Showing papers on "Kinematics equations published in 2013"

The Inverse Kinematics of Cooperative Transport With Multiple Aerial Robots

Abstract: This paper addresses the kinematics of cooperative transport of payloads suspended by multiple aerial robots with cables. In such problems, it is important to determine the positions of the aerial robots to achieve a specified position and orientation of the payload. In general, this inverse kinematics problem has no solutions for the case with one or two robots and infinitely many solutions for three or more robots. However, in the case with three robots, when the tensions of the cables are also specified, this inverse kinematics problem is shown to have a finite number of solutions. In order to obtain all possible solutions, an efficient analytic algorithm based on dialytic elimination is presented in this paper. Case studies with an equilateral triangle payload and a general payload are used for demonstration. In addition, a numerical procedure is developed to determine the set of allowable tensions. Finally, an approach for stability analysis is developed, and the stability of all equilibrium configurations is analyzed.

Complete analytical inverse kinematics for NAO

Abstract: The design of complex dynamic motions for humanoid robots is achievable only through the use of robot kinematics. In this paper, we study the problems of forward and inverse kinematics for the Aldebaran NAO humanoid robot and present a complete, exact, analytical solution to both problems, including a software library implementation for realtime onboard execution. The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to the three-dimensional physical space, whereas the inverse kinematics provide closed-form solutions to finding joint configurations that drive the end effectors of the robot to desired target positions in the three-dimensional physical space. The proposed solution was made feasible through a decomposition into five independent problems (head, two arms, two legs), the use of the Denavit-Hartenberg method, and the analytical solution of a non-linear system of equations. The main advantage of the proposed inverse kinematics solution compared to existing approaches is its accuracy, its efficiency, and the elimination of singularities. In addition, we suggest a generic guideline for solving the inverse kinematics problem for other humanoid robots. The implemented, freely-available, NAO kinematics library, which additionally offers center-of-mass calculations, is demonstrated in two motion design tasks: basic center-of-mass balancing and pointing to the ball.

Legged Self-Manipulation

Abstract: This paper introduces self-manipulation as a new formal design methodology for legged robots with varying ground interactions. The term denotes a set of modeling choices that permit a uniform and body-centric representation of the equations of motion - essentially a guide to the selection and configuration of coordinate frames. We present the hybrid system kinematics, dynamics, and transitions in the form of a consistently structured representation that simplifies and unites the account of these, otherwise bewilderingly diverse differential algebraic equations. Cleaving as closely as possible to the modeling strategies developed within the mature manipulation literature, self-manipulation models can leverage those insights and results where applicable, while clarifying the fundamental differences. Our primary motivation is not to facilitate numerical simulation but rather to promote design insight. We instantiate the abstract formalism for a simplified model of RHex, and illustrate its utility by applying a variety of analytical and computational techniques to derive new results bearing on behaviors, controllers, and platform design. For each example, we present empirical results documenting the specific benefits of the new insight into the robot's transitions from standing to moving in place and to leaping.

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

Abstract: In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Position, Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

Abstract: This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.

Constraint-based movement representation grounded in geometric features

Abstract: Robots that are to master everyday manipulation tasks need both: The ability to reason about actions, objects and action effects, and the ability to perform sophisticated movement control. To bridge the gap between these two worlds, we consider the problem of connecting symbolic action representation with strategies from motion control engineering. We present a system using the task function approach [1] to define a common symbolic movement description language which defines motions as sets of symbolic constraints. We define these constraints using geometric features, like points, lines, and planes, grounding the description in the visual percepts of the robot. Additionally, we propose to assemble task functions by stacking 1-D feature functions, which leads to a modular movement specification. We evaluate and validate our approach on the task of flipping pancakes with a robot, showcasing the robustness and flexibility of the proposed movement representation.

Implementing Extended Kinematics of a Cable-Driven Parallel Robot in Real-Time

Abstract: This paper describes the implementation of extended pulley kinematics for parallel cable robots. An algorithm for the extended kinematics taking into account cable pulleys is discussed and implemented in real-time. This solution uses an iterative solver which can be computationally costly, depending on convergence. The convergence was tested for a specific geometry and successfully implemented on the cable robot IPAnema. Accuracy of both the standard and extended kinematics were tested according to the ISO 9283 standard. The Absolute accuracy was measured to be 22.32 mm for the standard and 17.50 mm for the extended kinematics which shows some improvement. A method for testing accuracy of orientations is also introduced.

