 160 mm. In this study, a robot was implemented on the robot movement for moving forward, backward, sideways, and diagonal direction. Based on the data evaluation, it is determined that an angular error of 2.84% exists in the movement of the omnidirectional robot at a velocity of 0.256 m/s to 1.403 m/s.

A General Robot Inverse Kinematics Solution Method Based on Improved PSO Algorithm

Robots whose geometric structure does not meet the Pieper criterion are called general robots. For the inverse kinematic operation of general robots, the closed solution method cannot be solved, and the numerical solution calculation amount is too large and the singular position cannot be calculated. To solve this problem, this paper proposes an inverse kinematics calculation method based on improved particle swarm optimization (PSO) algorithm and applicable to general robots. In order to avoid the particle update rate not adapting to each stage of the optimization process, a nonlinear dynamic inertia weight adjustment method based on the concept of similarity is introduced, so that the search process is more robust; in addition, to overcome the problem of local optimal solution At the same time, multiple populations are introduced to perform optimization search at the same time, and the immigration operator is proposed to increase the diversity of the particle population in the iteration. This article uses Comau NJ-220 robot for test verification, compared with the original PSO and multi-subswarm algorithm, the results show that the proposed improved PSO has higher algorithm stability for general robot kinematics inverse solution problems, and can greatly improve the convergence accuracy and speed. This method provides a new solution to the field of robot inverse kinematics, and provides a more efficient and stable kinematics foundation for robot motion planning.

The control of a five-axis robotic arm and its experimental application

The study discusses the control of a five-axis robotic arm, the orbit planning involved, and experimental applications that make use of the arm. A robotic arm unit located at the Trakya University has been used for the study; LabVIEW 2010 (student edition) and MATLAB 2010a (student edition) applications have been used for the orbit planning programs and the arm has been successfully operated. Using the program developed, the coordinates of the starting and ending positions for the robotic arm have been specified on a three-dimensional Cartesian coordinate system and inverse kinematics computations have been performed, resulting in the movement of the arm.