Kinematics Optimization of a 3-SPS Parallel Redundant Motion Mechanism Using Conformal Geometric Algebra

2015 ◽  
Vol 789-790 ◽  
pp. 889-895
Author(s):  
Jahng Hyon Park ◽  
Jeseok Kim ◽  
Jin Han Jeong
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Inverse Kinematic ◽  
Fast Reaction ◽  
Inverse Kinematic Problem ◽  
Time Optimal ◽  
Parallel Link ◽  
Spherical Parallel Manipulator

In this paper, an actuation mechanism for high-speed aiming of a target is proposed. The mechanism is a 3DOF-SPS (spherical-prismatic-spherical) parallel manipulator and can be used for a missile defense system with a fast reaction time. This type of parallel mechanism has high rigidity against external disturbances and accordingly high stiffness and precision. The target aiming requires 2 degrees of freedom and this 3 DOF mechanism has one redundancy. For fast manipulation of the proposed mechanism, the redundancy can be exploited and an optimal solution can be found out of the infinite number of inverse kinematic solutions. For finding a near time-optimal solution, a cost function is formulated considering displacement of each parallel link and an optimization technique is used for solution of the inverse kinematic problem.

scholarly journals Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 747-767 ◽  
Author(s):  
Masayuki Shimizu
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Target Orientation ◽  
End Effector ◽  
Position And Orientation

SUMMARYThis paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

General method for kinematic synthesis of manipulators with task specifications

Robotica ◽  
1997 ◽  
Vol 15 (6) ◽  
pp. 653-661 ◽  
Author(s):  
F.B. Ouezdou ◽  
S. Régnier
Keyword(s):  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Synthesis Problem ◽  
Inverse Kinematic Problem ◽  
Kinematic Synthesis ◽  
Six Degrees Of Freedom ◽  
Cluttered Environment ◽  
Dimensional Parameters ◽  
Joint Limits ◽  
General Method

This paper deals with the kinematic synthesis of manipulators. A new method based on distributed solving is used to determine the dimensional parameters of a general manipulator which is able to reach a set of given tasks specified by orientation and position. First, a general Distributed Solving Method (DSM) is presented in three steps: the problem statement, the objective functions formulations and the minimum parameters values determination. Then, this method is applied to solve the synthesis of the Denavit and Hartenberg set of parameters of a manipulator with a given kinematic structure. In this case, the kind and the number of joints are specified and a set of constraints are included such as joint limits, range of dimensional parameters and geometrical obstacles avoidance. We show that if the Denavit and Hartenberg parameters (DH) are known, the synthesis problem is reduced to an inverse kinematic problem. We show also how the problem of robot base placement can be solved by the same method. A general algorithm is given for solving the synthesis problem for all kind of manipulators. The main contribution of this paper is a general method for kinematic synthesis of all kind of manipulators and some examples are presented for a six degrees of freedom manipulator in cluttered environment.

scholarly journals Kinematic Analysis and Trajectory Planning of the Orthoglide 5-Axis

2015 ◽  
Author(s):  
S. Caro ◽  
D. Chablat ◽  
P. Lemoine ◽  
P. Wenger
Keyword(s):  
Trajectory Planning ◽  
Kinematic Analysis ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Hybrid Architecture ◽  
Parallel Kinematic Machine ◽  
Control Loop ◽  
Parallel Kinematic

The subject of this paper is about the kinematic analysis and the trajectory planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of freedom parallel kinematic machine developed at IRCCyN and is made up of a hybrid architecture, namely, a three degrees of freedom translational parallel manipulator mounted in series with a two degrees of freedom parallel spherical wrist. The simpler the kinematic modeling of the Orthoglide 5-axis, the higher the maximum frequency of its control loop. Indeed, the control loop of a parallel kinematic machine should be computed with a high frequency, i.e., higher than 1.5 MHz, in order the manipulator to be able to reach high speed motions with a good accuracy. Accordingly, the direct and inverse kinematic models of the Orthoglide 5-axis, its inverse kinematic Jacobian matrix and the first derivative of the latter with respect to time are expressed in this paper. It appears that the kinematic model of the manipulator under study can be written in a quadratic form due to the hybrid architecture of the Orthoglide 5-axis. As illustrative examples, the profiles of the actuated joint angles (lengths), velocities and accelerations that are used in the control loop of the robot are traced for two test trajectories.

scholarly journals A Tabular Format for Computing Inverse Kinematic Equations for a 3DOF Robot Leg

10.5772/7234 ◽  
2009 ◽  
Vol 6 (3) ◽  
pp. 26 ◽  
Author(s):  
F. Nickols
Keyword(s):  
Power Series ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Coordinate Space ◽  
Power Series Method ◽  
Cylindrical Coordinate ◽  
Field Programmable ◽  
Robot Leg ◽  
Three Degrees Of Freedom

A method is presented for accurately computing the three servomechanism angles that place the leg tip of a 3DOF robot leg in cylindrical coordinate space, R, θ, Z. The method is characterized by (i) a multivariable integer power series for each degree of freedom that can be used to replace traditional trigonometrical functions, and, (ii) only integer numbers are used. A technique is shown that derives the coefficients, Ci j k, of each of the terms in the series that represents a servomechanism angle, S. This power series method has the advantage of; (i) satisfying accuracy requirements, (ii) producing a unique solution, (iii) high speed realtime computation, (iv) low memory requirement and (v) implementation into a generic algorithm or hardware such as a field programmable gate array. The series can represent many continuous kinematic systems just by changing the values of the coefficients. The coefficients are rapidly computed via a spreadsheet. The method can be extended to more than three degrees of freedom and also mapped into other coordinate frames such as a Cartesian or spherical.

