Showing papers on "Kinematics equations published in 2005"

Kinematics modeling and analyses of articulated rovers

Abstract: This paper describes a general approach to the kinematics modeling and analyses of articulated rovers traversing uneven terrain. The model is derived for full 6DOF (6-degree-of-freedom) motion, enabling movements in the x,y, and z directions, as well as pitch, roll, and yaw rotations. Differential kinematics is derived for the individual wheel motions in contact with the terrain. The resulting equations of the individual wheel motions are then combined to form the composite equation for the rover motion. Three types of kinematics, i.e., navigation, actuation, and slip kinematics are identified, and the equations and application of each are discussed. The derivations are specialized to Rocky 7, a highly articulated prototype Mars rover, to illustrate the developed methods. Simulation results are provided for the motion of the Rocky 7 over several terrains, and various motion profiles are provided to explain the behavior of the rover.

Natural resolution of ill-posedness of inverse kinematics for redundant robots: a challenge to Bernstein's degrees-of-freedom problem

Abstract: A robot designed to mimic a human becomes kinematically redundant, ieits total degrees of freedom becomes larger than the number of physical variables required for description of a given task Ki

Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism

Abstract: In this paper, the kinematics and inverse dynamics of a novel kind of mechanism called a general 3-PRS parallel mechanism is investigated. In the kinematics study, the inverse kinematics solution is derived in closed form, and the forward kinematics problem is resolved by the Newton iterative method seeking for an on-line solution to this issue. The inverse dynamics analysis is approached with two methods: Lagrangian formulations and principle of virtual work. After deriving the dynamic model by a Lagrangian formulation approach, the simulation results of two introduced examples quantitatively and qualitatively verify the accuracy of the derived dynamic equations. By introducing a simplifying hypothesis, a simplified dynamic model is set up using principle of virtual work, also a computer simulation is performed on this reduced model. The simulation results demonstrate that the simplified dynamic model is reasonable under such kind of assumptions through comparison with the precise model derived from the Lagrangian formulation. The inverse dynamics analysis provides a sound basis to develop controllers for controlling over a general 3-PRS parallel robot.

Generalized Stewart-Gough platforms and their direct kinematics

Abstract: In this paper, we introduce the generalized Stewart-Gough platform (GSP) consisting of two rigid bodies connected with six distance and/or angular constraints between six pairs of points, lines, and/or planes in the base and the moving platform, respectively. We prove that there exist 3850 possible forms of GSPs. We give the upper bounds for the number of solutions of the direct kinematics for all the GSPs. We also obtain closed-form solutions and the best upper bounds of real solutions of the direct kinematics for a class of 1120 GSPs.

A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm

Abstract: For robotic manipulators that are redundant or with high degrees of freedom (dof), an analytical solution to the inverse kinematics is very difficult or impossible. Pioneer 2 robotic arm (P2Arm) is a recently developed and widely used 5-dof manipulator. There is no effective solution to its inverse kinematics to date. This paper presents a first complete analytical solution to the inverse kinematics of the P2Arm, which makes it possible to control the arm to any reachable position in an unstructured environment. The strategies developed in this paper could also be useful for solving the inverse kinematics problem of other types of robotic arms.

Comparison of inverse kinematics solutions using neural network for 6R robot manipulator with offset

Abstract: An artificial neural network (ANN) using backpropagation algorithm is applied to solve inverse kinematics problems of industrial robot manipulator 6R robot manipulator with offset wrist was chosen as industrial robot manipulator because geometric feature of this robot does not allow solving inverse kinematics problems analytically In other words, there is no closed form solution for this problem In order to define orientation of robot end-effector, three different representations are used here: homogeneous transformation matrix, Euler angles and equivalent angle axis These representations were compared to obtain inverse kinematics solutions for 6R robot manipulator with offset wrist Simulation results show that prediction performance from the approximation accuracy point of view is satisfactory with low effective errors based on 10 degrees data resolution

An Analysis of the Inverse Kinematics for a 5-DOF Manipulator

Abstract: This paper proposes an analytical solution for a 5-DOF manipulator to follow a given trajectory while keeping the orientation of one axis in the end-effector frame. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analyzed systematically. The singular problem is discussed after the forward kinematics is provided. For any given reachable position and orientation of the end-effector, the derived inverse kinematics will provide an accurate solution. In other words, there exists no singular problem for the 5-DOF manipulator, which has wide application areas such as welding, spraying, and painting. Experiment results verify the effectiveness of the methods developed in this paper.

Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator

Abstract: This article introduces an exact method to solve the forward kinematics problem (FKP) specifically applied to spatial parallel manipulators. The majority can modeled by the 6-6 parallel manipulator. This manipulator is a hexapod made up of a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball or Cardan joints. In order to implement algebraic methods, the parallel manipulator kinematics will be formulated as polynomial equations systems where the equation number is equal to the unknown numbers. One position-based kinematics model will be identified to solve the difficult FKP. The selected proven algebraic method implements Grobner bases and constructs an equivalent univariate polynomial system. The exact resolution of this last system determines the real solution which exactly corresponds to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. We provide several examples o...

Modeling and controlling a robotic convoy using guidance laws strategies

Abstract: This paper deals with the problem of modeling and controlling a robotic convoy. Guidance laws techniques are used to provide a mathematical formulation of the problem. The guidance laws used for this purpose are the velocity pursuit, the deviated pursuit, and the proportional navigation. The velocity pursuit equations model the robot's path under various sensors based control laws. A systematic study of the tracking problem based on this technique is undertaken. These guidance laws are applied to derive decentralized control laws for the angular and linear velocities. For the angular velocity, the control law is directly derived from the guidance laws after considering the relative kinematics equations between successive robots. The second control law maintains the distance between successive robots constant by controlling the linear velocity. This control law is derived by considering the kinematics equations between successive robots under the considered guidance law. Properties of the method are discussed and proven. Simulation results confirm the validity of our approach, as well as the validity of the properties of the method.

Clifford Algebra Exponentials and Planar Linkage Synthesis Equations

Abstract: This paper uses the exponential defined on a Clifford algebra of planar projective space to show that the standard-form design equations used for planar linkage synthesis are obtained directly from the relative kinematics equations of the chain. The relative kinematics equations of a serial chain appear in the matrix exponential formulation of the kinematics equations for a robot. We show that formulating these same equations using a Clifford algebra yields design equations that include the joint variables in a way that is convenient for algebraic manipulation. The result is a single formulation that yields the design equations for planar 2R dyads, 3R triads, and nR single degree-of-freedom coupled serial chains and facilitates the algebraic solution of these equations including the inverse kinematics of the chain. These results link the basic equations of planar linkage design to standard techniques in robotics.

A method for robot navigation toward a moving goal with unknown maneuvers

Abstract: This paper deals with a method for robot navigation towards a moving goal. The goal maneuvers are not a priori known to the robot. Our method is based on the use of the kinematics equations of the robot and the goal combined with geometrical rules. First a kinematics model for the tracking problem is derived and two strategies are suggested for robot navigation, namely the velocity pursuit guidance law and the deviated pursuit guidance law. It turns out that in both cases, the robot's angular velocity is equal to the line of sight angle rate. Important properties of the navigation strategies are discussed and proven. In the presence of obstacles, two navigation modes are used: the tracking mode, which has a global aspect and the obstacle avoidance mode, which has a local aspect. In the obstacle avoidance mode, a polar diagram combining information about obstacles and directions corresponding to the pursuit is constructed. An extensive simulation study is carried out, where the efficiency of both strategies is illustrated for different scenarios.

A new spatial three-DoF parallel manipulator with high rotational capability

Abstract: This paper concerns the proposal and analysis of a novel spatial parallel manipulator. The parallel manipulator consists of a base plate, a movable platform, and three connecting legs. The moving platform has three degrees of freedom (DoFs), which are two degrees of translational freedom and one degree of rotational freedom, with respect to the base plate. The inverse and forward kinematics problems are described in closed forms and the velocity equation of the new parallel manipulator is given. Three kinds of singularities are presented. The workspace for the manipulator is analyzed systematically. Especially, the indices to evaluate the rotational capability of the moving platform of the manipulator will be defined and discussed in detail. Due to the high rotational capability performance, the proposed manipulator has wide application in the fields of industrial robots, simulators, micromotion manipulators, and parallel kinematic machines.

