Computation Of Inverse Kinematics Research Articles

Precise Calculation of Inverse Kinematics of the Center of Gravity for Bipedal Walking Robots

The walking of humanoid robots is dependent on the precise tracking of their center of gravity and foot trajectories. Trajectory tracking is achieved by mobilizing their joints to achieve the correct trajectory. Errors occur because of assumptions on tracking the center of gravity and the foot trajectories. In this study, a numerical algorithm was developed that produces an exact and single kinematic solution in which the center of gravity and foot trajectories can be tracked with the desired precision. The effectiveness of this algorithm was examined with a dynamic simulation and compared with a method given in the literature. The main highlight of this study, using the presented algorithm, is that the robot could walk even if the position of its center of gravity was lower than its hips, resulting in a tracking error that was smaller than that reported in the literature.

Adaptive Cartesian space control of robotic manipulators: A concurrent learning based approach

This work introduces a concurrent learning-based adaptive control design for end-effector tracking and the corresponding stability analysis for robotic manipulators. The presented controller is developed directly in Cartesian space, thereby removing the necessity for inverse kinematics calculations at the position level. The designed adaptive controller ensures global exponential tracking of the end-effector in Cartesian space. Moreover, the developed controller assures globally exponential convergence of uncertain dynamical parameters to their actual values without demanding persistence excitation conditions via a combination of a standard gradient-based adaptation with a novel integral concurrent learning component. The developed integral concurrent learning part operates both real-time output data and the most informative historical data gathered by employing the singular-value maximization algorithm (SVMA) to reduce the size of memory allocation. Lyapunov-based arguments are applied to ensure the exponential stability of the closed-loop system. Numerical studies are performed to depict the feasibility and performance of the proposed design.

Design and Test of Seed–Fertilizer Replenishment Device for Wheat Seeder

In view of existing problems, such as the seed and fertilizer supply link for wheat seeders still relying on manual installation and the lack of practical application equipment, a seed–fertilizer replenishment device based on the three-degree-of-freedom mechanical arm and screw conveying principle is designed using the seed box installation and supply as the operation scenario to replace the manual installation process. Combined with the requirements of the seed box replenishment operation, the key parameters of the replenishment robot arm and the screw conveyor auger are determined. Then, the kinematic model of the replenishment robot arm is established based on the modified D-H method, forward and inverse kinematics calculations are performed, and the workspace is analyzed using the Monte Carlo method. Based on this, the robotic arm task path is designed, the fifth-degree polynomial interpolation method is used to complete the trajectory planning, and MATLAB R2016a software is used to simulate the motion trajectories of each joint, verifying the feasibility of the trajectory planning solution. Finally, a prototype is trial-produced and quadratic regression orthogonal testing and response surface analyses are conducted to obtain the optimal working parameters of the replenishment device. The verification test shows that when the angular velocity of the lumbar joint of the replenishment device is 4°/s, the speed of screw conveyor is 90 r/min, and the angle of the big arm is 12°, the conveying loss rate is 3.98%, and the conveying efficiency is 0.833 kg/s. The relative errors with the theoretical optimal values are 4.2% and 2.4%, respectively, both less than 5%. The supply trajectory is reasonable, and the robot arm runs smoothly. This study can provide reference for the design of seed–fertilizer replenishment device for wheat seeders.

Design and experimentation of multi-fruit envelope-cutting kiwifruit picking robot.

Currently kiwifruit picking process mainly leverages manual labor, which has low productivity and high labor intensity, meanwhile, the existing kiwifruit picking machinery also has low picking efficiency and easily damages fruits. In this regard, a kiwifruit picking robot suitable for orchard operations was developed in this paper for kiwifruit grown in orchard trellis style. First, based on the analysis of kiwifruit growth pattern and cultivation parameters, the expected design requirements and objectives of a kiwifruit picking robot were proposed, and the expected workflow of the robot in the kiwifruit orchard environment was given, which in turn led to a multi-fruit envelope-cutting kiwifruit picking robot was designed. Then, the D-H method was used to establish the kinematic Equations of the kiwifruit-picking robot, the forward and inverse kinematic calculations were carried out, and the Monte Carlo method was used to analyze the workspace of the robot. By planning the trajectory of the robotic arm and calculating critical nodes in the picking path, the scheme of trajectory planning of the robot was given, and MATLAB software was applied to simulate the motion trajectory as well as to verify the feasibility of the trajectory planning scheme and the picking strategy. Finally, a kiwifruit picking test bed was set up to conduct picking tests in the form of fruit clusters. The results show that the average time to pick each cluster of fruit was 9.7s, the picking success rate was 88.0%, and the picking damage rate was 7.3%. All the indicators met the requirements of the expected design of the kiwifruit-picking robot.

