Closed Kinematic Chains Research Articles

Autonomous calibration of single-loop closed kinematic chains formed by manipulators with passive endpoint constraints

The authors present a kinematic calibration method that does not require endpoint measurements or precision points. By forming manipulators into mobile closed kinematic chains, it is shown that consistency conditions in the kinematic loop closure equations are adequate to calibrate the manipulator from joint angle readings alone. This closed-loop kinematic calibration method is an adaptation of an iterative least-squares algorithm used in calibrating open-chain manipulators. Example tasks include a fixed endpoint (zero-degree-of-freedom (DOF) task), the opening of a door (one-DOF task), and point contact (three-DOF task).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the structure of the minimum-time control law for multiple robot arms handling a common object

The problem of the structure of the minimum-time control for multiple robot arms cooperatively handling a common object is addressed. The dynamical system is modeled by considering the arms as closed kinematic chains. It is shown that the structure of the minimum-time control law for individual joint actuators requires that at least one of the actuators is always saturated on any finite-time subinterval, while the rest of them are either saturated or singular depending upon the motion configurations and robot parameters. Thus, it is suggested that the totally singular optimal control does not exist in this problem, while a partially singular control may occur. The theoretical result should provide insight into the dynamic characteristic of the multiple-robot system which can be valuable in the path planning and design specifications of the system. >

Simulation of cooperating robot manipulators on a mobile platform

The dynamic equations of motion are presented for two or more cooperating manipulators on a freely moving mobile platform. The system of cooperating robot manipulators forms a closed kinematic chain where the force of interaction must be included in the formulation of robot and platform dynamics. The formulation includes the full dynamic interactions from arms to platform and arm tip to arm tip, and the possible translation and rotation of the platform. The equations of motion are shown to be identical in structure to the fixed-platform cooperative manipulator dynamics. The structure of the closed-chain dynamics, allows the use of any solution for the open topological tree of base and manipulator links. The number of degrees of freedom (DOF) of the system is sufficiently large to make recursive dynamic calculation methods potentially more efficient than closed-form solutions. A complete simulation with two 6-DOF manipulators of a free-floating platform is presented along a with a multiple-arm controller to position the common load. >

A Solution for the Force Distribution Problem in Redundantly Actuated Closed Kinematic Chains

Proper control of robotic systems which incorporate closed kinematic chains is important in many applications. Among these are the multi-robot work cell and legged vehicles. In these no unique solution exists for the force distribution corresponding to a specified trajectory. A framework within which additional constraint equations may be written is presented here, and the force distribution solved in closed form for a walking machine application. These constraints are related to system performance goals of interest, such as improved traction and/or load sharing among the legs. The proposed technique is shown to be computationally simpler than other alternative solutions to the same problem.

Singularity analysis of closed-loop kinematic chains

The different kinds of singularities encountered in closed-loop kinematics chains are analyzed. A general classification of these singularities in three main groups, which is based on the properties of the Jacobian matrices of the chain, is described. The identification of the singular configurations is particularly relevant for hard automation modules or robotic devices based on closed kinematic chains, such as linkages and parallel manipulators. Examples are given to illustrate the application of the method to these mechanical systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Force Distribution in Walking Vehicles

This paper addresses the problem of the appropriate distribution of forces between the legs of a legged locomotion system for walking on uneven terrain. The legs of the walking machine and the terrain form closed kinematic chains. The system is statically indeterminate and an optimal solution is desired for force control of the legs. In addition, as unisense force limitations are imposed on the wrenches acting at the feet, it is important to be able to determine for any given configuration whether or not a set of valid contact forces can be found which will ensure the stability of the vehicle. Fast and efficient algorithms to solve these problems have been developed. The trade-off between computational simplicity and optimality makes it necessary to resort to suboptimal algorithms. In particular, schemes based on the Moore-Penrose Generalized Inverse, or the pseudo inverse, and linear programming were investigated. An active compliance control scheme with varying leg compliances is shown to be a suitable paradigm for control. A variation of the linear programming technique, that is well-suited to the problem of predicting instability in the vehicle, is also presented.

Dynamics of the manipulator with closed chains

The concept of dynamic equilibrium is used to derive a relation with which the actuator forces of a manipulator with a closed kinematic chain can be calculated in the same way as those of a manipulator with an open chain. Although the result is equivalent to that of J.Y.S. Luh and Y.F. Zheng (1985) the method provides physical insight into the dynamics of manipulators with closed kinematic chains. This relation also leads to the dynamic equations of motion with a minimal dimension for a closed kinematic chain. The semi-direct-drive robot is taken as an illustrative example. The numerical results verify the theory. The computational complexity of the inverse dynamics of this robot is also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamic analysis of a 6 DOF CKCM robot end-effector for dual-arm telerobot systems

In this paper, we present the dynamical analysis of a six-degree-of-freedom robot end-effector built to study telerobotic service and maintenance of NASA hardwares in space. The design of the end-effector is based on the concept of closed-kinematic chain mechanism capable of performing precise motion in a small workspace. After presenting a closed-form solution for the inverse kinematic problem, we employ the Lagrangian approach to derive a set of equations of motion for the end-effector where the generalized coordinates are selected to be the Cartesian coordinates. Computer simulation study shows that the centrifugal and Coriolis terms can be neglected fow slow motion. Effects of system parameters on the end-effector dynamics are also studied using computer simulation.

