Showing papers on "Kinematics equations published in 2017"

A New 6-DOF Quadrotor Manipulation System: Design, Kinematics, Dynamics, and Control

Abstract: The research on aerial manipulation has increased rapidly in recent years. In the previous work, a manipulator or a gripper is attached to the bottom of a quadrotor to facilitate the interaction with the environment. However, the previously introduced systems suffer from either limited end-effector degrees of freedom (DOF) or small payload capacity. In this paper, a quadrotor with a 2-DOF manipulator that has a unique topology to enable the end-effector to track a desired 6-DOF trajectory with minimum possible actuators is investigated. The proposed system is designed and modeled. However, such a system produces complexity in its inverse kinematics and control. A novel solution to the inverse kinematics problem is presented, which requires a solution of complicated algebraic/differential equations. Its accuracy is verified via numerical results. In order to solve the control problem, the system nonholonomic constraints are utilized with a model-free and low computation cost robust control technique. Moreover, the system stability proof under the proposed controller is carried out. A prototype of the proposed system is built and its design is verified via a flight test. In addition, the system feasibility and efficiency are enlightened.

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

Abstract: As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing. A novel hybrid manipulator for ultra-precision freeform polishing is proposed.Precession polishing process is adopted to produce Gaussian-like tool influence function.A detailed kinematics model of the hybrid manipulator is presented.An example of saddle surface finishing with this manipulator is analyzed theoretically.

Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints

Abstract: It is a common belief that service robots shall move in a human-like manner to enable natural and convenient interaction with a human user or collaborator. In particular, this applies to anthropomorphic 7-DOF redundant robot manipulators that have a shoulder-elbow-wrist configuration. On the kinematic level, human-like movement then can be realized by means of selecting a redundancy resolution for the inverse kinematics (IK), which realizes human-like movement through respective nullspace preferences. In this paper, key positions are introduced and defined as Cartesian positions of the manipulator's elbow and wrist joints. The key positions are used as constraints on the inverse kinematics in addition to orientation constraints at the end-effector, such that the inverse kinematics can be calculated through an efficient analytical scheme and realizes human-like configurations. To obtain suitable key positions, a correspondence method named wrist-elbow-in-line is derived to map key positions of human demonstrations to the real robot for obtaining a valid analytical inverse kinematics solution. A human demonstration tracking experiment is conducted to evaluate the end-effector accuracy and human-likeness of the generated motion for a 7-DOF Kuka-LWR arm. The results are compared to a similar correspondance method that emphasizes only the wrist postion and show that the subtle differences between the two different correspondence methods may lead to significant performance differences. Furthermore, the wrist-elbow-in-line method is validated as more stable in practical application and extended for obstacle avoidance.

Analytical inverse kinematic solution using the D-H method for a 6-DOF robot

Abstract: This paper proposes an analytical approach to solve inverse kinematics of a 6-DOF robot. The robot discussed here is designed with 6R configuration. The D-H model of the six-axis robot is built. The forward analytical solution is deduced using the D-H method. Then, analysis of inverse kinematics for the robot is presented. And finally, the validity of the inverse kinematic equations is verified. Forward kinematic equations and inverse kinematic equations are suitable for all kinds of robots with configuration similar to those of the robot in this paper.

An unsupervised learning based neural network approach for a robotic manipulator

Abstract: This paper presents a neural network approach for solving the inverse kinematics of a robotic manipulator. Inverse kinematics equations are more challenging than the forward kinematics equations and therefore are more computationally complex to solve. Here, we are using a neural network approach due to its ability to give more accurate results in complex situations as compared to the other approaches. Moreover, we are using this model for trajectory tracking of a two DOF robotic arm to test its validity in real life situations.

A Parallel Recursive Hamiltonian Algorithm for Forward Dynamics of Serial Kinematic Chains

Abstract: This paper presents a novel recursive formulation for the simulation of multibody system dynamics based on Hamilton's canonical equations. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration-based counterparts, it appears that there is a lack of dedicated parallel algorithms for multirigid body system dynamics based on this formulation. Serial kinematic chains are considered in this paper. Initially, the standard set of Hamilton's canonical equations is joined together with constraint equations at the velocity level. The reformulation determines the system's joint velocities and constraint force impulses in a divide and conquer manner resulting in logarithmic numerical cost for parallel implementation. Subsequently, the equations of motion are rearranged in order to obtain the time derivatives of the total joint momenta. In the case of the sequential implementation, the entire algorithm exhibits linear computational cost. Presented numerical method is exact and noniterative. Numerical test cases reveal negligible energy drift without the use of any additional constraint stabilization techniques. The results are compared against more standard acceleration based formulation and the outcome from real-life physical experiment.