Study on Singularity Passing Method for Large Industrial Robot Based on Proper Element Improvement of Inverse Matrix

Singularity has become a limitation to the expected diversification of industrial robot applications in production. Here, we propose a novel solution for the inverse kinematics of a 6-DOF manipulator that suppresses rapid joint rotation when passing through a singularity. The proposed method is based on the optimization of the inverse Jacobi cofactor matrix utilized in the inverse kinematics calculation. By optimizing only the elements related to the four and six joints of the cofactor matrix in the inverse matrix, we were able to suppress the divergence of the joint velocities and achieve smooth robot motion when the robot entered a singular posture at the wrist. The developed system application range and tuning gain that minimize the position and orientation error were also determined. Hence, the position and orientation errors were improved by approximately 76%, and rapid rotation of the joints was almost completely suppressed. The method did not require consideration of tools attached to the hand tip, and the hand tip position, orientation, and velocity were all maintained.

Simple Inverse Kinematics Computation Considering Joint Motion Efficiency.

Inverse kinematics (IK) is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple IK calculation scheme for an industrial serial manipulator. The proposed technique can calculate appropriate values of the joint variables to realize the desired end-effector position and orientation while considering the motion costs of each joint. Two scalar functions are defined for the joint variables: one is to evaluate the end-effector position and orientation, whereas the other is to evaluate the motion efficiency of the joints. By combining the two scalar functions, the IK calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the IK via the aforementioned optimization is constructed on the basis of the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA). The proposed scheme considers not only the accuracy of the position and orientation of the end-effector but also the efficiency of the robot movement. Therefore, it yields a practical result of the inverse problem. Moreover, the proposed algorithm is simple and easy to implement owing to the high-calculation efficiency of NLSPSA. Finally, the effectiveness of the proposed method is verified through numerical examples using a redundant manipulator.

夹持-拉断式苹果采摘机器人设计与实验

For the standardized apple orchards in China, which are mainly dwarfed and densely planted, firstly, according to the spatial distribution characteristics of fruits within the tree canopy, a clamping-pull-off apple picking robot was developed by analyzing the parameters of apple cultivation and picking methods, in order to replace the manual harvesting operation. Then, the D-H method was used to establish the kinematic Equations of the apple-picking robot, the forward and inverse kinematic calculations were carried out, and the Monte Carlo method was used to analyze the workspace of the robot. Through the robot picking task planning and the simulation of the trajectory of the robotic arm, the scheme of the robot's picking strategy was given, and MATLAB software was applied to simulate the motion trajectory as well as to verify the feasibility of the trajectory planning scheme and the picking strategy. Finally, an apple-picking test bed was set up, the corresponding picking control system program was designed, and 45 apples were selected for picking tests. The results showed that during the robot's picking process, the average time for picking each fruit was 7.59 seconds, the fruit recognition success rate was 86.67%, and the picking damage rate was 5.13%.

Heading control for quadruped stair climbing based on PD controller for the KRSRI competition

Quadruped, a robot that resembles four-legged animals, is developed for many purposes, such as surveillance and rescue. Such a caveat requires the robot to have the capability to overcome various terrain and obstacles. When moving across such a landscape, it is essential to maintain the robot's orientation steadily. Inclined terrains such as stairs have posed another challenge to the control strategy as the robot is unstable while climbing. Therefore, the contribution of this work is to address the need for heading control because of the relatively longer stairs used for the current competition compared to the past. The proposed control system simultaneously maintains the heading while keeping the body stable. The inertial measurement unit sensor carried by the robot would provide the pose needed for heading control calculations. The robot's heading becomes the base for the PD controller calculation. The final pose that stabilizes the robot while tackling heading error is a combination of correction from the PD controller and the stabilization part of the control strategy. Then, the leg servo angle determination deployed the inverse kinematics calculation from the suitable robot pose. The proposed method enabled the designed robot to maintain its heading with a 4.4-degree margin of error and stabilize the body. The quadruped also completes the stair climbing at the shortest time of 20 seconds with a speed of up to 5.5 centimeters per second.