Dynamics modeling of a Delta-type parallel robot (ISR 2013)

Abstract: This paper presents a simplified dynamics modeling and hardware implementation of a Delta-type parallel manipulator Due to complex kinematics, the Lagrangian equations of the first type is employed to derive the inverse dynamic equations Commercial Delta parallel robot can achieve more than 10m/s and 15g Accuracy and fast calculation of dynamics are very essential typically in computed torque control of a Delta-type parallel manipulator for high speed applications It is presented that the simplified dynamics equation matches very well with ADAMS modeling and the calculation time of the inverse kinematics and dynamics is less than 004msec

Inverse kinematics of a mobile robot

Abstract: The problem of kinematics is to describe the motion of the robotic system without consideration of the forces and torques causing the motion. This paper presents two methods to obtain the inverse kinematics of a mobile robot. In the first method, two rows of the forward kinematics are selected, the inverse of these two rows is obtained, and later the inverse matrix is combined with the third row of the forward kinematics. In the second method, the pseudo-inverse matrix of the forward kinematics matrix is obtained. The comparison result of the two proposed methods is presented. Two simulations show the effectiveness of the proposed inverse kinematics algorithm.

Modeling and motion analysis of four-Mecanum wheel omni-directional mobile platform

Abstract: Because of its comprehensive and flexible sporty performance, omni-directional mobile platform is widely used in industrial production, daily life as well as military fields Disposed on four terminals of the vehicle body, each wheel's movement is controlled by an independent motor respectively In this paper, we provide a structural analysis and motion resolving solution to the platform based on four separate Mecanum wheels We then study the proper layouts that meet the conditions required for full-directional movements Finally, we build the perspective mathematical model in its kinematics and dynamics terms

Path following control of planar snake robots using virtual holonomic constraints

Abstract: This paper considers path following control of planar snake robots using virtual holonomic constraints. We first derive the Euler-Lagrange equations of motion of the snake robot. Moreover, we integrate the effects of friction forces into these equations. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. In particular, we show that the constraint manifold can be made invariant by a suitable choice of feedback. Furthermore, we analytically design a smooth feedback control law to render the constraint manifold exponentially stable for the controlled system. We show that enforcing the appropriately defined virtual holonomic constraints implies that the robot converges to and follows a desired geometric path. Numerical simulations are presented to support the theoretical design.

Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator

Abstract: This work reports on the kinematics of a series-parallel manipulator built with two zero-torsion tangential parallel manipulators assembled in series connection. Although this mechanism has been widely studied, there are some topics that must be revised, e.g. the mobility analysis here reported shows that the robot under study is not precisely a six degrees of freedom spatial mechanism as it has been commonly considered. Furthermore, the traditional hexagonal coupler platform is replaced with a three-dimensional platform which yields a mechanism with a more general topology. The forward and inverse displacement analyses of the robot are obtained in semi-closed form solutions based on simple closure equations which are generated upon the coordinates of three points embedded to the moving platform while the input-output equations of velocity and acceleration of the semi-general series-parallel manipulator are easily derived by resorting to reciprocal-screw theory. A case study is included in order to show the application of the method of kinematic analysis.

Generalized humanoid leg inverse kinematics to deal with singularities

Abstract: We present here a simple technique of inverse kinematics to be used for humanoid legs. This technique has two advantages. First it permits to manage the stretched-legs space boundary singularities encountered with the classical inverse kinematics that uses a whole Jacobian matrix for all leg joint angle variations. This leg singularity configuration always appears when the humanoid robot has to get from the standing position with both legs stretched to a knee flexed position and vice-versa. Second the technique is independent of the convention of angle orientation at the hips and at the ankles. Therefore it does not require the specific solving for hip and ankle joint angles of the rotation matrix equations in the case of analytical geometric methods. The inverse kinematics proposed here is based on geometrical calculations to get knee coordinates, and on the decomposition of inverse leg kinematics, i.e. inverse kinematics at the hip for the one part, and inverse kinematics at the ankle for the other part. This calculation assumes that the leg has six rotary degrees of freedom, three at the hip, one at the knee, and two at the ankle. The orientation of rotary joints at the hip and at the ankle can be arbitrary.