Kinematics of a 3-DOF parallel manipulator with an R-P-S joint structure

Abstract: A new solution of the inverse kinematics task for a 3-DOF parallel manipulator with a R-P-S joint structure is obtained for a given position of end-effector in the form of simple position equations. Based on this the number of the inverse kinematics task solutions was investigated, in general, equal to four. We identify the size of the manipulator feasible area and simple relationships are found between the position and orientation of the platform. We prove a new theorem stating that, while the end-effector traces a circular horizontal path with its centre at the vertical z-axis, the norm of the joint coordinates vector remains constant.

Sizing a Serial Chain to Fit a Task Trajectory Using Clifford Algebra Exponentials

Abstract: In this paper we formulate the “generalized inverse kinematics problem” for a spatial serial chain, where the goal is to determine values for structural parameters as well as for the joint parameters. The kinematics equations of the chain are formulated first using matrix exponentials and then cast into a form based on exponentials in a Clifford algebra. These equations contain the coordinates of the joint axes explicitly and have a systematic structure that can be exploited in their solution. As an example we fit a seven degree-of-freedom CCS chain to a 12 position task trajectory. In this problem, we can also specify desired values for the first two joint angles, and compute the structural parameters and the remaining joint angles.

Virtual prototype simulation of hydraulic shovel kinematics for spatial characterization in surface mining operations

Abstract: Hydraulic shovels are large-capacity equipment for excavating and loading dump trucks in constrained surface mining environments. Kinematics simulation of such equipment allows mine planning engineers to plan, design and control their spatial environments to achieve operating safety and efficiency. In this study, a hydraulic shovel was modelled as a mechanical manipulator with five degrees of freedom comprising the crawler, upper, boom, stick, bucket and bucket door components. The model was captured in a schematic diagram consisting of a six-bar linkage using the symbolic notation of Denavit and Hartenberg (Ho and Sriwattanathmma 1989). Homogeneous transformation matrices were used to capture the spatial configuration between adjacent links. The forward kinematics method was used to formulate the kinematics equations by attaching Cartesian coordinates to the schematic shovel diagram. Based on the kinematics model, a 3D virtual prototype of the hydraulic shovel was built in the Automatic Dynamic Analysis ...

Differential kinematics of serial manipulators using virtual chains

Abstract: This paper presents a new approach to calculate the direct and inverse differential kinematics for serial manipulators. The approach is an extension of the Davies method for open kinematic chains based on a virtual kinematic chain concept introduced in this paper. It is a systematic method that unifies the kinematics of serial manipulators considering the type of kinematics and the coordinate system of the operational space and constitutes an alternative way to solve the differential kinematics for manipulators. The usefulness of the method is illustrated by applying it to an industrial robot.

Hyper-flexible robotic manipulators

Abstract: In this paper, the theoretical foundation of robotic systems with hyper-flexible bodies with one-dimensional topological structure such as hyper-flexible manipulators is provided. Based on the rigorous kinematics and dynamics of hyper-flexible bodies, we can find the essential knowledge on the system.

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

Abstract: Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Kinematic redundancy resolution for two cooperating underwater vehicles with on-board manipulators

Abstract: This paper studies the inverse kinematics problem for two underwater vehicles with on-board manipulators cooperating to carry a common rigid object. The coordinate frames are assigned to the system formed by the two underwater vehicle-manipulator mechanisms and the rigid load and a set of generalized coordinates are selected to describe the system configuration. The kinematic position and velocity relations are obtained. A kinematic model is formulated for the system to be used for solving the inverse kinematics problem. The pseudovelocities are introduced in order to incorporate the kinematic constraint equations into the kinematic velocity relations. A task-priority redundancy resolution technique is presented in which the kinematic redundancy is used to accomplish secondary tasks of the design choice.

Inverse kinematics, forward kinematics and working space determination of 3dof parallel manipulator with s-p-r joint structure

Abstract: This paper addresses the analysis of inverse kinematics, forward kinematics solutions and working space determination for the 3 degree-of-freedom (DOF) parallel manipulator with the S-P-R (Spherical-Prismatic-Revolute) joint structure. An effective approach is developed for the solution of inverse kinematics task in analytical form for given end-effector position. A method for working space determination which uses numerical solution of forward kinematics task is presented.

