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 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 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.

scholarly journals Contact-Rich Trajectory Generation in Confined Environments Using Iterative Convex Optimization

2020 ◽  
Author(s):  
Wei-Ye Zhao ◽  
Suqin He ◽  
Chengtao Wen ◽  
Changliu Liu
Keyword(s):  
Convex Optimization ◽  
Motion Planning ◽  
Real Time ◽  
Trajectory Generation ◽  
Robot Kinematics ◽  
Planning Problem ◽  
Robot Arm ◽  
Task Constraints ◽  
Robot Arms ◽  
Highly Nonlinear

Abstract Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot trajectory generation is highly nonlinear and nonconvex, which usually comes with collision avoidance constraints, robot kinematics and dynamics constraints, and task constraints (e.g., following a Cartesian trajectory defined on a surface and maintain the contact). The nonlinear and nonconvex planning problem is computationally expensive to solve, which limits the application of robot arms in the real world. In this paper, for redundant robot arm planning problems with complex constraints, we present a motion planning method using iterative convex optimization that can efficiently handle the constraints and generate optimal trajectories in real time. The proposed planner guarantees the satisfaction of the contact-rich task constraints and avoids collision in confined environments. Extensive experiments on trajectory generation for weld grinding are performed to demonstrate the effectiveness of the proposed method and its applicability in advanced robotic manufacturing.

Collision-free motion planning for two articulated robot arms using minimum distance functions

Robotica ◽  
1990 ◽  
Vol 8 (2) ◽  
pp. 137-144 ◽  
Author(s):  
C. Chang ◽  
M. J. Chung ◽  
Z. Bien
Keyword(s):  
Motion Planning ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Distance Functions ◽  
Free Motion ◽  
Planning Problem ◽  
Robot Arm ◽  
Robot Arms ◽  
Nonlinear Minimization ◽  
Articulated Robot

SummaryThis paper presents a collision-free motion planning method of two articulated robot arms in a three dimensional common work space. Each link of a robot arm is modeled by a cylinder ended by two hemispheres, and the remaining wrist and hand is modeled by a sphere. To describe the danger of collision between two modeled objects, minimum distance functions, which are defined by the Euclidean norm, are used. These minimum distance functions are used to describe the constraints that guarantee no collision between two robot arms. The collision-free motion planning problem is formulated as a pointwise constrained nonlinear minimization problem, and solved by a conjugate gradient method with barrier functions. To improve the minimization process, a simple grid technique is incorporated. Finally, a simulation study is presented to show the significance of the proposed method.

scholarly journals Trajectory representation and landmark projection for continuous-time structure from motion

2019 ◽  
Vol 38 (6) ◽  
pp. 686-701 ◽  
Author(s):  
Hannes Ovrén ◽  
Per-Erik Forssén
Keyword(s):  
Structure From Motion ◽  
Continuous Time ◽  
Spline Interpolation ◽  
Time Structure ◽  
Robot Arm ◽  
Good Sense ◽  
Trajectory Representation ◽  
Inertial Measurements ◽  
Derivatives Of ◽  
Fusion Framework

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a [Formula: see text]-continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyze the behavior of split spline interpolation on [Formula: see text] and on [Formula: see text], and a joint spline on [Formula: see text], and show that the latter implicitly couples the direction of translation and rotation. Such an assumption can make good sense for a camera mounted on a robot arm, but not for hand-held or body-mounted cameras. Our experiments in the Spline Fusion framework show that a split spline on [Formula: see text] is preferable over an [Formula: see text] spline in all tested cases. Finally, we investigate the problem of landmark reprojection on rolling shutter cameras, and show that the tested reprojection methods give similar quality, whereas their computational load varies by a factor of two.

Energy-Optimal Multi-Goal Motion Planning for Planar Robot Manipulators

2014 ◽  
Vol 163 (1) ◽  
pp. 80-104 ◽  
Author(s):  
Pierre Bonami ◽  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Motion Planning ◽  
Robot Manipulators ◽  
Planar Robot
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