Experimental kinematics modeling estimation for wheeled skid-steering mobile robots

Abstract: Skid-steering mobile robots, both wheels and tracked vehicles, are widely used because of their simple mechanism and robust However, due to the complex wheel-ground interactions and the kinematics constraints, it is a challenge to understand the kinematics and dynamics of such a robotic platform In this paper, we develop a kinematics modeling estimation scheme to analyze the skid-steering wheeled mobile robot based on the boundedness of the Instantaneous Centers of Rotation (ICRs) of treads on the 2D motion plane, and the parameters of this model are determined based on experimental analysis We study the relationship between the ICRs of the robot treads and two physical factors, ie, the radius of the path curvature and the robot speed Moreover, an ICRs coefficient and a nondimensional variable are introduced An approximating function is used to describe the relationship To validate the obtained results, the proposed model has been applied to a popular research robotic platform, Pioneer P3-AT It is empirically demonstrated that the developed model improves dead-reckoning performance of this skid-steering robot

The dynamic characteristics of the manipulator with parallel kinematic structure based on experimental data

Abstract: Dynamics of manipulator with parallel kinematics is examined in the article with the help of mathematical models which characterize interrelations between the control signals, disturbances and the platform's center of mass co-ordinates

Kinematics of Hex-Piderix - A Six-Legged Robot - Using Screw Theory

Abstract: In this paper the kinematic analysis of a six-legged robot, hereafter named Hex-piderix, is carried out. A three revolute (3R) chain has been chosen for each limb in order to mimic the leg structure of an insect. The rotation matrix, with unitary vectors, and the Denavit-Hartenberg (D-H) conventions are used to find the pose of the thorax. The problem of inverse position is solved by geometrical analysis. The direct and inverse infinitesimal kinematics are obtained by the reciprocal screw theory, considering a suction cup attached to each leg and modelling it as a UP linkage. A numerical example of the thorax pose was made by solving the equations obtained from the direct position analysis. The equations of the inverse position analysis were solved to obtain the angles of the joints. Finally, the velocity values of the thorax obtained from the infinitesimal kinematics were validated by simulating the movements of Hex-piderix using specialized software.

Inverse kinematics Analysis of 6-RRCRR parallel manipulators

Abstract: This paper presents a solution to the inverse kinematics of 6-RRCRR parallel manipulators with orthogonal non-intersecting RR-joint configuration. The inverse kinematics solution of such parallel robots compared with that of parallel robots with orthogonal intersecting RR-joint or universal joint configuration is more complex due to the existence of RR-joint variables. A novel methodology is established to define 6 independent variables of the actuators and 12 dependent RR-joint variables using the pose of the mobile platform with respect to the base frame. The constraint of RR-joints are analysed and the numerical algorithm to obtain joint variables is assessed. The forward kinematics of a 6- RRCRR parallel manipulator is modelled and computational analysis is performed in order to numerically verify the accuracy and effectiveness of the proposed methodology for the inverse kinematics analysis. Numerical results of a trajectory tracking simulation are provided. The results verify high accuracy for the proposed inverse kinematics solution of this special family of parallel micromanipulators.

Learning an internal representation of the end-effector configuration space

Abstract: Current machine learning techniques proposed to automatically discover a robot's kinematics usually rely on a priori information about the robot's structure, sensor properties or end-effector position. This paper proposes a method to estimate a certain aspect of the forward kinematics model with no such information. An internal representation of the end-effector configuration is generated from unstructured proprioceptive and exteroceptive data flow under very limited assumptions. A mapping from the proprioceptive space to this representational space can then be used to control the robot.

Configuration space control of a parallel Delta robot with a neural network based inverse kinematics

Abstract: This paper describes configuration space control of a Delta robot with a neural network based kinematics. Mathematical model of the kinematics for parallel Delta robot used for manipulation purposes in microfactory was validated, and experiments showed that this model is not describing “real” kinematics properly. Therefore a new solution for kinematics mapping had to be investigated. Solution was found in neural network utilization, and it was used to model robot's inverse kinematics. It showed significantly better mapping between task space coordinates and configuration (joint) space coordinates than the mathematical model, for the workspace of interest. Consequently positioning accuracy improvement is expected. Neural network is then used as a part of the control system. Applied control strategy was configuration space acceleration control with disturbance observer.

Differential Kinematics for Calibration, System Investigation, and Force Based Forward Kinematics of Cable-Driven Parallel Robots

Abstract: In this paper the differential kinematics for cable-driven robots is derived and the use for calibration, system investigation and a force based forward kinematics is shown. The Jacobians for each part of the kinematic chain are derived with respect to the platform pose and the most important system parameters. Beside the consideration of geometrical quantities, the differential relations between non-geometrical quantities such as cable stiffness and cable forces are determined. The decomposition in the most fundamental Jacobians allows to analyse and compute more complex relations by reassembling the Jacobians as needed. This approach allows more insight in the system behavior and enables the reuse of the individual modules. The purpose of this paper is to provide the framework and the key equations and to show the use for calibration, force based forward kinematics and system analysis as well as for control purposes.