Motion planning for mobile robots using inverse kinematics branching

Abstract: A novel algorithm for planning robotic manipulation tasks is presented in which the base position and joint motions of a robot are simultaneously optimized to follow a smooth desired end-effector trajectory. During the optimization routine, the manipulator's base position and joint motions are planned simultaneously by strategically moving a set of virtual robot arms (each representing a single configuration in a sequence) branching from a common base to a number of assigned target poses associated with a task. Additional goals (e.g. collision avoidance) and hard constraints, including joint limits are also incorporated. The optimization problem at the core of this method is a quadratic program, allowing constrained high-dimensional problems to be solved in very little time. This method has successfully planned motions allowing an 8-DOF manipulator to paint walls, and has proven to be highly efficient and scalable in practice.

Adaptive control of an exoskeleton robot with uncertainties on kinematics and dynamics

Abstract: In this paper, we propose a new adaptive control technique based on nonlinear sliding mode control (JSTDE) taking into account kinematics and dynamics uncertainties. This approach is applied to an exoskeleton robot with uncertain kinematics and dynamics. The adaptation design is based on Time Delay Estimation (TDE). The proposed strategy does not necessitate the well-defined dynamic and kinematic models of the system robot. The updated laws are designed using Lyapunov-function to solve the adaptation problem systematically, proving the close loop stability and ensuring the convergence asymptotically of the outputs tracking errors. Experiments results show the effectiveness and feasibility of JSTDE technique to deal with the variation of the unknown nonlinear dynamics and kinematics of the exoskeleton model.

Pick and place trajectory planning of planar 3-RRR parallel manipulator in the presence of joint clearance

Abstract: In this paper, the pick and place trajectory planning of a planar 3-RRR parallel manipulator is studied in the presence of joint clearance, which is one of the main sources of error in the positioning accuracy. Joint clearance can be modeled as a massless virtual link, with its direction determined from dynamic analysis. A 3–4–5 interpolating polynomial is used to plan the trajectories for the manipulator in the vertical and horizontal planes, in the presence of clearances. We compare the trajectories with those in the ideal cases, i.e., without clearances at the joints, and demonstrate that one can easily compensate for the errors in the trajectories by appropriate changes of the inputs. A similar method works for the compensation of the errors due to clearances at the joints, in trajectory planning of any parallel manipulator with any running speeds and payloads.

Knife-Edge Motion on a Surface as a Nonholonomic Control Problem

Abstract: This letter studies a new formulation for the kinematics of a knife-edge moving on an arbitrary smooth surface in ${\mathbb {R}^{3}}$ . The kinematics equations for a knife-edge, viewed as a rigid body, are constrained by the requirement that the knife-edge maintain contact with the surface. They describe the constrained translation of the point of contact of the knife-edge on the surface and the constrained attitude of the knife-edge as a rigid body. These equations for the knife-edge kinematics in ${\mathbb {R}}^{3}$ are expressed in a geometric form, without the use of local coordinates; they are globally defined without singularities or ambiguities. The kinematics equations can be expressed in several simplified forms and written as a drift-free nonlinear control system. Comments are made about interesting motion planning and path planning problems. The kinematics equations are specialized for two specific surfaces defined in ${ {\mathbb {R}}^{3}}$ , namely, a flat plane and the surface of a sphere. Results for the flat plane are compared with standard results obtained using local coordinates; results for the sphere, in contrast, require full attention to the 3-D geometry.

Inverse kinematics solution using neural networks from forward kinematics equations

Abstract: This paper presents the inverse kinematics solution using the neural network for a robotic arm in 3-dimension. This paper creates neural networks to represent x, y and z position of the end-effector in the forward kinematics equations. The structure of the network has 4 layers; input layer, 2 hidden layers, and output layer. The input and output layers are defined as robotic arm angle and position of the end-effector, respectively. Then, the network updates the weights by the backpropagation with variable learning rate algorithm until reaching criteria that the output of the network is equal to the desired positions. Finally, the inverse kinematics solution is defined by the optimal weights of the network. To evaluate the performance algorithm, the MATLAB Program is used to demonstrate the robotic arm movement in 3-dimension. As a result, the proposed algorithm can help the robotic arm move to the desired position quickly and correctly.

