Computer Aided Synthesis of Piecewise Rational Motions for Spherical 2R and 3R Robot Arms

2006 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Spline Interpolation ◽  
Joint Motion ◽  
Robot Arm ◽  
Spherical Robot ◽  
End Effector ◽  
Kinematic Constraints ◽  
Robot Arms ◽  
Revolute Joints ◽  
Computer Aided ◽  
Circular Interpolation

This paper deals with the problem of synthesizing piecewise rational spherical motions of an object that satisfies the kinematic constraints imposed by a spherical robot arm with revolute joints. The paper brings together the kinematics of spherical robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Using quaternion kinematics of spherical arms, it is shown that the problem of synthesizing the Cartesian rational motion of a 2R arm can be reduced to that of circular interpolation in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a spherical 3R arm can be reduced to that of constrained spline interpolation in two separate planes. Due to the limitation of circular interpolation, for spherical 2R robot arm, only C1 continuous rational motions are generated. In this case, for applications that require C2 continuous motions, the paper presents a method for generating a C2 continuous joint motion that approximates a given C1 rational motion of the end-effector. For spherical 3R arm, C2 continuous rational motions are generated exactly.

Computer Aided Synthesis of Piecewise Rational Motions for Spherical 2R and 3R Robot Arms

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Motion Planning ◽  
Spline Interpolation ◽  
Robot Arm ◽  
Spherical Robot ◽  
Kinematic Constraints ◽  
Robot Arms ◽  
Revolute Joints ◽  
Computer Aided ◽  
Planar Robot ◽  
Circular Interpolation

This paper deals with the problem of synthesizing smooth piecewise rational spherical motions of an object that satisfies the kinematic constraints imposed by a spherical robot arm with revolute joints. This paper brings together the kinematics of spherical robot arms and recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. The kinematic constraints under consideration are workspace related constraints that limit the orientation of the end link of robot arms. This paper extends our previous work on synthesis of rational motions under the kinematic constraints of planar robot arms. Using quaternion kinematics of spherical arms, it is shown that the problem of synthesizing the Cartesian rational motion of a 2R arm can be reduced to that of circular interpolation in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a spherical 3R arm can be reduced to that of constrained spline interpolation in two separate planes. We present algorithms for the generation of C1 and C2 continuous rational motion of spherical 2R and 3R robot arms.

Computer Aided Synthesis of Piecewise Rational Motions for Planar 2R and 3R Robot Arms

2006 ◽  
Vol 129 (10) ◽  
pp. 1031-1036 ◽  
Author(s):  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Motion Planning ◽  
Spline Interpolation ◽  
Circular Ring ◽  
Robot Arm ◽  
Kinematic Constraints ◽  
Robot Arms ◽  
Revolute Joints ◽  
Computer Aided ◽  
Planar Robot ◽  
Circular Interpolation

This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. This paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that for the case of a planar 2R arm, the problem of rational motion synthesis can be reduced to that of circular interpolations in two separate planes and that for the case of a planar 3R arm, the problem can be reduced to a combination of circular interpolation in one plane and a constrained spline interpolation in a circular ring on another plane. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated that satisfy the kinematic constraints exactly. For applications that require C2 continuous motions, this paper presents a method for generating C2 continuous motions that approximate the kinematic constraints for planar 2R and 3R robot arms.

Computer Aided Synthesis of Piecewise Rational Motions for Planar 2R and 3R Robot Arms

2006 ◽  
Author(s):  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Spline Interpolation ◽  
Joint Space ◽  
Circular Ring ◽  
Robot Arm ◽  
Kinematic Constraints ◽  
Robot Arms ◽  
Revolute Joints ◽  
Computer Aided ◽  
Planar Robot ◽  
Circular Interpolation

This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. The paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that the problem of synthesizing the Cartesian rational motion of a planar 2R arm can be reduced to that of circular interpolations in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a planar 3R arm can be reduced to that of circular interpolation in one plane and constrained spline interpolation in a circular ring. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated. For applications that require C2 continuous motions, the paper presents a joint-space based method for generating a C2 continuous motion that approximates a given C1 rational motion of the end link.

scholarly journals Shape Design Optimization of a Robot Arm Using a Surrogate-Based Evolutionary Approach