Normalised-generalised-velocity-component-based controller for a rigid serial manipulator

Abstract: A controller based on first-order decoupled equations of motion for application to rigid serial manipulators is presented. The equations result from a modification of equations expressed in generalised velocity components form. It is shown that using the proposed quasi-velocities i.e. normalised generalised velocity components (NGVCs) leads to differential equations that contain the identity mass matrix (instead of a diagonal matrix). Using the proposed controller and equations written in terms of NGVCs it is possible to obtain information on the system dynamics. The considered controller is stable in the Lyapunov sense. Experimental results obtained on a two-degree-of-freedom manipulator illustrate the effectiveness of the proposed technique.

A new ZMP constraint equation with application to motion planning of humanoid using kinematic redundancy

Abstract: The human body exploits "redundant degree of freedom" to execute various motions in a suitable fashion. This work deals with development of effective redundancy resolution algorithms for the motion control of humanoid. Differently from the typical kinematically redundant robots that are attached to the fixed ground, the ZMP condition should be taken into account in the human body motion in order to guarantee the system stability. For this, a geometric constraint equation is derived by reshaping the existing ZMP equation. This constraint equation is formed like a second order kinematic equation, which enables one to plan the ZMP trajectory in a feedforward fashion. This constraint equation and the kinematic equation of the humanoid model are solved together. A sequential redundancy resolution algorithm exploiting the remaining kinematic redundancy is also proposed to optimize several secondary criteria such as joint limit index and manipulability. The feasibility of the proposed algorithms is verified by simulating a stable standing up motion and a planar walking motion though planar 5 DOF and 6 DOF humanoid models.

Neural network solution for the forward kinematics problem of a redundant hydraulic shoulder

Abstract: In this paper, a neural network based solution for forward kinematics analysis of a hydraulic shoulder is presented The shoulder has three degrees of freedom rotational motion produced by four hydraulic cylinders which makes it a redundant parallel robotic shoulder Unlike the serial robots, forward kinematics problem of parallel robots is not easily solved because of the nonlinearity and complexity of the parallel robot's kinematic equations and there are several solutions which are almost impossible to be found analytically The neural network used in this paper is of the feedforward net type and a multi-layer back propagation procedure is utilized to train the network A simulation study is performed using two types of trajectories to illustrate the advantages of the proposed method in solving the forward kinematics problem of the redundant mechanism The results show the method provides a fast solution and good tracking performance

Solution for One Type of Inverse Kinematics Sub-problem in Screw Theory and Its Application

Abstract: In order to solve the robot inverse kinematics in screw theory, the motion equation is usually divided into several sub-problems. At present, the combination of ordinary sub-problem cant achieve the inverse kinematics of all type of robots. A new type of sub-problem is proposed in this paper, and its solution and constraint conditions are given. In addition, its application in parallel robots with RTS chain is demonstrated to verify its feasibility. Finally, a method using the combination of the motion screws with the same effect on the reference point is obtained to simplify robot inverse kinematics.

Hybrid Target Tracking Manipulation Theories for Combined Force and Position Control in Open and Closed Loop Manipulators

Abstract: This paper presents a new manipulation theory for controlling compliant motions of a robotic manipulator. In previous closed loop control methods, both direct kinematics and inverse kinematics of a manipulator must be resolved to convert feedback force and position data from Cartesian space to joint space. However, in many cases, the solution of direct kinematics in a parallel manipulator or the solution of inverse kinematics in a serial manipulator is not easily available. In this study, the force and position data are packed into one set of “motion feedback,” by replacing the force errors with virtual motion quantities, or one set of “force feedback,” by replacing motion errors with virtual force quantities. The joint torques are adjusted based on this combined feed back package. Since only Jacobian of direct kinematics or Jacobian of inverse kinematics is used in the control scheme, the computational complexity is reduced significantly. The applications of this theory are demonstrated in simulation experiments with both serial and parallel manipulators.Copyright © 2005 by ASME