Singularity-Tolerant Inverse Kinematics for Bipedal Robots: An Efficient Use of Computational Power to Reduce Energy Consumption

Abstract: We propose a nonlinear inverse kinematics formulation which solves for positions directly. Compared to various other popular methods that integrate velocities, this formulation can better handle fast, asymmetric, and singular-postured balancing tasks for humanoid robots. We also introduce joint position and velocity boundaries as inequality constraints in the optimization to ensure feasibility. Such boundaries provide safety when approaching or getting away from joint limits or singularities. Besides, mixing positions and velocities in our proposed algorithm facilitates recovery from singularities, which is very difficult for conventional inverse kinematics methods. Extensive demonstrations on the real robot prove the applicability of the proposed algorithm while improving power consumption. Our formulation automatically handles different numerical and behavioral difficulties rising from singularities, which makes it a reliable low-level conversion block for different Cartesian planners.

Inverse Kinematics of a 7R 6-DOF Robot with Nonspherical Wrist Based on Transformation into the 6R Robot

Abstract: The 7R 6-DOF robots with hollow nonspherical wrist have been proven more suitable for spray painting applications. However, the inverse kinematics of this kind of robot is still imperfect due to the coupling between position and orientation of the end-effector (EE). In this paper, a new and efficient algorithm for the inverse kinematics of a 7R 6-DOF robot is proposed. The proposed inverse kinematics algorithm is a two-step method. The geometry of the 7R 6-DOF robot is analyzed. A comparison between the 7R 6-DOF robot and the well-known equivalent 6R robot is made. Based on this comparison, a rational transformation between these two kinds of robots is constructed. Then the general inverse kinematics algorithm of the equivalent 6R robot is applied to calculate the approximate solutions of the 7R 6-DOF robot, in the first step. The Damped Least-Squares (DLS) method is employed to derive the exact solutions, in the second step. The accuracy and efficiency of the algorithm are tested on a 7R 6-DOF painting robot. The results show that the proposed algorithm is more advantageous in the case without an approximate solution, such as the initial point of a continuous trajectory.

Compliant and coordinated control method for in-orbit capturing process of space robot

Abstract: The invention discloses a compliant and coordinated control method for the in-orbit capturing process of a space robot. The compliant and coordinated control method includes the steps that a space robot model oriented to control is established according to dynamics and kinematics equations; a mechanical arm compliant capturing control rule is established according to the space robot model oriented to control; a base posture control rule based on a base gas spraying device is determined; a mechanical arm compliant control loop is established according to the mechanical arm compliant capturing control rule; a base posture control loop is established according to the base posture control rule and a PSR pulse modulator; the control amounts calculated by the mechanical arm compliant control loop and the base posture control loop serve as the control input of a mechanical arm of a space robot system and the control input of the base gas spraying device of the space robot system correspondingly; and meanwhile control force of the base serves as a feed-forward item and is input into the mechanical arm control rule to offset the interference of base control to mechanical arm tail end compliant control. By means of the compliant and coordinated control method, stability of the base is ensured while a target is stably captured.

Design and kinematics of serial/parallel hybrid robot

Abstract: Nowadays contemporary economic growth and increasing industrial needs demand robots to have a multifunctional properties such as a wide applicability, precision, wide workspace and simple robot-human interface. Modern, robot industry presents two types of robot architecture: serial and parallel, serial robots have a wide workspace, easy forward kinematics and have a wide applicability in industry, while parallel manipulators are not applies widely in industry. However, parallel manipulator has some beneficial properties as well, such as rigidity, high payload capacity and high precision. Although majority robots in industry are serial manipulators, but some areas of industry where requires high precision and rigidity utilizes parallel manipulators such as medicine, pharmacy and microchip assembling industry. The novelty of this project is creating of new type of robot combination: common serial manipulator with Delta robot. Furthermore, to investigate capabilities of this Hybrid robot in terms kinematics, dynamics, payload capacity and accuracy. Moreover, this research will explain serial/parallel hybrid manipulator design structure, workspace control system and kinematics of both manipulators as well

Kinematic Modeling for a Class of Free-Floating Space Robots

Abstract: This paper investigates the kinematics of free-floating space robots during motion planning for target capture. First, generalized kinematic mapping of free-floating space robots with open-chain multibody structures is established. To predict the reaction movement of spacecraft caused by the motions of its manipulators, a dynamic coupling matrix concept, the main contribution of this paper, is proposed to explicitly express position kinematics. The feasibility and effectiveness of the presented numerical implementation algorithms are then verified by solving forward and inverse kinematics problems. Then, applications in workspace analysis and motion planning are described. Finally, a discussion of the framework is presented.