Application of direct and inverse kinematics and dynamics in motion planning of manipulator links

For the synthesis of manipulators and robots, an accurate analysis of the movements of the individual links is essential. This thesis deals with motion planning of the effector of a multi-linked manipulator. An important topic in this area is the orientation and position of links and kinematic pairs in space. In particular, attention should be paid to the position of their endpoint as well as other significant points. Trajectory planning allows the manipulator to perform complex tasks, such as picking and placing objects or following a particular path in space. Overall, trajectory planning of a multibody manipulator involves a combination of direct and inverse kinematics calculations, as well as control theory and optimization techniques. It is an important process enabling manipulators to perform complex tasks such as assembly, handling and inspection. In the design of robot kinematic structures, simulation programs are currently used for their kinematic and dynamic analysis. The proposed manipulator was first solved by inverse kinematics problem in Matlab. Subsequently, the trajectories of the end-effector were determined in Matlab by a direct kinematics problem. In Simulink, using the SimMechanics library, the inverse problem of dynamics was used to determine the trajectories of the moments.

An analytical approach based on Dixon resultant for the inverse kinematics of 6R robot manipulators with offset wrists

6-revolute (6R) robot manipulators with offset wrists are widely applied in industrial scenarios. However, the autonomous and highly-precise manipulations of these robots are restricted for online industrial uses due to the lack of effective inverse kinematic methods. The inverse kinematic problem for 6R robot manipulators with offset wrists is addressed with a novel kinematic modelling and elimination approach in this study. To begin, kinematic models with non-redundant equations for joint variables are established An improved Dixon elimination approach is then introduced for inverse kinematic calculation to reduce the high computational cost and get rid of the singularity issues. The core is to efficiently extract the linear terms from variable sequences, such that the number of terms can be reduced in the polynomial equations. By further examining the characteristics of offset wrists, the fourth and fifth joint variables are eliminated from kinematic formulas, without increasing the polynomial degrees. The formulas are demonstrated to produce a polynomial with a single joint variable and a minimum degree using the elimination approach. Finally, experiments are carried out to verify the computing performance of the inverse kinematic problem. The main focus of this study is to develop a systematic and automatic procedure for solving the inverse kinematic problem for 6R robot manipulators with offset wrists and producing highly precise and efficient solutions by means of a novel modelling and elimination method.

Gravitation search-based hybrid algorithm for solving inverse kinematics of an n-link redundant manipulator

Abstract Inverse kinematics is one of the most complicated problems in robotics. The inverse kinematics calculation is the basis for any industrial robot’s ability to plan and follow a trajectory. This paper proposes a hybrid algorithm, e3GSA, based on the gravitational search algorithm (GSA) for solving the inverse kinematics problem of an n-link redundant robot manipulator. The algorithm’s efficiency was evaluated using a fitness function comprising of position error, orientation error, and collision error, and it was found to perform better than the conventional GSA in simulations. A generalized framework was proposed and tested by simulating a 6-, 8-, and 12-link robot manipulators. Experimental validation is carried out using a 6-link robot manipulator, which shows that the simulation data are on par with the experimental data. The proposed algorithm was also found to perform adaptively with faster convergence rates and lesser computation time, making it a better choice for other engineering problems that can be transformed into optimization problems.

A Closed-Loop Dynamic Controller for Active Vibration Isolation Working on A Parallel Wheel-Legged Robot

Serving the Stewart mechanism as a wheel-legged structure, the most outstanding superiority of the proposed wheel-legged hybrid robot (WLHR) is the active vibration isolation function during rolling on rugged terrain. However, it is difficult to obtain its precise dynamic model, because of the nonlinearity and uncertainty of the heavy robot. This paper presents a dynamic control framework with a decentralized structure for single wheel-leg, position tracking based on model predictive control (MPC) and adaptive impedance module from inside to outside. Through the Newton-Euler dynamic model of the Stewart mechanism, the controller first creates a predictive model by combining Newton-Raphson iteration of forward kinematic and inverse kinematic calculation of Stewart. The actuating force naturally enables each strut to stretch and retract, thereby realizing six degrees-of-freedom (6-DOFs) position-tracking for Stewart wheel-leg. The adaptive impedance control in the outermost loop adjusts environmental impedance parameters by current position and force feedback of wheel-leg along Z-axis. This adjustment allows the robot to adequately control the desired support force tracking, isolating the robot body from vibration that is generated from unknown terrain. The availability of the proposed control methodology on a physical prototype is demonstrated by tracking a Bezier curve and active vibration isolation while the robot is rolling on decelerate strips. By comparing the proportional and integral (PI) and constant impedance controllers, better performance of the proposed algorithm was operated and evaluated through displacement and force sensors internally-installed in each cylinder, as well as an inertial measurement unit (IMU) mounted on the robot body. The proposed algorithm structure significantly enhances the control accuracy and vibration isolation capacity of parallel wheel-legged robot.