Kinematic analysis and workspace determination of a 6 dof ckcm robot end-effector

This paper presents the analysis of a 6 DOF robot end-effector built to study telerobotic assembly of NASA hardwares in space. Since the end-effector is required to perform high precision motion in a limited workspace, closed-kinematic chain mechanism is chosen for its design. A closed-form solution is obtained for the inverse kinematic problem and an iterative procedure employing Newton-Raphson method is proposed to solve the forward kinematic problem. A study of the end-effector workspace results in a general procedure for the workspace determination based on the link constraints. Computer simulation results are presented.

Dynamic modeling of closed-chain robotic manipulators and implications for trajectory control

A simple, physically insightful method for dynamic modeling of manipulators containing closed kinematic chains is presented. Founded on D'Alembert's principle, the method centers around a transformation from the well-understood dynamics of serial and open-chain mechanisms to closed-chain dynamic robot models. The framework for the closed-chain dynamic robot model fosters straightforward extensions of serial robot engineering activities in the areas of digital simulation, real-time control, parameter identification, and optimal path planning to closed-chain manipulators. The algorithms needed to realize these extensions are detailed, and the important concepts are highlighted with an example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New nonlinear control algorithms for multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space. >

Force distribution in closed kinematic chains

The problem of force distribution in systems involving multiple frictional contacts between actively coordinated mechanisms and passive objects is examined. The special case in which the contact interaction can be modeled by three components of forces (zero moments) is particularly interesting. The Moore-Penrose generalized inverse solution for such a model (point contact) is shown to yield a solution vector such that the difference between the forces at any two contact points projected along the line joining the two points vanishes. Such a system of contact forces is described by a helicoidal vector field which is geometrically similar to the velocity field in a rigid body twisting about an instantaneous screw axis. A method to determine this force system is presented. The possibility of superposing another force field which constitutes the null system is also investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cooperative control of two arms in the transport of an inertial load in zero gravity

In designing a robot control system for dual arm configurations, the control engineer is faced with two challenges: to derive the equations of motion for a given situation, and to meet certain desired control requirements (for instance, minimum energy). The former may involve closed kinematic chains, such as the case when the two arms are grasping a common object. The latter usually involves nonlinear optimization. These issues are considered in the context of transporting an inertial load using two planar three-link arms. A generalized 'reduction transformation' is applied to the dynamics to remove the singularity in the system equations. A suboptimal minimum energy method is presented to reduce a difficult 12-state, six-control nonlinear optimization to two independent, nonconflicting suboptimizations. A simulation example is provided to illustrate the degree of energy reduction possible using the optimal arm torque distribution that was developed. >

Position and force control of coordinated multiple arms

A technique is presented for controlling multiple manipulators which are holding a single object and therefore form a closed kinematic chain. The object, which may or may not be in contact with a rigid environment, is assumed to be held rigidly by n robot end-effectors. The derivation is based on setting up constraint equations which reduce the 6*n degrees of freedom of n manipulators each having six joints. Additional constraint equations are considered when one or more degrees of freedom of the object is reduced due to external constraints. Utilizing the operational space dynamic equations, a decoupling controller is designed to control both the position and the interaction forces of the object with the environment. Simulation results for the control of a pair of two-link manipulators are presented. >

Formulation of the kinematic model of a general (6 DOF) robot manipulator using a screw operator

AbstractIn general, the manipulator's end‐effector can be located in a desired position and orientation in its work‐space through angular and/or linear displacements of its joints. These joint coordinates can be obtained by solving the loop‐closure equation of the manipulator's kinematic model. The most common method for obtaining this equation is based on the point coordinates 4×4 homogeneous transformation matrix. This method uses a special set of frames which are adapted to the manipulator's configuration. Within the last few years there has been some interest in the use of screw operators (line transformations) to model the kinematic configuration of manipulators and to form the loop‐closure equation. In this article, a kinematic model of a general (6 DOF) manipulator is obtained through the application of a screw operator (dual‐unit quaternion) to represent the screw displacements of the line coordinates of the manipulator link and joint axes. The loop‐closure equation of the closed kinematic chain is obtained by introducing a hypothetical link/joint at the manipulator's end‐effector location. The resultant non‐linear loop‐closure equation is then solved for the joint coordinates using a numerical technique. The method is illustrated with an example.