Online learning of humanoid robot kinematics under switching tools contexts

Abstract: In this paper a novel approach to kinematics learning and task space control, under switching contexts, is presented. Such non-stationary contexts may appear in many robotic tasks: in particular, the changing of the context due to the use of tools with different lengths and shapes is herein studied. We model the robot forward kinematics as a multi-valued function, in which different outputs for the same input query are related to actual different hidden contexts. To do that, we employ IMLE, a recent online learning algorithm that fits an infinite mixture of linear experts to the online stream of training data. This algorithm can directly provide multi-valued regression in a online fashion, while having, for classic single-valued regression, a performance comparable to state-of-the-art online learning algorithms. The context varying forward kinematics is learned online through exploration, not relying on any kind of prior knowledge. Using the proposed approach, the robot can dynamically learn how to use different tools, without forgetting the kinematic mappings concerning previously manipulated tools. No information is given about such tool changes to the learning algorithm, nor any assumption is made about the tool kinematics. To our knowledge this is the most general and efficient approach to learning and control under discrete varying contexts. Some experimental results obtained on a high-dimensional simulated humanoid robot provide a strong support to our approach.

Kinematic and Workspace Analysis of a Parallel Robot Used in Security Applications

Abstract: This paper proposes a surveillance and defense system based on a 3SPS-1S parallel manipulator The central constraining leg of the mechanism increases the stiffness of the system and forces the manipulator to have three pure rotation degrees of freedom In this paper, the inverse kinematic equation is presented The forward kinematics problem is solved using a geometrical approach, and then a unique solution to the forward kinematics is obtained using artificial neural networks and Newton-Raphson's method A method to calculate the workspace is proposed, and then a method to maximize the workspace while maintaining the parameters of the robot as close as possible to a desired size is proposed Finally the Jacobian matrix is obtained and analyzed in order to calculate the singularities of the manipulator

A method of inverse kinematics of a 7-function underwater hydraulic manipulator

Abstract: The work presented in this paper focus on underwater operation technology, combined with the kinematics structure characteristics of a self-developed 7-function underwater hydraulic manipulator, a method of the manipulator's inverse kinematics is proposed. Using the combined method, in the case of knowing the manipulator end-effector's position and attitude, analytic solution of each joint can be solved quickly. This method is combined with the characteristics of Euler method and geometric method, the former three joint angles are achieved through the Euler method, and the last three joint angles are obtained through geometric method. The effectiveness of the method is verified by simulation and experiment on writing word “SIA”.

A complete solution to the inverse kinematics problem for 4-DOF manipulator robot

Abstract: A complete closed-form solution to the inverse kinematics problem for a 4-DOF manipulator robot is proposed. With the discussion of the existence of the offset and the distance between the axis of 1st joint and 2nd joint, all the possible solutions and singular configurations are presented. “Task attitude” is defined to describe the orientation of the end effector, which is convenient to solve the inverse kinematics problems in engineering. Finally, simulation of path-planning is performed, and the efficiency of the proposed method is verified through Mathematica.

A method for decentralized formation building for unicycle-like mobile robots

Abstract: The paper presents a method for decentralized flocking and global formation building for a network of unicycles described by the standard kinematics equations with hard constraints on the vehicles linear and angular velocities. We propose decentralized motion coordination control algorithms for the robots so that they collectively move in a desired geometric pattern from any initial position. There are no predefined leaders in the group and only local information is required for the control. The effectiveness of the proposed control algorithms is illustrated via computer simulations.

Real-time Inverse Kinematics of redundant manipulator using a hybrid (analytical and numerical) method

Abstract: Inverse Kinematics (IK) of redundant manipulators has been an active research problem in the field of robotics for a long time. Many solutions exist, though the focus here is to solve the problem of inverse kinematics (both position and orientation) in real-time for a 7 DOF redundant manipulator with spherical wrist. In other words, a computationally efficient way. The approach taken here attempts to decouple the redundant manipulator at the wrist, thus solving for the first four angles satisfying the wrist position and the last three angles satisfying the End Effector (EE) position and orientation. A hybrid approach of using analytical and numerical methods is undertaken to improve the computational efficiency, and the performance is compared with pure numerical methods. Various paths are generated using this method and tested for performance in terms of accuracy and speed. Finally, simulations on a Motoman IA20 redundant manipulator are shown to display satisfactory performance.