Admissible trajectory determination for two cooperating robot arms

Robotica ◽  
1988 ◽  
Vol 6 (2) ◽  
pp. 107-113 ◽  
Author(s):  
Joonhong Lim ◽  
Dong H. Chyung
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Experimental System ◽  
Inverse Kinematic ◽  
Robotic Hands ◽  
Robot System ◽  
Inverse Kinematic Problem ◽  
Six Degrees Of Freedom ◽  
Joint Variable ◽  
Trajectory Determination

SUMMARYThe problem of finding an allowable object trajectory for a cooperating two-robot system is investigated. The purpose is to move an object from one point to another by firmly grasping it at two different points using two robotic hands. The major difficulty is caused by the fact that, unless the robots have true six degrees of freedom, the trajectories the object can follow are severely limited and, in general, are difficult to find. The method proposed in the paper is based on reformulating the problem as a nonlinear optimization problem with equality constraints in terms of the joint variables. The optimization problem is then solved numerically on a computer. The solution automatically gives the corresponding joint variable trajectories as well, thus eliminating the need for solving the inverse kinematic problem. The method has been successfully applied to a real experimental system.

A Novel Shoulder Exoskeleton Robot Using Parallel Actuation and a Passive Slip Interface

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Justin Hunt ◽  
Hyunglae Lee ◽  
Panagiotis Artemiadis
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Glenohumeral Joint ◽  
Translational Motion ◽  
Euler Angle ◽  
Inverse Kinematic ◽  
New Method ◽  
Novel Technologies ◽  
Manipulator Design ◽  
Spherical Parallel Manipulator

This paper presents a five degrees-of-freedom (DoF) low inertia shoulder exoskeleton. This device is comprised of two novel technologies. The first is 3DoF spherical parallel manipulator (SPM), which was developed using a new method of parallel manipulator design. This method involves mechanically coupling certain DoF of each independently actuated linkage of the parallel manipulator in order to constrain the kinematics of the entire system. The second is a 2DoF passive slip interface used to couple the user upper arm to the SPM. This slip interface increases system mobility and prevents joint misalignment caused by the translational motion of the user's glenohumeral joint from introducing mechanical interference. An experiment to validate the kinematics of the SPM was performed using motion capture. The results of this experiment validated the SPM's forward and inverse kinematic solutions through an Euler angle comparison of the actual and command orientations. A computational slip model was created to quantify the passive slip interface response for different conditions of joint misalignment. In addition to offering a low inertia solution for the rehabilitation or augmentation of the human shoulder, this device demonstrates a new method of motion coupling, which can be used to impose kinematic constraints on a wide variety of parallel architectures. Furthermore, the presented device demonstrates a passive slip interface that can be used with either parallel or serial robotic systems.

scholarly journals Kinematic Analysis of a Parallel-Sequential Structure Mechanism with Five Degrees of Freedom

2019 ◽  
pp. 18-24
Author(s):  
G.S. Filippov
Keyword(s):  
Numerical Experiment ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Parallel Structure ◽  
Kinematic Pair ◽  
Inverse Kinematic Problem ◽  
Sequential Structure ◽  
Spine Movement ◽  
Three Degrees Of Freedom

The article presents a synthesis of a mechanism of parallel-sequential structure with five degrees of freedom capable of processing objects with an extended dimention in one direction, wherein the considered mechanism can have a high bearing capacity. Corresponding problems are associated with manufacturing jet turbine airfoil as well as vertebrae operations (on the human spine). Movement along a coordinate that is linked to large dimensions of a processed object is provided using the initial translation pairs equipped with a motor. It is followed by a flat partial parallel structure mechanism with three degrees of freedom, and further – by a revolute kinematic pair. A kinematic analysis of the considered mechanism is performed, and the inverse kinematic problem is solved. The Angeles-Gosselin method for parallel structure mechanisms is used when performing velocity calculations of the parallel-sequential structure mechanism. The results of the numerical experiment are presented.

scholarly journals Optimal predictive steering control for autonomous runway exits

2020 ◽  
Vol 12 (12) ◽  
pp. 168781402098086
Author(s):  
Zexin Huang ◽  
Matthew Best ◽  
James Knowles
Keyword(s):  
High Speed ◽  
Optimal Solution ◽  
Optimal Controller ◽  
Feedback Gain ◽  
Steering Control ◽  
Operational Parameters ◽  
Pilot Model ◽  
Look Ahead ◽  
Time Optimal ◽  
Aircraft Configurations

In this paper, we present a real-time optimal controller, Predictive Steering Control (PSC), to perform high-speed runway exit manoeuvres. PSC is developed based on a time-varying LQR with look-ahead. The aircraft’s ground dynamics are described by a high-fidelity nonlinear model. The proposed controller is compared with an Expert Pilot Model (EPM), which represents a pilot, in several different speed runway exit manoeuvres. With an improved road preview mechanism and optimal feedback gain, the predictive steering controller outperforms the expert pilot’s manual operations by executing the runway exit manoeuvre with a lower track error. To investigate the optimality of PSC, its solution is further optimised using a numerical optimal controller Generalized Optimal Control (GOC). PSC is shown to be close to the final optimal solution. To study robustness, PSC is tested with various aircraft configurations, road conditions and disturbances. The simulation results show that PSC is robust to disturbances within a normal range of operational parameters.

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