Inverse kinematics of a 7-DOF redundant robot manipulator using the active set approach under joint physical limits

Abstract: This paper presents a new approach for an online solution of the inverse kinematics problem based on nonlinear optimization for robots with joint physical constraints The inverse kinematics problem is stated as a constrained nonlinear optimization problem and is solved using Kuhn--Tucker conditions analysis The nonlinear multivariable optimization problem is locally converted into independent local linear constrained subproblems and each subproblem is analytically solved For each joint, position limits and velocity limits are considered as physical constraints The proposed structure benefits from a very low complexity design The proposed method is fast and requires few calculations The convergence of the proposed algorithm is proven based on the Lyapunov function While keeping the algorithm stable, it can navigate the manipulator to a desired position under joint physical limits The algorithm is simulated on a 7-DOF PA-10 manipulator Results indicate good efficiency for the proposed structure in constrained path planning of joint space

Inverse kinematic analysis of the general 6R serial manipulators based on unit dual quaternion and Dixon resultant

Abstract: This article addresses the inverse kinematic problem of the general 6R serial robot via unit dual quaternion and Dixon resultant. Firstly, we show quaternion and dual-quaternion. Secondly, by the quaternion and dual quaternion theory, unit dual quaternion kinematics equations of 6R robots are derived. Thirdly, the solution process was constructed via elimination method and Dixon resultant; According to Dixon resultant, we get a 6th-order determinant which is equal to zero, and we can get a 16th-order polynomial in single variable from the determinant. All roots are obtained by a series of solving processes. Finally, the numerical example verifies the correctness of the solution process.

Motion planning for a knife-edge on the surface of a hyperboloid

Abstract: This paper presents a motion planning strategy for a knife-edge moving on the surface of a hyperboloid First, kinematics equations for the knife-edge are developed without the use of local coordinates so that the mathematical model is globally defined and have no singularities or ambiguities Then, a novel motion planning algorithm has been constructed using the concept of ruled surfaces The computer simulations demonstrate the effectiveness of the algorithm for any initial and final position/direction of the knife-edge on the surface of the hyperboloid

Forward kinematics modeling of spatial parallel linkage mechanisms based on constraint equations and the numerical solving method

Abstract: In order to solve general kinematics modeling problems and numerical stability problems of numerical methods for spatial parallel linkage mechanisms, a general modeling method and its numerical solving algorithm is proposed. According to the need for avoiding direct singular configurations, valid joint variable space and valid forward kinematics solutions (VKSs) are defined. Taking numerical convergence near singular points into account, the pseudo-arc length homotopy continuation algorithm is given to solve the kinematics model. Finally as an example, the joint variable space of the general Stewart platform mechanism is analyzed, which is proved to be divided into subspaces by direct singular surfaces. And then, forward kinematics solutions of 200 testing points are solved separately using the pseudo-arc length homotopy continuation algorithm, the Newton homotopy continuation algorithm and the Newton–Raphson algorithm (NRA). Comparison of the results shows that the proposed method is convergent to the same solution branch with the initial configuration on all the testing points, while the other two algorithms skip to other solution branches on some near singular testing points.

A general analytical algorithm for collaborative robot (cobot) with 6 degree of freedom (DOF)

Abstract: The Forward and inverse kinematics of the robot is the connection of mechanical system motion and control system. There is no closed form solution for inverse kinematics of 6 DOF robots currently. The method of numerical iterative algorithm is used usually, but which is hard to ensure the requirement of real-time and accuracy. Considering the application and characteristic of cobot, we designed the mechanical structure and distributed the 6 DOF of it. This paper uses the analytical method to get the consequence of the forward and inverse kinematics of the robot. It ensures the most important characteristics of real-time and accuracy. It can also get the singularity of the robot easily. At last, we verified the method by simulation in MATLAB.

Structural analysis of robot machine mechanisms with parallel kinematics

Abstract: Выполнен критический анализ существующих методик структурного анализа механизмов параллельной структуры, составляющих основу станков нового поколения с параллельной кинематикой. Разработана методика структурного анализа этих механизмов, основанная на декомпозиции кинематической цепи механизма с использованием наиболее подходящих структурных моделей. Приведены примеры применения методики. Ключевые слова: роботы-станки с параллельной кинематикой, механизмы параллельной структуры, структурный анализ, структурные модели, декомпозиция системы, композиция системы.

A geometric solution for inverse kinematics of redundant teleoperated surgical snake robots

Abstract: Pure analytical and numerical approaches are found undesirable for solving inverse kinematics of redundant robots. This is due to huge iterative procedures required to determine efficient joint configuration(s) for given target. In this paper, a new geometric method is presented for solving the inverse kinematics of snake robots ideal for real-time teleoperated surgery of internal organs. The method was applied to a 10-link redundant robotic model, capable of spatial navigation. Simulation result from the via-paths of circular track and human signature shows that the proposed method is fast and accurate in determining joint angles necessary to reach given target points with worst case mean error of x=0.608±0.231mm.