Constrained Relations between Two Coordinated Industrial Robots for Motion Control

Tasks for two coordinated industrial robots always bring the robots in contact with the same object. Physically the three form a closed kinematic chain mechanism. When the chain is in motion, the positions and orientations of the two robots must satisfy a set of holonomic equality canstraints for every time instant. To eliminate motion errors between them, we assign one of them to carry the major part of the task. Its motion is planned accordingly. The motion of the second robot is to follow that of the first robot, as specified by the re lations of the joint velocities derived from the constraint conditions. Thus if any modification of the motion is needed in real time, only the motion of the first robot is modified. The modification for the second robot is done implicitly through the constraint conditions. Specifically, when the joint displacements, velocities, and accelerations of the first robot are known for the planned or modified motion, the corre sponding variables for the second robot and the forces/torques can be determined through the constrained relations.

Application of the Vector-Network Method to Constrained Mechanical Systems

The vector-network technique is a methodical approach to formulating equations of motion for unconstrained dynamic systems, utilizing concepts from graph theory and vectorial mechanics; it is ideally suited to computer applications. In this paper, the vector-network theory is significantly improved and extended to include constrained mechanical systems with both open and closed kinematic chains. A new formulation procedure is developed in which new kinematic constraint elements are incorporated. The formulation is based on a modified tree/cotree classification, which deviates significantly from previous work, and reduces the number of equations of motions to be solved. The dynamic equations of motion are derived, with generalized accelerations and a subset of the reaction forces as solution variables, and a general kinematic analysis procedure is also developed, similar to that of the dynamic formulation. Although this paper restricts most discussions to two-dimensional (planar) systems, the new method is equally applicable to 3-dimensional systems.

Dynamics of manipulation mechanisms with constrained gripper motion. Part I

AbstractThis article deals with the dynamics of closed kinematic chains obtained from open ones by introducing some constraints upon the motion of the last segment. Such problems apear very often in practical manipulator operation (writing task, assembling, etc.). The reduced position vector is defined and the dynamic model formed so as to allow the calculation of both the relative motion with respect to the constraint and the reactions, of the constraint. Impact problems are discussed also. Finally, a surface‐type constraint is considered.

協調制御を必要としない歩行機械に関する研究

Legged locomotion over irregular terrain is composed of body propelling motion and terrain adapting motion. Although conventional walking machines with three active degrees of freedom (d.o.f) for each leg can adapt their feet on irregular ground using flexible leg freedom, such machines generally require a tremendously complex control scheme for the body propelling motion, because cooperational control of leg freedoms in stance is required for a system with several closed kinematic chains between the body and the ground. To cope with this problem, a walking machine with decoupled freedoms, described in this paper, is based on the idea that body propelling motion is realized by only one degree of freedom and can be perfectly decoupled from the freedoms for terrain adaptability. In this type walking machine, the control system is perfectly released from the control of closed kinematic chains. Therefore it can be expected that the control algorithm will become much easier than that of conventional walking machines having three active d.o.f. per each leg. First, the authors discuss such walking machines and make clear the quadruped walking model with minimum active d.o.f. through basic considerations of freedoms of walking machines. Next, according to observations of animal locomotion, a hexapod walking machine (MELWALK) with decoupled freedoms using an approximate straight line mechanism is developed in order to realize faster and simpler walking machines than the quadruped one. As the foot pattern of this walking machine is limited to only one pattern, other kinds of freedoms are established to implement a body direction changing motion and a terrain adapting motion. Rotational freedom other than propulsion is added to implement the body direction changing motion, and extension and contraction freedom to the legs are also added to implement the terrain adapting motion. Although more than two active d.o.f. for each leg are desirable for terrain adaptability, the proposed walking machine has only one active d.o.f. for simplicity. Experiments are carried out to certify the body propelling motion, terrain adapting motion and body direction changing motion. It can be recognized from the trajectory of LED that the body proceeds along an approximate straight line close to an exact one. Body direction changing motion is implemented with relatively high speed. Furthermore in order to check energetic efficiency, the power consumed by DC motor is also measured using MELWALK MARK-I. Several features of the proposed hexapod walking machine are revealed through these experiments.

4536021 Emergency Unlocking mechanism for door of automobile : Haru Mochida, Yokohama, Japan assigned to Nissan Motor Co Ltd

Static balancing through passive devices is a suitable strategy to reduce motor loads for numerous applications in the automation and robotics fields. Many known methods require initially defining which balancing elements to install, thus possibly limiting the compensation effectiveness, since potentially optimal solutions may be neglected. This work presents an approach to statically balance linkages characterized by open and/or closed kinematic chains. The proposed algorithm searches for possible balanced variants of the mechanism that can be arranged by installing combinations of counterweights and springs, without auxiliary linkages. If solutions are found, the corresponding balancing parameters are tuned for optimizing the mechanism energy consumption, by considering the mechanism dynamics when performing its operational tasks. Actual benefits and drawbacks of the variants are assessed through quantitative criteria. The corresponding performance indicators are proposed as a guideline for designers to identify the most convenient balancing solutions. The implemented procedure is general and suitable to study any mechanism admitting closed-form solutions for its forward kinematics. A case study concerning an industrial palletizing robot is reported as an example of application. Overload issues affecting the robot actuators are solved through gravity compensation. The results achieved for the industrial problem prove the procedure effectiveness.