2020 ◽  
Vol 10 (7) ◽  
pp. 2223 ◽  
Author(s):  
J. C. Hsiao ◽  
Kumar Shivam ◽  
C. L. Chou ◽  
T. Y. Kam
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Shape Design ◽  
Optimization Approach ◽  
Robot Arm ◽  
Shape Design Optimization ◽  
Robot Arms ◽  
Conflicting Objectives ◽  
Computer Aided

In the design optimization of robot arms, the use of simulation technologies for modeling and optimizing the objective functions is still challenging. The difficulty is not only associated with the large computational cost of high-fidelity structural simulations but also linked to the reasonable compromise between the multiple conflicting objectives of robot arms. In this paper we propose a surrogate-based evolutionary optimization (SBEO) method via a global optimization approach, which incorporates the response surface method (RSM) and multi-objective evolutionary algorithm by decomposition (the differential evolution (DE ) variant) (MOEA/D-DE) to tackle the shape design optimization problem of robot arms for achieving high speed performance. The computer-aided engineering (CAE) tools such as CAE solvers, computer-aided design (CAD) Inventor, and finite element method (FEM) ANSYS are first used to produce the design and assess the performance of the robot arm. The surrogate model constructed on the basis of Box–Behnken design is then used in the MOEA/D-DE, which includes the process of selection, recombination, and mutation, to optimize the robot arm. The performance of the optimized robot arm is compared with the baseline one to validate the correctness and effectiveness of the proposed method. The results obtained for the adopted example show that the proposed method can not only significantly improve the robot arm performance and save computational cost but may also be deployed to solve other complex design optimization problems.

Extended kinematic path control of robot arms

Robotica ◽  
1987 ◽  
Vol 5 (1) ◽  
pp. 45-53 ◽  
Author(s):  
Evgeny Krustev ◽  
Ljubomir Lilov
Keyword(s):  
Path Planning ◽  
Control Method ◽  
Sliding Mode ◽  
Joint Motion ◽  
Robot Arm ◽  
Extended Form ◽  
Robot Arms ◽  
Path Control ◽  
Arm Motion

SUMMARYPath planning a robot arm motion essentially requires that the constraints of the joint variables and the vector of the joint motion rates are taken into account. In order to satisfy the constraints of the joint variables a sliding mode is being employed together with the developed kinematic path control method. The extended form of the kinematic path control method, here proposed, treats simultaneously the constraints of the joint variables and the vector of joint motion rates in path planning a robot arm motion.

A 7R-Based, Two Degrees of Freedom Robomech

2000 ◽  
Author(s):  
Ahmad A. Smaili
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Architecture ◽  
Degree Of Freedom ◽  
Robot Arm ◽  
End Effector ◽  
Kinematic Constraints ◽  
Two Degrees Of Freedom ◽  
Synthesis Procedure ◽  
Two Degree Of Freedom

Abstract A robomech is a crossbreed of a mechanism and a robot arm. It has a parallel architecture equipped with more than one end effector to accomplish tasks that require the coordination of many functions. Robomechs with multi degrees of freedom that are based on the 4R and 5R chains have found their way into the literature. This article presents a new, two-degree of freedom robomech whose architecture is based on the 7R chain. The robomech is capable of performing two-function tasks. The features, kinematic constraints, and synthesis procedure of the robomech are outlined and an application example is given.

Computer Aided Synthesis of Rational Motion Under Kinematic Constraints of Spatial SS Open Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Numerical Algorithm ◽  
Smooth Curve ◽  
Dual Quaternion ◽  
Open Chain ◽  
End Effector ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Computer Aided ◽  
Quaternion Representation ◽  
Iterative Numerical Algorithm

In this paper, we study the problem of rational motion interpolation under kinematic constraints of spatial SS open chains. The objective is to synthesize a smooth rational motion that interpolates a given set of end effector positions and satisfies the kinematic constraints imposed by spatial SS open chains. The kinematic constraints under consideration define a constraint manifold representing all the positions available to the end effector. By choosing dual quaternion representation for the displacement of the end effector, the problem is reduced to designing a smooth curve in the space of dual quaternions that is constrained to lie inside the constraint manifold of the spatial SS open chain. An iterative numerical algorithm is presented that solves this problem effectively. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational planar and spherical motions for open and closed chains under kinematic constraints.