A closed-form solution for inverse kinematics of redundant space manipulator with multiple joint offsets

This paper proposes a novel parameterization analytical method to solve the inverse kinematics of a redundant space manipulator, which has link offsets at the shoulder, elbow, and wrist parts. Due to the manipulator’s particular configuration, current arm angle concepts cannot provide the analytical solution directly. Hence, this paper defines a new arm angle parameter that describes the manipulator’s redundancy and obtains the closed-form solutions directly. This is because, unlike manipulators without offset links, existing approaches involve parameters that may cause the inverse kinematic solution to fail when applied to the manipulator type considered in this work. Specifically, we analyze the parameter interplay on the inverse kinematic computation and then investigate the relations between the singularity and arm angle based on the singularity conditions of the Jacobian matrix. Besides, a semi-analytical method is proposed to determine the feasible arm angle intervals, while avoiding the singularity and inverse kinematic computation. Finally, a simple approach is proposed to compute the arm angle according to the feasible intervals. The proposed method has obvious geometric significance, is suitable for configuration control, and can be implemented in real-time control systems.

Open-source software library for real-time inertial measurement unit data-based inverse kinematics using OpenSim.

Inertial measurements (IMUs) facilitate the measurement of human motion outside the motion laboratory. A commonly used open-source software for musculoskeletal simulation and analysis of human motion, OpenSim, includes a tool to enable kinematics analysis of IMU data. However, it only enables offline analysis, i.e., analysis after the data has been collected. Extending OpenSim's functionality to allow real-time kinematics analysis would allow real-time feedback for the subject during the measurement session and has uses in e.g., rehabilitation, robotics, and ergonomics. We developed an open-source software library for real-time inverse kinematics (IK) analysis of IMU data using OpenSim. The software library reads data from IMUs and uses multithreading for concurrent calculation of IK. Its operation delays and throughputs were measured with a varying number of IMUs and parallel computing IK threads using two different musculoskeletal models, one a lower-body and torso model and the other a full-body model. We published the code under an open-source license on GitHub. A standard desktop computer calculated full-body inverse kinematics from treadmill walking at 1.5 m/s with data from 12 IMUs in real-time with a mean delay below 55 ms and reached a throughput of more than 90 samples per second. A laptop computer had similar delays and reached a throughput above 60 samples per second with treadmill walking. Minimal walking kinematics, motion of lower extremities and torso, were calculated from treadmill walking data in real-time with a throughput of 130 samples per second on the laptop and 180 samples per second on the desktop computer, with approximately half the delay of full-body kinematics. The software library enabled real-time inverse kinematical analysis with different numbers of IMUs and customizable musculoskeletal models. The performance results show that subject-specific full-body motion analysis is feasible in real-time, while a laptop computer and IMUs allowed the use of the method outside the motion laboratory.

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.

A Deep Learning Approach to Navigating the Joint Solution Space of Redundant Inverse Kinematics and Its Applications to Numerical IK Computations

As an increasing number of robotic manipulators possess seven or more degrees-of-freedom (DoF), solving inverse kinematic (IK) for kinematically redundant manipulators is becoming critical. Numerical optimizations are commonly used to solve the problem due to their generality and accuracy. Unfortunately, they typically only generate one joint solution at a time, despite the multiple joint configurations that redundant manipulators can provide to move the end-effector to a target position. The long iterative optimization process is also a concern, particularly if extra constraints such as obstacle avoidance have to be evaluated. In this paper, we show that numerical methods may be complemented by deep learning to overcome these limitations. Through deep learning, the solution space of redundant IK may be learned with neural networks (NNs), which allows multiple distinct joint solutions corresponding to a given target position to be obtained by navigating the solution space. The main challenge is to overcome the one-to-one functional mapping of NNs. This paper solves this problem with a novel probabilistic encoding of manipulator poses and their corresponding infinite number of joint solutions. Two examples are presented to demonstrate the application of the proposed method to facilitate numerical IK computations: (1) finding a good initial joint solution to bootstrap the numerical IK calculation, and (2) evaluating extra constraints, such as obstacle avoidance, off the optimization iterations. Experiments show that the proposed method can accelerate the execution of different numerical IK modules in the popular IKpy package up to 50% for a 7-DoF manipulator, depending on the accuracy required.

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.