An Investigation Into the Compliance of SCARA Robots. Part I: Analytical Model

1988 ◽  
Vol 110 (1) ◽  
pp. 18-22 ◽  
Author(s):  
H. A. ElMaraghy ◽  
B. Johns
Keyword(s):  
Degrees Of Freedom ◽  
Torsional Stiffness ◽  
Force Model ◽  
Robot Arm ◽  
Relative Significance ◽  
End Effector ◽  
Scara Robot ◽  
Revolute Joints ◽  
Tool Axis ◽  
Assembly Tasks

A special class of robots suited for assembly tasks called SCARA (Selective Compliance Assembly Robot Arm) provides a degree of built-in flexibility due to robot structure. In such robots there are three revolute joints and a prismatic joint. They offer four degrees of freedom consisting of rotation about two vertical and parallel axes at the revolute joints, and translation and rotation about the tool axis. Some models offer additional degrees of freedom at the end effector. Structural compliance can arise due to the stiffness of the robot links, drive system, grippers as well as the assembled parts. The largest effect is due to the drive torsional stiffness followed by the grippers, workpieces and the robot tool link. Knowledge of the inherent flexibility is extremely useful in designing tooling and fixtures, in laying out the assembly work cell according to the amount of compliance available in various regions of the robot work envelope, in guarding against wedging and jamming and in specifying external Remote Centre Compliance devices (RCC) if necessary. In this paper the various sources of compliance built into a SCARA robot system are outlined together with their relative significance. A mathematical model which expresses the end effector deflection as a function of the robot Jacobian and the drive compliance parameters in Cartesian coordinates has been developed. The modified generalized assembly force model developed for the Selective Compliance Assembly Robot Arms (SCARA), used in this investigation, is described. Constraints required to prevent jamming and wedging of parts during assembly are outlined. The application of this compliance model for both rotational and prismatic part insertion is described. The conditions required to obtain true or semi-compliance centres for the SCARA robot end effector are derived and discussed.

Influence of Gravity on the Manipulability Ellipsoid for Robot Arms

1992 ◽  
Vol 114 (4) ◽  
pp. 723-727 ◽  
Author(s):  
P. Chiacchio ◽  
S. Chiaverini ◽  
L. Sciavicco ◽  
B. Siciliano
Keyword(s):  
Case Studies ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Task Space ◽  
End Effector ◽  
The Core ◽  
Gravitational Forces ◽  
Robot Arms ◽  
Original Approach

The dynamic manipulability ellipsoid is a common tool in robotics to measure the ability of a manipulator to produce arbitrary accelerations of the end-effector for a given set of torques at the joints. This article is intended to demonstrate that for a robot arm, when gravitational forces (due to arm and payload) are properly embedded into the derivation of the ellipsoid, these do not cause a compression in the volume of the ellipsoid, as stated in the original approach, but they just produce a translation of the ellipsoid which in general occurs along all task space directions. Further, we characterize the ellipsoid for redundant manipulators by investigating the properties of the manipulator Jacobian involved in the core of the ellipsoid. Numerical case studies are developed.

scholarly journals Chaos Stabilization and Tracking Recovery of a Faulty Humanoid Robot Arm in a Cooperative Scenario

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 87-101
Author(s):  
Said Khan ◽  
Samir Bendoukha ◽  
Salem Abdelmalek
Keyword(s):  
Humanoid Robot ◽  
Sliding Mode ◽  
Elbow Flexion ◽  
Shoulder Abduction ◽  
Robot Arm ◽  
End Effector ◽  
Safety Issues ◽  
Robot Arms ◽  
Shoulder Flexion ◽  
Chaos Stabilization

Synchronised motion is an important requirement for two cooperating humanoid robot arms. In this work a cooperative scenario is considered where two humanoid robot arms (using 4DOF each, namely Shoulder Flexion Joint, Shoulder abduction Joint, Humeral rotation joint and Elbow Flexion Joint) motion are synchronized. The master robot arm is controlled by a sliding mode controller and the slave robot arm is synchronized using a basic PD plus adaptive control, employing the position and velocity errors between the master and the slave. During the operation, if a joint of the slave robot arm saturates or malfunctions (for instance, Elbow flexion joint does not respond or free swinging), consequently, slave robot arm will go into chaos (i.e., chaotic motion of the end effector). In this case, a chaos controller kicks in to recover and re-synchronize the motion of the slave robot arm end effector. This re-synchronization is extremely important to complete the task in hand to address any safety issues arising from any joint malfunction of the slave robot. Effectiveness of the scheme is tested in simulation using Bristol Robotics Laboratory Humanoid BERT II arms.

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